university of groningen formalizing the minimalist program ...the minimalist program pro efsc hrift...

University of Groningen

Formalizing the minimalist programVeenstra, Mettina Jolanda Arnoldina

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Formalizing

the Minimalist Program

Mettina Veenstra

Groningen Dissertations in Linguistics 24

ISSN 0928-0030

Rijksuniversiteit Groningen

Formalizing

the Minimalist Program

Proefschriftter verkrijging van het doctoraat in de

Letterenaan de Rijksuniversiteit Groningen

op gezag van deRector Magni�cus Dr. F. van der Woude

in het openbaar te verdedigen opdonderdag 11 juni 1998

des namiddags te 2.45 uur

door

Mettina Jolanda Arnoldina Veenstra

geboren op 7 juni 1967te Rotterdam

Promotor: Prof. Dr. Ir. J. NerbonneReferenten: Dr. G. Bouma en Dr. C.J.W. Zwart

Voor mijn ouders

Acknowledgements

As a student of Scandinavian languages and literature, my interest in syntaxwas aroused by the lectures of Godelieve Laureys. This resulted in thefact that I became a student of General Linguistics as well. There, JanKoster gave me a solid basis in generative syntax. However, after sometime Jan de Vuyst from the `vakgroep Alfa-informatica' convinced me thathis department could really give me what I was looking for. This turned outto be true, and after I received my `doctoraal' in computational linguistics,Gosse Bouma provided me with a PhD project which combined generativesyntax and computational linguistics. I am really grateful to all the peoplementioned above for guiding me along the winding road that lead to myPhD project.

Throughout the project, my promotor John Nerbonne supported me ina very personal way. Although generative syntax is not his �rst �eld ofinterest, we had many inspiring discussions on my topic. I am very gratefulto him for broadening my (computational-)linguistic horizon, and for alwaysletting me walk into his o�ce when I had burning questions.

I would like to thank my `referenten' Gosse Bouma and Jan-WouterZwart for all their valuable help. Gosse read every paper and chapter Iwrote in an accurate and critical way and he often helped me with myimplementations. Jan-Wouter was always willing to discuss his own workfrom my computational perspective, and furthermore, he provided me withnumerous useful suggestions to improve my manuscript. I would also liketo thank the members of my thesis committee Jan Koster, Gerard Renardelde Lavalette and Ed Stabler for reading the manuscript.

I owe a lot to Rix Groenboom, Gerard Renardel de Lavalette and ErikSaaman from the department of Computing Science in Groningen for provid-ing me with a formal-speci�cation language to write down the formalization.I would like to pronounce my special gratefulness to Erik, whose accurateway of working was invaluable for the realization of the formalization.

The `vakgroep Alfa-informatica' was a very enjoyable working environ-ment over the years. Erik Tjong Kim Sang and Bert Bos were the most

i

wonderful o�ce mates I could wish. I thank them and all my other for-mer colleagues, especially Alessandro Allodi, Gosse Bouma, Duco Dokter,Harry Gaylord, Joop Houtman, Mark-Jan Nederhof, John Nerbonne, RobKoeling, Dimitra Kolliakou, Edwin Kuipers, Gertjan van Noord, Petra Smitand George Welling for all the fun and the moral and intellectual support.I have very good memories of the `borrels', the yearly dinner in John andEllen's garden, the Lauwersloop, the weekend at Texel, the sailing trip onthe Lauwersmeer, and the volleyball matches on Friday afternoons.

I thank Gertjan van Noord for his help with my head-corner parser, andShoji Yoshikawa and the `secretariaat' for the practical support.

I shared some pleasant pastime with my former colleagues and friendsAnastasia Giannakidou, Lily Grozeva, Jelly de Jong, Karen Lattewitz, KimSauter, Petra Smit and Sjoukje van der Wal at the `Harmoniegebouw', butalso at places like Terschelling, Nieuweschans, Zevenhuizen, the woods inDrenthe and at several AIO courses. Particularly, I would like to displaymy deepest admiration for the achievement of Jelly, Karen and Kim tobreak into our house the night before Ynze and I got married without usnoticing. Ladies, it is entirely clear you missed out on a career in burglary(and catering).

To work o� the emotions the writing of a dissertation brings along, Ibene�ted a lot from the numerous talks and phone calls with my dear friendsAstrid Oldenziel and Freya Stob. Another way to get relaxed were theweekly sessions with the band the Lawaaio's. I would really like to thankJeroen van Berge, Rix Groenboom, Constantijn Heessen, Han Limburg, andlast but not least our ex-drummer Ed Loonstra for all the noise, fun andlovely food.

I thank my present colleagues at Halloween Research, especially Mar-greet de Bloeme, for giving me the opportunity to get my dissertation readyfor printing. Furthermore, I thank Rob Koeling and Kim Sauter for beingmy `paranimfen'.

I am very grateful to my parents and my brother Chris for always en-couraging and helping me to reach my goals. Especially, I would like tothank my father for all the stimulating phone calls and my mother for allthe Tuesdays she took o� and all the kilometres she travelled to take careof Menno so that I could get my dissertation ready for printing.

Last but not least I owe a lot to Ynze and Menno for all the distractionthey gave me. I especially thank Menno for letting me give birth to mymanuscript just before entering the world himself. I thank Ynze for the in-valuable psychological coaching, for his humour, for reading mymanuscript,and for the way he looked after me in the busy weeks before the deadlines.

ii

Contents

Introduction 1

1 The Minimalist Program 3

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Word order, phrase structure and movement . . . . . . . . . . 61.3 Directionality . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 Lexical insertion, Spell-Out, and Logical Form . . . . . . . . 111.5 Movement and feature checking . . . . . . . . . . . . . . . . . 141.6 The operations Merge and Move . . . . . . . . . . . . . . . . 161.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Implementations 25

2.1 Merge and Move . . . . . . . . . . . . . . . . . . . . . . . . . 262.1.1 The implementation . . . . . . . . . . . . . . . . . . . 262.1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 292.1.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . 302.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 A minimalist head-corner parser . . . . . . . . . . . . . . . . 322.2.1 Head-corner parsing . . . . . . . . . . . . . . . . . . . 322.2.2 Structure-building operations and head-corner parsing 342.2.3 The algorithm . . . . . . . . . . . . . . . . . . . . . . 352.2.4 Parsing versus generation . . . . . . . . . . . . . . . . 382.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 40

3 Formalization 41

3.1 Why formalization? . . . . . . . . . . . . . . . . . . . . . . . . 413.2 The FSA method and the language AFSL . . . . . . . . . . . 473.3 Verb movement . . . . . . . . . . . . . . . . . . . . . . . . . . 543.4 The formalization . . . . . . . . . . . . . . . . . . . . . . . . . 57

4 Trees 61

iii

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.2 The formalization . . . . . . . . . . . . . . . . . . . . . . . . . 624.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 Feature structures 73


6 Lexicon 85

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.2 The formalization . . . . . . . . . . . . . . . . . . . . . . . . . 896.3 The lexicon in Chomsky's 1993 framework . . . . . . . . . . . 996.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7 X-Theory 101

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.2 The formalization . . . . . . . . . . . . . . . . . . . . . . . . . 1057.3 Two-level X-Theory . . . . . . . . . . . . . . . . . . . . . . . 1197.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

8 Chains 129


9 Interfaces 149

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1499.2 The formalization . . . . . . . . . . . . . . . . . . . . . . . . . 1519.3 Interfaces in Chomsky's framework . . . . . . . . . . . . . . . 1649.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

10 Concluding remarks 169

Appendix: Unify 173

Bibliography 177

Samenvatting 185

iv

Introduction

The Minimalist Program [Cho93, Cho95] is a relatively new approach togenerative linguistics. The theory is still in development and this causesde�nitions of important notions to be a constant subject of change. Onecould draw the conclusion that the right time for formalization of the theoryhas not come yet. However, I think that to dispose over clear de�nitionsof the theory in some stage of the development will be of use for linguistsworking inside and outside the minimalist framework.

For linguists working in the �eld, a formalization can provide hold fordiscussions and furthermore, a formalization allows errors to be detectedthat are hard to discover otherwise. For example, it can facilitate the de-tection of inconsistencies that may be introduced when fundamental notionsare rede�ned.

For linguists working in other frameworks, who did not follow the de-velopment of the theory from the beginning, the informal descriptions ofthe Minimalist Program are di�cult to follow. The Minimalist Programcould become more accessible when they can dispose over a formalizationof some fragment of the theory at a certain point in the development. Inthe following chapters I will provide such a formalization of a minimalistdescription of a small fragment of Dutch.

In Chapter 1 I will outline Chomsky's 1993 version of the MinimalistProgram. The two small implementations in Prolog described in Chapter 2are based on this version of the Minimalist Program. The objective of theimplementations was to examine the possibilities of implementing and for-malizing fragments of the Minimalist Program. After the implementationsI decided to use a formal-speci�cation language instead of the programminglanguage Prolog to continue the project. The idea behind this choice is thata speci�cation language is more appropriate for formulating explicit de�ni-tions than a programming language, even a language for logic programmingsuch as Prolog.

The advantages of using a formal-speci�cation language and of formal-ization in general are outlined more elaborately in Chapter 3. Furthermore,

1

2 INTRODUCTION

this chapter contains a description of the formal-speci�cation language thatis used, an introduction to a fragment of a version of the Minimalist Programby Zwart [Zwa97], and a brief description of the formalization.

The formalization consists of two parts: a formalization of a fragment ofChomsky's 1993 version of the Minimalist Program, and a formalization ofa fragment of Zwart's 1997 version of the Minimalist Program. The reasonthat Zwart's version is applied is that it contains ideas which I need forthe proper description of certain phenomena in Dutch. The formalization isdiscussed more elaborately in the Chapters 4 through 9. Each chapter con-tains the description of a di�erent module of the formalization. In principlethe Chapters 4 through 9 only deal with the formalization of Zwart's frame-work, as considerable parts of this framework are identical to Chomsky's1993 framework. However, if relevant di�erences between Chomsky's 1993framework and Zwart's framework occur within a module, these di�erencesare described in a separate section of the relevant chapter.

Chapter 1

The Minimalist Program

In this chapter I will give a brief introduction to the Minimalist Program[Cho93]. The two implementations described in Chapter 2 are based onthis version of the Minimalist Program. The formalization presented in theChapters 4 through 9 is also based on this version of the Minimalist Programas well as on a version of the Minimalist Program that was developed byZwart [Zwa97]. The latter version is a combination of Chomsky's 1993version of the Minimalist Program (cf. [Cho93]), Chomsky's 1995 versionof the Minimalist Program (cf. [Cho95]), and some new ideas of Zwart thatenable the proper description of verb movement in Germanic languages suchas Dutch, which show an asymmetry between main and subordinate clauseswith respect to the position of the �nite verb.

An introduction to Zwart's version of the Minimalist Program is given inChapter 3. More detailed descriptions of certain aspects of this version aregiven in the Chapters 4 through 9. In this chapter I will restrict myself toa global description of Chomsky's 1993 version of the Minimalist Program[Cho93].

1.1 Introduction

The Minimalist Program [Cho93, Cho95] is a linguistic theory which orig-inated from an almost forty year long tradition of generative linguistics.This tradition was initiated by Noam Chomsky [Cho57, Cho65].

Two of the main objectives of the generative tradition, and of many otherlinguistic theories nowadays, are to reach descriptive and explanatory ade-quacy. Descriptive adequacy is reached when the knowledge of the speakersof each natural language is explicitly described. Explanatory adequacy isreached when it can be explained how it is possible that people acquire

3

4 CHAPTER 1. THE MINIMALIST PROGRAM

language. We operationalize these by requiring a de�nition of `well-formedphrase' (for descriptive adequacy) and a characterization of `possible humanlanguage' (for explanatory adequacy).

The linguists from before the generative tradition, studying languagefrom the point of view of traditional grammar, did not formulate their ques-tions in such a way that descriptive adequacy could be reached according toChomsky [Cho65, Page 5]. Only very super�cial descriptions of for exam-ple, the way questions are formed were produced. Chomsky's recognition ofthe complexity of language lead to the requirement that a linguistic theorymust be explanatorily adequate, as in principle all people manage to learnlanguages in a relatively short time when they are children. Note that weare dealing with �rst language acquisition here.

The idea of universal grammar (UG) arose: people are born with innateknowledge about language, and they can learn any natural language theyare exposed to, and possibly more than one, in the �rst years of their lives.This implies that languages must have a great deal in common. Since thereundeniably are di�erences between languages we can assume that the ac-quisition of a language consists of the �xing of a limited number of optionsprovided by UG.

However, descriptive interest pushed explanatory adequacy to the back-ground. Many of the described phenomena appeared to be more intricatethan one could imagine in advance, and a whole range of construction-speci�c and language-speci�c rule systems was developed.

In the Principles and Parameter approach [Cho81] the idea of explana-tory adequacy was restored. It was assumed that the theory of UG con-sists of principles and parameters. Principles are language-independent andconstruction-independent laws that apply to every natural language. Thedi�erences between languages are captured by the parameters. The numberof parameters and the number of possible values per parameter are �nite.

The latest development in the Principles and Parameters approach is theMinimalist Program [Cho93, Cho95]. This research program is `minimal'in the sense that explanatory adequacy is aimed for by `minimization' ofthe theoretical apparatus. Every detail of the theory is reconsidered in acritical way and eliminated if it does not seem to have a legitimate reasonof existence. In other words, the scienti�c rule of keeping a theory as simpleas possible is applied.

An example of minimization of the theory is the elimination of two ofthe four levels of representation from the preceding versions of generativelinguistic theory. The two levels of representation that are maintained inthe Minimalist Program are:

� Phonetic Form (PF): an (abstract) representation of sound

1.1. INTRODUCTION 5

� Logical Form (LF): an (abstract) representation of meaning

The two levels of representation that are abandoned in the MinimalistProgram are:

� D(eep)-Structure: the level at which lexical insertion operates, whichis de�ned by predicate/argument relations, and where the words of asentence are represented in a basic (construction-independent) order.

� S(urface)-Structure: a representation of a sentence `as it is pro-nounced', i.e. with the words ordered for instance as an active declar-ative clause (He saw her.), as a question (Who saw her?) or as apassive construction (She was seen.). S-Structure is de�ned by gram-matical relations such as case. It is assumed that S-Structures can beconstructed from D-Structures by moving zero or more constituents.Slightly simplifying we could say that the above example sentenceswere all based on the same D-Structure. For the active declarativeclause no movement is involved, i.e. S-Structure equals D-Structure.In the passive construction the object her moves to the subject po-sition and appears there as she. In the Wh-question the subject hemoves to a special position for Wh-words and appears there as who.1

D-Structure is eliminated in the Minimalist Program by collapsingrewrite rules, lexical insertion and movements. In the following sectionswe will learn more about the treatment of rewrite rules, lexical insertionand movements in the Minimalist Program. In Section 1.6 we will see howrewrite rules, lexical insertion and movements are collapsed.

S-Structure is also abandoned as an independent level of representation.It is replaced by `Spell-Out' about which we will learn more later in thischapter.

What distinguishes D-Structure and S-Structure from LF and PF is thatthe former two are internal levels of representation while the latter two areexternal levels of representation. LF and PF feed into systems external tothe syntactic component and therefore it is not possible to eliminate them.Since D-Structure and S-Structure do not feed into external systems, theycan be eliminated.

1A Wh-question is a question containing an interrogative word starting with `wh' inEnglish, for example who.


1.2 Word order, phrase structure and move-

ment

Within the Minimalist Program, word order variation is derived by move-ment. Constituents such as verbs are moved from one position to anotherin the syntactic representation of a sentence.

In earlier versions of the Chomskyan theory, part of the word orderdi�erences between languages were taken care of by the theory of phrasestructure: the relative order of the constituents in the right-hand side ofrewrite (or phrase structure) rules was not �xed universally. The right-handside is the part to the right of the arrow (see Example 1.1). Rewrite rules arerules that express the relative hierarchical and linear order of constituents.Illustrations of rewrite rules can be found in Example 1.1. The rewrite rulein (a) expresses that a sentence (S) consists of a noun phrase (NP), e.g. thegirl, followed by a verb phrase (VP), e.g. drives the car.2 The verb phrasein its turn consists of a verb (e.g. drives, sleeps) and possibly an NP (see(b)). Note that a transitive verb such as to drive may occur with a nounphrase, while an intransitive verb like to sleep may not. This optionalityof the object is expressed by the brackets around the NP in the VP-rule in(b). See Example 1.2 for a tree that can be built using the rewrite rulesgiven in Example 1.1. As was stated above, rewrite rules, and of course thetrees that are based on them, express the relative hierarchical and linearorder of constituents. Note that the tree in Example 1.2 expresses, amongother things, the relative hierarchical di�erences between S and VP, as Sis located higher up in the tree than VP, and the relative linear di�erencesbetween the subject NP and the object NP, as the subject NP is located tothe left of the object NP.

Example 1.1

(a) S ! NP VP(b) VP ! V (NP)

Example 1.2

S

NP VP

the girl V NP

drives the car

2Noun phrases nowadays often are called determinerphrases, as the determiner insteadof the noun is considered to be the head of the phrase (cf. [Abn87]).

1.2. WORD ORDER, PHRASE STRUCTURE AND MOVEMENT 7

X-Theory was developed because there appeared to be many recurringpatterns in phrase structure rules that asked for a generalization. X-Theorywas based on proposals by Chomsky [Cho70]. Lexical properties were re-moved from phrase structure rules in order to obtain a simple set of univer-sal, category-independent phrase structure rules. For instance, the speci�cphrase structure rules in Example 1.3 are replaced by the more general rulein Example 1.4, where X and Y are used as variables for lexical categoriessuch as noun (N), verb (V) and preposition (P).3

Example 1.3

(a) V ! V, NP(b) P ! P, NP(c) N ! N, PP

Example 1.4

X ! X, YP

With the introduction of X-Theory the relative linear order in the right-hand side of the rewrite rules is still not �xed universally. The relativeorder is subject to parametric variation between languages. For instance,in some languages the verb appears after the subject and the object (SOV-languages) and in other language the verb appears in between the subjectand the object (SVO-languages). As we will see in Section 1.3, Kayne[Kay94] assumes that the theory of grammar requires a version of X-Theorywhere the relative linear order of the constituents in the right-hand side ofthe rewrite rules is universal.

Within the minimalist framework, sentences in all languages have thesame phrase structure consisting of a lexical domain (VP) and a functionaldomain. The most generally accepted functional projections are CP (Com-plementizer Phrase), AgrSP (Agreement Phrase for the Subject), TP (TensePhrase) and AgrOP (Agreement Phrase for the Object) (see Example 1.5).The lexical domain is the locus of insertion of the verb and its arguments.These are inserted in fully in ected form (stem plus in ectional a�xes).The functional projections are occupied by features associated with in ec-tional morphology. As we will see in Section 1.5, the lexical elements moveto the functional domain to `check' their features. Note that the indexesi, j, k and l in Example 1.5 indicate the trajectories the di�erent lexicalconstituents followed. In the Sections 1.4 through 1.6 I will give a moreelaborate description of minimalist trees such as the tree in Example 1.5.

3For applications and revisions of X-Theory: cf. [Jac77, Sto81, Muy82, Stu85].


In Section 1.7 I will show how a minimalist tree is built. In that sectionmany of the notions introduced in the Sections 1.4 through 1.6 are applied.

Example 1.5

CP

C

C AgrSP

thatl

NP AgrS

shei

AgrS TP

T AgrS ei T

AgrO T T AgrOP

ek

V AgrO ej AgrO

hatesk

AgrO VP

ek

ei V

V NP

ek catsj

In Section 1.6 we will see that rewrite rules, or rather X-rules, are appliedas part of the structure-building operations Merge and Move within theminimalist framework.

1.3 Directionality

As was mentioned in the previous section, Kayne [Kay94] assumes in hisLinear Correspondence Axiom (LCA) that the theory of grammar requiresa version of X-Theory where the relative linear order of the constituents inthe right-hand side of the rewrite rules is universally �xed. Example 1.6shows the �xed relative order of the constituents within a phrase (XP) thatKayne proposes.

Kayne assumes that the left daughter of XP is always the speci�er andthat the head is always located to the left of the complement. Furthermore,Kayne assumes that adjuncts always appear to the left of the node they

1.3. DIRECTIONALITY 9

adjoin to, as we see in Example 1.7. In earlier versions of generative lin-guistic theory, a parameter was supposed to determine the relative linearorder of speci�ers, heads, and complements per language. For instance, aspeci�er could either appear as the right daughter or as the left daughter ofXP. In the minimalist framework, the above parameter would be redundantbecause movement takes care of word order di�erences between languages,as we saw in the previous section. We do not need a second mechanism toderive word order di�erences since all possible orders can be derived withthe help of movement. From the minimalist point of view, redundancy is avalid reason to reconsider legitimacy of a mechanism of the theory.

Example 1.6

XP

YP X

(Speci�er)

X ZP

(Head) (Complement)

Example 1.7

XP

YP X

(Speci�er)

X ZP

(Complement)

W X

(Adjunct) (Head)

Summarizing, we can say that Kayne draws the conclusion that theparameter determining the relative linear order of speci�ers, adjuncts, headsand complements is super uous. Therefore Kayne looks for reasons for aspeci�c �xed order.

Kayne deduces the relative linear ordering of the speci�er, adjunct, headand complement of an XP from the assumption that the linear ordering ofthe terminals of a tree is determined by the hierarchy of a tree. Before wewill have a closer look at this assumption, I need to explain two importantnotions: `dominate' and `c-command'.

A de�nition of the notion `dominate' is given in De�nition 1.1. On thebasis of this de�nition we can conclude that in Example 1.8 XP dominatesYP, but also ZP.


De�nition 1.1

A node � dominates a node � if and only if � is the mother of � or if thereexists a node of which � is the mother and that dominates �

The notion `c-command' is de�ned in De�nition 1.2 (see also [Rei81] and[Cho86b, Page 8]). On the basis of this de�nition we can conclude that inExample 1.8 YP c-commands ZP, but not that ZP c-commands YP.

De�nition 1.2

A node � c-commands a node � if and only if � does not dominate �, andevery node that dominates � also dominates �

Having discussed the notions `dominate' and `c-command', we can returnto Kayne's claim that the the linear ordering of the terminals of a tree isdetermined by the hierarchy of a tree.4 Kayne supposes that if a node �of a tree asymmetrically c-commands another node � of that same tree,than the terminal (lexical) elements dominated by � linearly precede theterminal (lexical) elements dominated by �. By `asymmetrical c-command'is meant that two nodes may not c-command each other.

Example 1.8

XP

YP XP

Y X ZP

Kayne needs a more restrictive de�nition of c-command than De�nition1.2, since according to this de�nition in Example 1.8 YP c-commands X,while at the same time XP c-commands Y.5 It is crucial that the c-commandrelation between two nodes � and � is asymmetrical, as it is impossiblethat � precedes � while at the same time � precedes �. However, withthe current de�nition of c-command this is not the case. Therefore Kayneapplies a modi�ed de�nition of c-command, as we will see below.

In Kayne's new de�nition � c-commands � if and only if:

� � and � are not segments (see below),

� � excludes � (see below), and

4Note that Kayne restricts himself to binary branching trees [Kay94, Page 4].5Note that in Example 1.8 the intermediate bar-level (e.g. X) does not occur. In

Chapter 7 we will argue why we do not follow this approach to X-Theory.

1.4. LEXICAL INSERTION, SPELL-OUT, AND LOGICAL FORM 11

� every that dominates � also dominates �.

A node � is a segment if and only if it is not a head or a direct projectionof the head. For instance, in Example 1.8 X is the head, the lower XP isthe direct projection of the head, and the higher XP is a segment. A node� excludes a node � if and only if no segment of � dominates �.

In Example 1.8 the higher XP does not c-command Y since XP is asegment. The lower XP does not c-command Y either, since the lower XPdoes not exclude Y.

YP does c-command X in Example 1.8 since it is not a segment, it ex-cludes X and every that dominates YP also dominates YP also dominatesX.

Now, we can conclude that the structure in Example 1.9, where thecomplement (ZP) precedes the head (X) and the speci�er (YP), is incorrect.For instance, YP c-commands X, but Y does not linearly precede X.

Example 1.9

XP

XP YP

ZP X Y

Hence, from the assumptions given by Kayne, we deduce that in a phrasethe head is preceded by the speci�er and followed by the complement. Inthe next section we will see how this in uences the direction of movementsin the Minimalist Program.

1.4 Lexical insertion, Spell-Out, and Logical

Form

Within the minimalist approach not only phrase structure, but also possiblemovements are universal. Hence it follows that a given constituent (e.g. thesubject) has to cover the same path through the tree in all languages. Aconstituent always travels from its position of lexical insertion low in thetree, to its Logical Form (LF) position higher up (see Figure 1.1 on Page13). For instance, in Example 1.5 (repeated here as 1.10) we see that thesubject she (with index i) is inserted in the lexical domain (VP), and movesto the functional projection AgrSP via TP. The LF-position is the highestposition a constituent reaches, and therefore the LF-position of she is withinAgrSP. The verb hates (with index k) moves considerably more often than


the subject. It moves from VP to AgrOP to TP to AgrSP, which also isthe LF-position of the verb. As we will see in Section 1.5, a lexical elementmay only move to a given functional projection if it needs to check one ormore features there.

Example 1.10

CP

C

C AgrSP

thatl

NP AgrS

shei

AgrS TP

T AgrS ei T

AgrO T T AgrOP

ek

V AgrO ej AgrO

hatesk

AgrO VP

ek

ei V

V NP

ek catsj

Somewhere in between the position of lexical insertion and the LF-position of a constituent, we �nd the position where the constituent is `pro-nounced'. In Example 1.10 the `pronunciation position' is marked becausethis is the only position in the chain of movements where the constituentis actually written down. The other positions are just marked by the letter`e' (for empty) with an index. Note that the pronunciation position mayvery well coincide with the position of lexical insertion or the LF-position,or even with both as it is the case with the complementizer that in Example1.10, which does not move at all.

The pronunciation position is determined by the optional rule of Spell-Out. Therefore we will replace the term pronunciation position with theterm `Spell-Out position'. Since languages may di�er in word order, theymay di�er as to the point in the derivation where Spell-Out applies. In

1.4. LEXICAL INSERTION, SPELL-OUT, AND LOGICAL FORM 13

Section 1.5 we will see how the Spell-Out position of a given constituent ina given language is determined.

In Figure 1.1 we see that the movements that take place before Spell-Outare called overt movements, while the movements after Spell-Out are calledcovert movements. This terminology is used because only the movementsthat take place before Spell-Out in uence the sentence as we perceive it.In Section 1.5 I will go more deeply into the reasons for assuming covertmovement.

Lexicon

overt

8>><>>:

????????��!

Spell-Out

covert

8>><>>:

???????yLFLogical Form

PFPhonetic Form

Figure 1.1: The derivation of a sentence

Summarizing, we can say that the lexicon is consulted in the lowestposition of a chain, the Spell-Out position is higher than and to the left ofthe position of lexical insertion, and the LF-position is higher than and tothe left of the Spell-Out position. Note that it might be the case that twoor more of these three positions coincide.

The fact that movement is always directed towards the left is deducedfrom Kayne's ideas as described in Section 1.3. We assumed there thatspeci�ers and heads are located to the left of complements. Since move-ment is only possible when it is aimed towards head and speci�er positions,movement is always leftward, as we will see in Section 2.1.

The fact that movement is always upward can be deduced from thefact that derivation trees are built up in a bottom up way, as we will see inSection 1.6. Constituents move from the lexical domain (VP) at the bottomof the derivation tree to the functional domain (AgrOP, TP etc.) higher upin the derivation tree. Since moving constituents must have features thatcan be checked against features in the functional domain (see earlier in thissection and Section 1.5), it is not possible to move nodes without lexical


content. Therefore, the position of lexical insertion is by de�nition lowerthan (or equal to) the Spell-Out position and the LF-position.

1.5 Movement and feature checking

In the minimalist framework all movements are caused by feature check-ing requirements. The functional projections (AgrSP, TP etc.) as well asthe lexical projections in a derivation tree, contain features such as caseand agreement. The features of lexical constituents consist of three di�er-ent types: formal (also syntactic or in ectional) features, semantic features,and phonological features [Cho95, Page 229�].6 Semantic and phonologicalfeatures are considered to be relevant at respectively the interfaces LF andPF. Formal features are the features that cause the movements within thederivation. Movement enables the features of the moved lexical constituentto be compared with those of the landing site in a functional projection.Such a comparison is called feature checking. For instance, as we see in Ex-ample 1.10, the subject NP moves to AgrSP to check its agreement featuresand the verb moves to TP to check its tense features.

After features of a lexical constituent have been checked against thoseof a functional head, they are deleted. Below we will see why the featuresare deleted from the functional projections. Furthermore, we will see thedi�erence between overt and covert movement.

Both the deletion of features and the di�erence between overt and covertmovement are connected with the principle of Full Interpretation. The prin-ciple of Full Interpretation requires that the interface representations of asentence consist entirely of legitimate objects (Economy of Representation).Which objects are legitimate at the interface levels LF and PF will becomeclear later on in this section.

In Figure 1.1 we see that Spell-Out determines the point in the derivation(from lexical insertion to LF) where instructions are given to the interfacelevel PF. This follows directly from the de�nition of Spell-Out because theSpell-Out position is the position in a derivation where a constituent is aswe perceive a sentence. Of course we want the constituents of a sentenceto enter the interface level PF in the order in which they are pronouncedso that we will perceive them in the correct order. The instructions thatare given to PF consist of the features of the constituents in Spell-Outpositions. The PF-representation of a sentence is the sentence as we hear it.This representation is based on the phonological features of the constituentsin the Spell-Out positions (cf. [Cho95, Page 230]). Since heads enter the

6Note that the division in three types of features is �rst introduced in Chomsky's 1995framework. Although this chapter is an introduction to Chomsky's 1993 framework I willintroduce the division here for the sake of clarity.

1.5. MOVEMENT AND FEATURE CHECKING 15

derivation in fully in ected form (cf. [Cho93, Page 27�]), PF does not playa role in determining the morphology of words.

The features of the functional projections can either be strong or weakaccording to the Minimalist Program. Weak features are `invisible' andstrong features would be `visible' at the interface level PF. But then fea-tures, being purely syntactic/formal features, cannot be interpreted at PF.Therefore, all visible features have to be deleted before Spell-Out, since syn-tactic/formal features are illegitimate objects at PF. The principle of FullInterpretation namely causes a derivation of a sentence to fail or `crash'when one of the interface representations contains illegitimate objects, anddeletion of checked formal features can prevent the derivation from crash-ing. Since weak features are invisible at PF only strong features have to beeliminated after they are checked in overt syntax.

Languages that di�er in word order di�er only in having di�erent strongand weak features. The strong/weak parameter is even supposed to be theonly parameter in the Minimalist Program. This would make the MinimalistProgram an explanatorily adequate theory, since it explains why childrencan acquire language in a relatively short time.

The fact that the strong/weak parameter is the only parameter, in com-bination with the fact that all movements are universal in the MinimalistProgram, leads to the conclusion that all lexical items must contain thesame features in all languages, because it is not possible that functionalheads contain di�erent features in di�erent languages (since this would im-ply another parameter). Of course, it is possible that very similar lexicalitems have di�erent values for the same feature in di�erent languages. Forinstance, a certain noun can be masculine in one language and feminine inthe other.

There is a chance that a given constituent lands at more than one po-sition with di�erent strong features as it travels from its position of lexicalinsertion to its LF-position. In such cases the highest position with strongfeatures is the Spell-Out position, since Full Interpretation requires that allstrong features are removed before PF.

At the interface level LF not only strong but also weak formal featuresare visible. As the derivation crashes if any visible formal features are leftat LF, the constituents of a sentence have to keep on moving until all in ec-tional features are deleted. Hence, the LF-position of a given constituent ina given construction is universal. The LF-order of the constituents repre-sents the meaning of the sentence. Legitimate objects at LF are predicates,arguments, modi�ers and operator-variable constructions (cf. [Cho93, Page27]) but also semantic features such as [artifact] (cf. [Cho95, Page230]).Note that movement of a lexical constituent to a functional projection isonly possible if the features of the moving element and its landing site


match. If one or more features of a given lexical constituent do not matchwith the features of any of the landing sites (i.e. node within the functionaldomain) of the relevant phrase structure, the derivation of that sentencecrashes.

Summarizing, we could say that a tree is an LF-representation if alllexical constituents in the tree have checked all their formal features. Hence,covert movement is needed because generally by the time of Spell-Out notall formal features are actually checked.

Movement from the position of lexical insertion to the Spell-Out positionof a constituent occurs as follows. The (lexical) constituent moves to alanding site (in the functional domain). It checks its features against thefeatures of the landing site. Movement is called overt movement until thehighest position with strong features is reached. This highest position withstrong features is the PF-position of the constituent. The movements thattake place between Spell-Out and LF are covert, as was mentioned in Section1.4. This does not imply that no feature checking takes place after Spell-Out, only that no checking of strong features remains. The ending point ofthe path is the (universal) LF-position of the constituent.

A derivation of a sentence converges only when it does not crash at PF,nor at LF. To avoid having the derivation crash, formal features have to bedeleted by movement of lexical constituents in the course of the derivation.We could say that the point in the derivation where Spell-Out applies isdeducible from a requirement imposed on PF and LF. This requirementis called Full Interpretation and it implies that, as we saw above, no un-interpretable object may emerge at the interface levels PF and LF. SinceSpell-Out is deducible from PF and LF, it can replace the independent inter-face level S-Structure from earlier versions of generative linguistic theory,as I already mentioned in Section 1.1. The di�erence between overt andcovert movement that I mentioned at the beginning of this section is causedby the fact that PF and LF di�er as to which objects are interpretable.

1.6 The operations Merge and Move

The central operations of the Minimalist Program are Merge and Move.7

Merge is a structure-building operation that builds trees in a bottom-upway as is illustrated in Example 1.11. Two trees (V and NP) are combinedinto one. One of these two is called the target (V). A projection of thetarget (V) is added to the target. The projection of the target has two

7Note thatMove andMerge are called respectivelythe singulary and the binary versionof Generalized Transformation in [Cho93]. The notions Move and Merge are introducedby Chomsky [Cho95]. I use the notionsMove and Merge instead of the old terms, becausethe former are the more popular at the moment.

1.6. THE OPERATIONS MERGE AND MOVE 17

daughters: the target itself and an empty position. The empty position issubstituted for by the second tree (NP). This second tree is itself built upin other applications of Merge and/or Move. The target in Example 1.11 isobtained directly from the lexicon. It is not a constituent that is the resultof earlier applications of the operation Merge and/or Move.

Example 1.11

V

see

NP

her

V

V e

see

V

V NP

see her

Move is an operation that moves a tree within a tree. The operationcombines a target with a moved tree. It is assumed that movement isalways leftward and that heads and speci�ers, which are the only positionsto move to, are always to the left in the tree (see Section 1.4). These twoassumptions in combination with the fact that Merge and Move are bottom-up operations, e�ect that the moved tree has to be contained in the treethat was built so far. Chomsky [Cho93, Page 23] argues that the movedtree must be contained in the target.8 Illustrations of the operation Movecan be found in Example 1.5, repeated here as Example 1.12. There is a NPin the speci�er position of AgrSP. To move this NP to the speci�er positionof AgrSP, AgrS is taken as a target tree (the projection above AgrS doesnot exist yet at that moment). AgrSP is added as a projection of AgrS andan empty position is created as the sister of AgrS. This empty position issubstituted for by the NP from the speci�er position of the VP.

The tree in Example 1.12 illustrates di�erent kinds of movement.The chain with the index k illustrates head movement. The verb moves

from its base position in the VP to AgrO, T and AgrS. The verb adjoinsto those heads to check its features against the features that are presentthere.9

The chains i and j show movement to speci�er positions. The subjectand the object move to the functional domain to check their features. Forexample, subject-verb agreement is checked in AgrSP by moving both thesubject and the verb to AgrSP.

Now I will return to the elimination of D-Structure, which I mentionedearlier in Section 1.1. I claimed there that in the Minimalist Program, D-Structure can be eliminated by collapsing rewrite rules, lexical insertion andmovements. Here we will see that the structure-building operations Moveand Merge open up possibilities to eliminate D-Structure. In earlier versionsof generative grammar, D-Structure was a representation that was based on

8See also Subsection 2.1.3.9See [Cho93, Page 11].


rewrite rules and lexical insertion. A D-Structure representation of a sen-tence was built by deducing a structure from the rewrite rules and �llingit with items from the lexicon. By applying movements to D-Structure, S-Structure was derived. In the Minimalist Programmovements, rewrite rulesand lexical insertion are combined in the structure-building operations Moveand Merge. Hence, in earlier versions of generative grammar one �rst ap-plied all rewrite rules and then all transformations, while in the MinimalistProgram rewrite rules intermingle in application with the transformational(Move) rules.

Example 1.12

CP

C

C AgrSP

thatl

NP AgrS

shei

AgrS TP

T AgrS ei T

AgrO T T AgrOP

ek

V AgrO ej AgrO

hatesk

AgrO VP

ek

ei V

V NP

ek catsj

Firstly, that movement is now a part of the structure-building opera-tions is self-evident. Secondly, rewrite rules, or rather X-rules are consultedby the operations Merge and Move in the Minimalist Program. The struc-tures that are built must be correct according to X-Theory. Thirdly, lexicalitems are not introduced `all at once', to speak in Chomsky's terms, in theMinimalist Program, as was done at D-Structure in earlier versions of gen-erative linguistics. In the Minimalist Program, derivation trees of sentencesare built in a bottom-up way by applying structure-building operations.Lexical items �rst are introduced when the position in the tree where they

1.7. SUMMARY 19

belong is created. The `all-at-once' representation of lexical material wasthe reason of existence of D-Structure.

The fact that movements, rewrite rules and lexical insertion are com-bined in the structure-building operations Merge and Move blurs the di�er-ence between D- and S-Structure and makes it plausible that D-Structurecan be eliminated.10

1.7 Summary

I will summarize the above by describing the derivation of the correct struc-ture for the sentence She hates cats more or less from start to �nish. Theonly part I will skip is the derivation of the internal structure of the NPsshe and cats.

The derivation starts with the introduction of the verb hates from thelexicon (lexical insertion). This verb serves as the target at this point. TheV hates projects to V and selects a complement cats (see Example 1.13).11

The fact that V projects to V and the fact that the complement occurs leftof the head is deduced from X-Theory. Hence, in the step described herethe V hates and the NP cats are merged into a V.12

Example 1.13

V

V NP

hatesk

catsj

In the next step V is the target. V is merged with the NP she byprojecting it to VP and selecting the NP she as its speci�er sister (seeExample 1.14). Again, X-Theory is consulted to determine that VP is theprojection of the target and to determine the relative order of the speci�erand the target.13

10The all-at-once nature of D-Structure has often been consideredproblematic in recentresearch. See for instance: [KJ85, LU88, Leb88, Bro93].

11Normally, as a �rst step, hates receives an empty sister, which in a second step is �lledwith the complement cats. This intermediate step is left out for the sake of simplicity.

12The complement cats itself is built up by applications of lexical insertion, X-Theory,Merge and Move that are not described here.

13The speci�er she is built up by applications of lexical insertion, X-Theory, Merge andMove that are not described here.


Example 1.14

VP

NP V

shei

V NP

hatesk

catsj

The next step, which actually consists of two separate steps, is a Moveoperation. The V hates which is contained in the VP moves to AgrO byadjoining to it (see Example 1.15).14 AgrO is the target of the operation andmerges with VP. To enable movement of V to AgrO, AgrO is disconnected.Next it is linked with the rest of the structure again via its projection(AgrO). Then it receives V as its sister by movement from within VP.15

As we saw earlier in this chapter, movement must be associated withfeature checking. In this case the object agreement and the object case fea-tures of V are checked against the agreement and case features of AgrO.16 Ofcourse, also in this step and in all the following steps X-Theory is consulted.

Example 1.15

AgrO

AgrO VP

V AgrO NP V

hatesk

shei

ek NP

catsj

14See Subsection 2.1.3 for a de�nition of the domain where a moving tree must comefrom.

15Cf. [Cho95, Page 260].16In Chapter 5 the features that are applied in the Minimalist Program are described

in detail.

1.7. SUMMARY 21

In the next step AgrO is the target. It projects to AgrOP and selectsa speci�er (see Example 1.16). Since this step is a Move operation thespeci�er must be a subtree contained in the tree built so far. The speci�erthat is selected is a `copy' of the complement of V, i.e. the NP cats. Notethat the speci�er of AgrOP contains an empty copy. This is caused by thefact that the features of the NP cats are not checked against strong featuresand hence the Spell-Out position of the NP cats is in situ. The case andagreement features of the NP are checked against the case and agreementfeatures of AgrO.

Example 1.16

AgrOP

ej AgrO

AgrO VP

V AgrO NP V

hatesk

shei

ek NP

catsj

Subsequently, verb movement takes place again. This time by adjoiningAgrO, including V, to T (see Example 1.17).17 The tense feature of V ischecked against the tense feature of T.

Next, I assume that the speci�er of VP moves to the speci�er of TPto check its case feature against the case feature of T (see Example 1.18).Chomsky assumes that there is no movement to the speci�er of TP. Insteadhe assumes that the case feature of the subject (she in our example) ischecked against the case feature of T within AgrSP. This is possible since TAdjoins to AgrS, as we will see in the next step of this derivation. However,for reasons that are explained in Section 8.2, I will assume that the subjectmoves to the speci�er of TP.

17The reason why not only V moves, but rather AgrO including V lies in the factthat sometimes lexical constituents check their features against a functional projection� by moving to another functional projection �, to which the head of � is adjoined. Forinstance, according to Chomsky [Cho95, Page 174] the case feature of the subject NP ischecked against T in the speci�er position of AgrSP.


Example 1.17

T

T AgrOP

AgrO T ej AgrO

V AgrO ek VP

hatesk

NP V

shei

ek NP

catsj

Example 1.18

TP

NP T

shei

T AgrOP

AgrO T ej AgrO

V AgrO ek VP

hatesk

ei V

ek NP

catsj

The last two steps of the derivation are summarized in Example 1.19.V reaches its Spell-Out position in AgrS. It checks its subject agreementfeature against the strong agreement feature of AgrS. Likewise, the subjectNP she reaches its Spell-Out position by checking its agreement featureagainst the strong agreement feature of AgrS.

1.7. SUMMARY 23

Example 1.19

AgrSP

NP AgrS

shei

AgrS TP

T AgrS ej T

AgrO T ek AgrOP

V AgrO ej AgrO

hatesk

ek VP

ei V

ek NP

catsj

Chapter 2

Implementations

In this chapter I will present two small implementations which I used toexplore the possibilities of the formalization of the Minimalist Program.

In Section 2.1 I will give a survey of structure-building operationswithin the minimalist framework [Cho93].1 The survey is based onan implementation of the operations Move and Merge in Prolog. Theimplementation, which is described in Subsection 2.1.1, shows in detailwhich operations are needed to build minimalist trees. It reveals thatsome sub-cases of Merge and Move are not (su�ciently) described in theliterature. In Subsection 2.1.2 I will give a schematic overview of whatwe learned from the implementation and in Subsection 2.1.3 I will showthat the general ideas in the literature have to be reconsidered to be ableto capture all structure-building operations. This does not mean that theideas are wrong, but it does mean that they are incomplete.

In Section 2.2 I will describe a head-corner parser for a fragment ofthe Minimalist Program [Cho93].2 I will argue that, because of the natureof the structure-building operations of the Minimalist Program, head-cornerparsing is a suitable parsing technique for the Minimalist Program.

Furthermore, I will put forward a proposal to treat functional and lexicalheads di�erently. Functional heads are not treated as head-corners of theirmothers by the minimalist head-corner parser that is described here.

The parser that is described here only covers simple declarative sen-tences, possibly with a subordinate clause.

1This section is based on [Vee94].2This section is based on [Vee95a] and [Vee95b].

25

26 CHAPTER 2. IMPLEMENTATIONS

2.1 Merge and Move

2.1.1 The implementation

In the implementation that is discussed here, I endeavoured to cover allstructure-building operations that are needed to build a tree according tothe Minimalist Program. The only structure-building operation that is notcovered is the adjunction operation with two maximal projections of whichthe result is given in Example 2.1. The reason for the absence of thisoperation is the fact that it is not needed in the fragment that is coveredby this chapter or later chapters of this work. Furthermore, this type ofadjunction is considered to be impossible by many linguists (see for instanceKayne [Kay94]).

Example 2.1

XP

YP XP

The implementation covers three main operations: one concerning heads,one concerning complements and one concerning speci�ers. In Example 2.2I show the positions that heads, complements and speci�ers occupy withina maximal projection XP. The three operations each consist of one or moresub-cases. The number of sub-cases corresponds to the number of possibletypes of �llers for the relevant position. In this way, the implementationgives a clear view of all structure-building operations that are needed tobuild minimalist trees. All the operations and their sub-cases will be dis-cussed below.

Example 2.2

XP

YP X

(Speci�er)

X ZP

(Head) (Complement)

The operation concerning head positions consists of two sub-cases. Onesub-case is a Merge operation that is used to create heads by extractingfeature structures from the lexicon. I will call this lexical insertion. Thehead is taken as the target. X is projected to X and the sister of X is

2.1. MERGE AND MOVE 27

�lled with a complement which itself is also built by the structure-buildingoperations Merge and/or Move. The other sub-case is a Move operation thatserves to create an adjunction structure. The structure that arises when thehead or adjunction structure Y adjoins to the head X is given in Example2.3. Y originates from a position within ZP. This kind of movement is calledhead movement.

Example 2.3

X

X ZP

Y X

Example 2.4

CP

C

C AgrSP

thatl

NP Agr

Billi

AgrS TP

T AgrS ei

T

AgrO T ek AgrOP

V AgrO ej AgrO

meetsk

ek VP

ei

V

ek NP

Wimj

The operation for complement positions consists of only one sub-case.It is a Merge operation which �lls complement positions with maximal pro-jections (XPs). For instance, in Example 2.4, the complement NP Wim has


been merged into its position as a sister to V. Movement to complement po-sition does not exist.3 I suggest to call all types of insertion in complementposition tree insertion.

The operation concerning speci�er positions consists of two sub-cases.The �rst sub-case is a Move operation. I suggest calling this type of move-ment to-speci�er movement. The element moved originates from a speci�eror complement position lower in the tree. For instance, in Example 2.4,the NP (with the index i) in the speci�er position of the VP, is moved tothe speci�er position of TP for feature checking. An example of to-speci�ermovement originating from complement position is the movement of theobject NP with the index j, which is located in the complement position ofthe VP. This NP has to move to the speci�er position of AgrOP to checkcertain features.

The second sub-case of the operation concerning speci�ers does not in-volve movement. It is a Merge operation that combines a target (X) and amaximal projection (YP). The maximal projection is the speci�er. Speci�erpositions can only be �lled by NPs. In Example 2.4 this sub-case only occursonce: V is merged with an NP, which is represented by an empty positionwith the index i since it overtly moved to the speci�er of TP. Complementpositions are less sensitive concerning �ller trees.4 For instance, AgrSP oc-curs as the complement of C, VP occurs as the complement of AgrO etc.Tree insertion in the sense of the insertion of an NP in speci�er position canonly occur in the lexical domain because that is the only place where we caninsert new lexical material.5 A third sub-case for speci�er positions wouldhave been needed for the insertion of determiners in the speci�er positionof an NP (see Example 2.5), but we will see that with a slight modi�cationwe can eliminate this sub-case.

Example 2.5

NP

Det N

the

N

book

Until now, the only lexical insertion was the insertion of a head from thelexicon. A category that is spoiling the assumption that lexical insertion

3Cf. [Cho93, Page 23].4See also [Hoe91, Page 27].5An exception to this rule may be the insertion of adverbs (cf. [Zwa93, Page 94]) and

complementizers (see the head of the CP in Example 2.4).


is head insertion is the determiner. In my implementation I �rst chose touse NPs instead of DPs (see Example 2.6).6 This was done for reasons ofsimplicity. Only NPs of the type name, personal pronoun, noun and nounplus determiner are included. The NP analysis seemed su�cient for thisgoal. In the end this appeared to be an ine�cient solution because thedeterminer in an NP analysis is not a head. In the DP analysis on the otherhand, the determiner is a head (D) which takes an NP as its complement.In short we could say that it is more e�cient to adopt the DP analysisbecause in that case we only have tree insertion (no lexical insertion) inspeci�er position and there is only one type of lexical insertion and that isthe insertion of a head from the lexicon. The implementation was adjustedto the use of DPs instead of NPs. Therefore the third sub-case of the caseconcerning speci�ers was no longer needed.

Example 2.6

DP

D

D NP

the book

2.1.2 Overview

All operations that are discussed in Subsection 2.1.1 except for the operationconnected with the NP analysis are summarized in Table 2.1.

Table 2.1

Structure-building operations of the Minimalist Program

tree lexical to-speci�er headinsertion insertion movement movement

Merge X X - -Move - - X X

head - X - Xcomplement X - - -speci�er X - X -

from head - - - Xfrom complement - - X -from speci�er - - X -

6See [Abn87] for a description of the determiner phrase.


In the �rst two rows of the table, we see that tree insertion and lex-ical insertion are associated with the operation Merge, while to-speci�ermovement and head movement, of course, are associated with the operationMove.

The number of crosses in the rows head, complement and speci�er in thetable corresponds to the total number of sub-cases. There are two operationsto create heads (lexical insertion and head movement), two operations tocreate speci�ers (tree insertion and to-speci�er movement), and there is oneoperation to create complements (tree insertion).

The only operations that have crosses in the last three rows are themovement operations in the third and fourth column. This follows becausemovement operations are the only operations that take elements from otherpositions to speci�er or head positions.

2.1.3 Problems

During the implementation of Move and Merge it turned out that the de-scriptions in Section 1.6 do not cover all the operations that we need tobuild the trees that the minimalist framework requires. In this section wesaw that Chomsky [Cho93, Page 23] argues that the moved tree must becontained in the target tree. Here I will argue why this is not always thecase.

Head movement, which is a Move operation, yields an adjunction struc-ture. When a head is moved, it is adjoined to another head that is higher inthe tree. It receives a position that is created by an adjunction operation.For example, when a verb from within the VP is moved to AgrO to checkits features, we get the structure given in Example 2.7.

Example 2.7

AgrO

AgrO VP

V AgrO DP V

blamesk Kohli

ek DP

Kokj

If we have a closer look at head movement, it does not seem to �t intothe de�nition of the operation Move. Chomsky only illustrates the Moveoperation with an example of XP-movement. In the case of XP-movement(= to-speci�er movement) the target is a Y (see Example 2.8). Y has twodaughters: Y and ZP. The target tree, Y, contains the element XP that ismoved to the speci�er position of YP.


Example 2.8

YP

XP Y

Y ZP

In the case of head movement, the moved element is not contained bythe target tree, but by the complement of the target phrase marker. Forinstance, in Example 2.7, the sister of V (the lower AgrO) is the targettree.7 The higher AgrO is the projection of the target. Example 2.7 showsthat the target AgrO is a terminal element. Hence, it is impossible that themoved V comes from the target. Instead, the moved element comes fromthe VP-complement. Therefore, I need to rede�ne `Move operation' as inDe�nition 2.1.

De�nition 2.1

A Move operation is a structure-building operation in which a moved ele-ment is combined with a target tree to form a new tree. The element thatis moved has to be contained in the complement domain of the head of thetarget tree.8

If we adopt this de�nition both to-speci�er movement and head move-ment are covered.

In Subsection 2.1.1 I refer to Chomsky [Cho93] for the reason why move-ment to complement positions is not possible. Now that we have adoptedthe new de�nition for the notion `Move operation', I can come up witha very clear reason why movement to complement positions is impossible.The new de�nition says that moved elements must originate from the com-plement domain. From this de�nition we can derive that it is impossible tomove an element to a position that is �lled with the tree from which theelement should originate. Therefore, movement to complement positions isexcluded.

2.1.4 Summary

In this section I discussed an implementation of the ideas about structure-building operations in the Minimalist Program [Cho93]. The implementa-

7See Section 1.7 for a detailed description of head movement.8For the de�nition of `complement domain' see [Cho93, Page 11] and Chapter 8. At

this point we simply will assume that the complement domain is the complement.


tion covers both Move and Merge operations. It is concluded that thereare three kinds of Merge operations (that is: tree insertion in the comple-ment and the speci�er position and lexical insertion in the head position)and two kinds of Move operations (that is: head movement and to-speci�ermovement).

I demonstrated that it is possible to implement the structure-buildingoperations as described by Chomsky when some slight modi�cations aremade. A new de�nition of the Move operation is given, which says that themoved element in a Move operation has to be contained in the complementdomain of the head of the target tree, not in the target tree as the originalde�nition says. From this new de�nition we can derive that movement tothe complement position is impossible. An element (tree) cannot be movedto a position that contains the tree from which the moved element mustoriginate.

2.2 A minimalist head-corner parser

In this section I will discuss a head-corner parser which associates an in-put string with trees such as the one in Example 2.10, where each chainonly contains one visible (i.e. nonempty) element.9 The visible elementrepresents the Spell-Out position of the chain.

2.2.1 Head-corner parsing

The main idea behind head-driven parsing [Kay89] is that the lexical entriesfunctioning as heads contain valuable information for the parsing process.For example, if a verb is intransitive it will not require a complement, whileit will require a complement if it is a transitive verb. Therefore, the headis parsed before its sisters in a head-driven parser. A head-corner parser[Kay89] [BvN93] is a special type of head-driven parser. Its main charac-teristic is that it does not work from left to right but instead works bidi-rectionally. That is, �rst a potential head of a phrase is located and nextthe sisters of the head are parsed. The head can be in any position in thestring and the non-head sisters can either be to the right or to the left.

Top-down and bottom-up information is combined in head-cornerparsers. The top-down information is contained in the head-corner rela-tion. The head-corner relation is the re exive and transitive closure of thehead relation. An example of two categories that stand in a head relationare N and NP, i.e. N is the head of NP. X-Theory contains the followinggeneral rule (Example 2.9):

9Note that each chain has its own index.

2.2. A MINIMALIST HEAD-CORNER PARSER 33

Example 2.9

XP ! YP X

The head of a rule is one of its right-hand side daughters (in this caseX). Given the fact that the Minimalist Program assumes X-Theory, it ismost natural to assume that N is the head of NP and N is the head ofN. The head-corner relation is transitive and therefore both N and N arehead-corners of NP.

A head-corner parser starts the parsing process with a prediction step.This step is completed when a lexical head is found that is head-cornerof the goal according to the head-corner table. The goal is the type ofconstituent that is parsed, i.e. the root of the tree that is built. Then anX-rule is selected in which the lexical head is in the right-hand side. Thesisters of the head are parsed recursively. In the minimalist head-cornerparser that I am proposing here, a head always has only one sister becauseminimalist trees are at most binary branching. The left-hand side of therule is consulted to �nd the mother of the head. Then the head-corner tableis used to decide whether this mother is a head-corner of the goal. If thisis the case the whole process is repeated by selecting a rule with the newhead-corner (i.e. the mother of the �rst head-corner) in its right-hand side.The sisters are parsed recursively, etcetera.

In Chapter 1 it was claimed that movement is invariably leftward andthat Move and Merge are bottom-up operations. The VP is built beforeother projections. Constituents of VP are moved to higher projections bythe operation Move. Suppose that the parser should consider AgrS as thehead-corner of AgrSP, which would accord with X-Theory (see Example2.10). Then the head (AgrS), which should be �lled with an adjoined verbby movement from T, is created before T, AgrO and V. To avoid thesepurely top-down steps the head-corner table for the minimalist head-cornerparser is not constructed completely according to X-Theory. For instance,instead of AgrO, VP is the head-corner of AgrO. This processing solution isfaithful to the ideas of the Minimalist Program in the sense that in this waythe tree is built up in an absolutely bottom-up way (i.e. starting from V)so that a position that should be �lled by movement is always created afterthe position from which the moved element comes. Hence, the parser is notlooking for the grammatical head of functional projections but instead itlooks for the lexical basis. When parsing a sentence, the parsing processalways starts with the verb and not with one of the functional heads. TheMinimalist Program postulates functional heads which have no phonologicalcontent. Lexical heads like verbs are more useful for the parsing process, aswe already saw at the beginning of Subsection 2.2.1.

The list in Example 2.11 illustrates that functional heads like AgrO


and AgrS are not considered as head-corners. Lexical projections like VPand NP are treated according to X-Theory. If we consider the head-cornertable in Example 2.11 in combination with the tree in Example 2.10 weestablish the fact that the parser searches its way down to the verb as soonas possible. The top-down prediction step moves from the goal AgrSP toAgrS to AgrOP to AgrO to VP to V and �nally to the lexical head-cornerV where the bottom-up process starts as the Minimalist Program requires.

Example 2.10

AgrSP

DP AgrS

shei

AgrS TP

T AgrS ei T

AgrO T ek AgrOP

V AgrO ej AgrO

hatesk

ek VP

ei V

ek DP

catsj

Example 2.11

Elements of the head-corner relation:

hc(AgrS,AgrSP). hc(VP,AgrO).hc(TP,AgrS). hc(V,VP).hc(T,TP). hc(V,V).hc(AgrOP,T). hc(N,NP).hc(AgrO,AgrOP). hc(N,N).

2.2.2 Structure-building operations and head-cornerparsing

If we have a closer look at the de�nitions of Merge and Move we see thatthey resemble the strategy of head-corner parsing a lot. In both cases westart with a head. In the case of Merge and Move this is called the targettree; in the case of head-corner parsing it is called the (lexical) head-corner.


In both cases we use an X-rule to obtain more information about themother and the sister of the head. In the de�nitions of Merge and Move thesister also has to be built up by Merge and/or Move or it is an XP that ismoved from a position lower in the tree to this position. In the parser thatis discussed here a sister is parsed or the sister is linked to a lower position(see Subsection 2.2.3).

The next step for Merge and Move is to consider the new phrase markerthat is built as the new target tree and apply Merge or Move to this tree.The next step in the parsing process is to check if the mother of the head-corner is a head-corner of the goal. If this holds, the whole process startsagain with the mother as a head-corner.

2.2.3 The algorithm

The parser that is discussed here is based on the head-corner parser in[BvN93]. In a head-corner parser, the positions the words of an input stringoccupy in relation to each other is essential. Each word is assigned twonumbers which indicate its position in the sentence. For instance, if asentence consists of three words the �rst word is assigned the numbers 0and 1, the second word is assigned the numbers 1 and 2 and the third wordis assigned the numbers 2 and 3. Hence, the third word of the sentence isthe word that is located between the second and the third position of thesentence.

The position numbers play an essential part in the parsing process. If weare looking for a head-corner within a sentence from position 0 to position8, the position numbers of the head-corner may never be lower than 0 orhigher than 8. Suppose we �nd a head-corner from position 5 to position6. Then we know that if the head-corner has a sister it must have 5 as itsrightmost position if it is a left sister, or 6 as its leftmost position if it is aright sister, since sisters, of course, are adjacent.

The minimalist head-corner parser presented here mainly consists of thefollowing three predicates: parse, head corner and predict. The parsingprocess starts with calling parse. As we see below parse calls among otherthings the predict and the head corner predicate.

In the predicate parse below, E0 indicates the �rst position of the sen-tence that is parsed and E indicates the last position of the sentence thatis parsed. P0 and P indicate the �rst and last position, respectively, of thespeci�c constituent that is parsed at a given moment. The �rst time thepredicate parse is called, P0 equals E0 and P equals E, since the constituent(Cat) we are looking for is the category of a complete sentence (for instance,AgrOP). In later calls, E0 and E always indicate the �rst and last positionof the complete sentence but P0 and P can for instance relate to an NP thatis parsed at that moment.


As we saw earlier, the idea behind head-corner parsing is to �nd a head-corner and to parse its sisters recursively. Detecting a new head-corner isthe main task of the parse predicate.

% parse(Cat/CatTree,P0,P,E0,E) if there is a Cat from position

% P0 to P

% in the sentence, within the range E0, E

parse(Goal,P0,P,E0,E) :-

predict(Goal,Lex,Q0,Q),

between(Q0,Q,E0,E), % Q0 and Q are between E0 and E

head_corner(Lex,Goal,Q0,Q,P0,P,E0,E).

The predicate predict locates a lexical head-corner. The relation hc im-plements the head-corner table.

% predict(Goal/GoalTree,Lex/LexTree,Q0,Q)

% if Lex from position Q0 to Q may be head-corner of Goal

predict(Goal/_,Lex/tree(Lex,w(Word)),Q0,Q) :-

hc(Lex,Goal),

chart(Word,Q0,Q),

lex(Word,Lex).

Because trees in the Minimalist Program are at most binary branching,there will never be both left and right daughters in the same rule (in ad-dition to the head). Furthermore, there is always at most one right or leftdaughter in each rule. It is impossible to parse both the left and the rightdaughters within the same head corner clause. We need separate clausesto parse left and right daughters (see respectively the third and the sec-ond head corner clause given below). For example, the second head cornerclause parses a sister of the head-corner which is to the right of the head-corner. The position of the head-corner is from Q0 to Q1. The position ofthe sister is from Q1 to Q, with Q <= E and Q0 <= Q1 <= Q (see theline parse(Dtr/DtrTree,Q1,Q,Q1,E) in the second head corner clause belowand Example 2.12). If Q0 = Q1 the head is empty (e.g. because it movedto another position in the tree).

Example 2.12

��

E0

@@

@@@@

@

E

��

Q0@

@@@@@

Q@

@@@

Q1head-corner sister


The predicate rule implements X-rules. In these rules Small representsthe head-corner, Dtr represents the sister of the head-corner and Mid rep-resents their mother. The �rst argument of the predicate rule indicatesat which side of the head-corner the other daughter of Mid can be found.The third argument is the left-hand side of the X-rule. The second and thefourth argument represent the right-hand side of the X-rule.

head_corner(Small,Small,P0,P,P0,P,_,_).

head_corner(Small/SmallTree,Goal/GoalTree,Q0,Q1,P0,P,E0,E) :-

rule(right,Small/SmallTree,Mid/MidTree,Dtr/DtrTree),

parse(Dtr/DtrTree,Q1,Q,Q1,E),

hc(Mid,Goal),

head_corner(Mid/MidTree,Goal/GoalTree,Q0,Q,P0,P,E0,E).

head_corner(Small/SmallTree,Goal/GoalTree,Q1,Q,P0,P,E0,E) :-

rule(left,Small/SmallTree,Mid/MidTree,Dtr/DtrTree),

parse(Dtr/DtrTree,Q0,Q1,E0,Q1),

hc(Mid,Goal),


In addition, we need separate clauses for Merge and Move. As we con-cluded in Subsection 2.2.2, Merge has a lot in common with head-cornerparsing. Therefore the plain head corner clauses as given above representMerge. To account for movement I added movement predicates after thecall to parse in a head corner clause. The example given below is the clausethat describes movement to speci�er positions.


rule(left,Small/SmallTree,Mid/MidTree,Dtr/DtrTree),

parse(Dtr/DtrTree,Q0,Q1,E0,Q1),

to_specifier_movement(MidTree,_SubTree,DtrTree)

hc(Mid,Goal),


DtrTree is the constituent that is moved to a speci�er position. Theroot of MidTree gets the moved constituent as its left daughter. SubTreecontains the position where the moved constituent comes from. To checkif it is possible to move the constituent from SubTree to MidTree a sim-ple solution is chosen. Within the predicate to speci�er movement, a ta-ble with possible movements is consulted: move(speci�er:X,speci�er:Y), ormove(complement:X,speci�er:Y). 10 X and Y represent respectively the cat-egory of the root of SubTree and the category of the root of MidTree. Ifa possible movement from SubTree to MidTree exists, the features and thechain indexes of the starting and �nal position of the moved constituent are

10See also Chapter 8.


uni�ed. Head movement is treated in a way similar to movement to speci�erpositions.

The fact that functional heads are not head-corners causes the neces-sity of an unusual head corner clause. The clause below is needed to beable to consider the linguistic head as a daughter and the complementas a head-corner (compare the second through fourth argument of rule inthe clause below with the same arguments within the head corner clausesabove). The following clause uses a rightward rule to �nd a daughter to theleft of the head-corner. The type of rule that is used is comparable with thehead corner clause above that is used to parse right daughters, but the in-dexes for the sentence positions in this clause are the same as the indexes inthe head corner clause above that is used to parse left daughters. The pred-icate functional ensures that Dtr is a functional head. In the head cornerclause for movement to speci�er positions, Mid should also be functional.Here it is not necessary to add the predicate functional because all possiblemovements are movements to functional projections. Therefore it would beredundant to prove that Mid is functional.


rule(right,Dtr/DtrTree,Mid/MidTree,Small/SmallTree),

functional(Dtr),

parse(Dtr/DtrTree,Q0,Q,E0,Q1),

hc(Mid,Goal),


An example of the application of the head corner clause that is givenabove is the case in which Small is a VP. A rule that could apply in thiscase is the rule where Dtr is AgrO and Mid is AgrO. AgrO is the regularhead of the rule, but VP is the head-corner in our parser. Therefore therightward rule can be applied to �nd a daughter that is to the left of thehead-corner.

2.2.4 Parsing versus generation

At the end of Subsection 2.2.1 I chose not to consider functional heads ashead-corners of their mothers. This choice was made because the structure-building operation Merge starts with constructing a VP before the projec-tions to which constituents from VP are moved are constructed. Anothermotivation to start with VP is that V contains information that is useful forthe rest of the structure-building process. For instance, if the verb is intran-sitive we know that V does not require a complement sister, and we knowthat we do not need an AgrOP on top of VP to check the features of theobject. The fact that V contains lexical information and functional headslike AgrO and AgrS do not, could be used as a justi�cation for the fact that


the latter are not head-corners. The main idea of head-driven parsing is, aswas stated before, that heads contain relevant information for the parsingprocess, and that they consequently should be parsed before their sisters.In the Minimalist Program not all heads are lexical. Functional projectionsdo not have phonological content. They obtain their phonological contentvia movement of elements from positions lower in the tree. This specialstatus of functional heads makes them less useful in the parsing process.

The Minimalist Program is a generative framework. Grammatical de-scriptions are cast in terms of rules to generate structural descriptions. Be-cause we are dealing with parsing (as opposed to generation) here, there arecertain further mechanisms postulated by the parser, ones not foreseen inthe the purely linguistic framework. In the minimalist framework, lexicalinformation belonging to a chain is available from the moment that the �rstposition of the chain is created, because that is the moment when the lexiconis consulted. Lexical elements enter the tree at the bottom of their chainand the lexical information that they bring can be used during the wholelength of the tree-building process. For example, a verb enters the chain inthe head position of VP. Therefore, the lexical information belonging to theverb can be utilized to determine whether the verb needs a complement ornot. Later on in the process, the lexical information can guide the decisionwhether an AgrOP should be build. An AgrOP is namely only needed in atransitive sentence.

When parsing a sentence the lexicon is not by de�nition consulted atthe beginning of the chain. Example 2.10, repeated here as 2.13, shows atree that contains traces and visible constituents. The position containinga visible constituent is the Spell-Out position of that chain. The parserconsults the lexicon at the moment in which the Spell-Out position of achain is reached. Consequently, when a trace is created before Spell-Out,the features belonging to that trace are unknown. Because all positionsin a chain are linked, the features of all traces of a chain are known assoon as the Spell-Out position is reached. For instance, in Example 2.13I assume that the PF-position of the verb is where it is adjoined to AgrS.In that case there is a trace in V, and at the moment in which it shouldbe determined whether the verb needs a complement or not, the featuresof V are still unknown. Therefore the parser will have to backtrack to trydi�erent possibilities.

It can be concluded that the absolute bottom-up approach for the build-ing of trees is more useful for generation than for parsing. In generation,lexical information can be used as soon as a position that is the beginningof a chain is created. In parsing we will have to wait until the Spell-Outposition is reached. In spite of this, I chose not to consider functional headsas heads in order to specify an absolutely bottom-up process. This bottom-


up approach is preferred because in this way a position to which a certainconstituent is moved is created after the position from which the constituentis moved. If we do not choose this approach, sometimes positions will becreated which need a moved element from a subtree that does not exist yet.This could be ine�cient, and it is not a direct implementation of the ideasof the minimalist framework.

Example 2.13

AgrSP

DP AgrS

shei

AgrS TP

T AgrS ei T

AgrO T ek AgrOP

V AgrO ej AgrO

hatesk

ek VP

ei V

ek DP

catsj

2.2.5 Summary

It appeared to be possible to implement the ideas that are described here ina head-corner parser. A distinction is made between lexical and functionalheads. Functional heads are not possible head-corners, while lexical headsare. In this way the parser is forced to built up trees in a bottom-up way,which makes that the parser can simulate the bottom-up structure-buildingoperations Merge and Move in a faithful way.

Chapter 3

Formalization

This chapter contains a global description of a project on formalization offragments of the Minimalist Program [Cho93], and of ideas of Zwart [Zwa97]in combination with a revised version of the Minimalist Program [Cho95].The project was carried out in cooperation with the Department of Comput-ing Science of the University of Groningen. There, Erik Saaman (in coop-eration with Gerard Renardel de Lavalette and Rix Groenboom) developeda formal-speci�cation language called AFSL (Almost Formal Speci�cationLanguage) in which the formalization of the Minimalist Program is written(See [Saa] and [Gro97].). The project on the formalization of a fragment ofthe Minimalist Program served as a case study for the formal-speci�cationlanguage AFSL. Another case study for AFSL was on formalizing rules foranaesthesiologists. The use of AFSL within this case study and the formalmodel are presented in [GSRRdL96], the full speci�cation can be found in[GRdL96]. For the arti�cial intelligence aspects (the diagnostic reasoningprinciples) I refer to [RdLGR+97].

In Section 3.1 of this chapter I will advance several reasons for formal-ization. Section 3.2 contains a brief description of the formal-speci�cationlanguage AFSL. In Section 3.3 I will discuss the di�erences between Chom-sky's 1993 framework as discussed in Chapter 1 and Zwart's 1997 frame-work. And �nally, in Section 3.4 I will discuss which parts of the MinimalistProgram are covered by the project described here and in what way.

3.1 Why formalization?

The objective of the formalization project described here is to obtain aformal and explicit version of a part of the Minimalist Program [Cho93],

41

42 CHAPTER 3. FORMALIZATION

[Cho95], [Zwa97].1 After the two implementation projects described inChapter 2 there appeared to be enough reason to start with the formal-ization of the relevant parts of the theory before implementing them.

I used the two implementation projects, both conducted in the program-ming language Prolog, to get an impression of the possibilities of formalizingparts of the Minimalist Program. The projects, which were both based onChomsky's 1993 version of the minimalist theory, revealed that the mainproblem was to �nd clear and explicit de�nitions of the relevant notions inthe literature. This lack of explicitness was a reason for not continuing aproject on the formalization of an earlier version of Chomskyan linguistictheory [Dor93]. I think, on the other hand, that formalization can contributeto the development of new theories such as the Minimalist Program. Byproviding formal de�nitions of important notions it becomes, for instance,easier to �nd inconsistencies and insu�ciencies in the theory.

I concluded that it would be more interesting to come up with clear def-initions of a range of important notions from the Minimalist Program thanto build working implementations. Since speci�cation languages can be con-sidered to be a middle course between natural languages and programminglanguages, as we will see further on in this section, a formal-speci�cationlanguage seemed to be more appropriate for this goal than a programminglanguage. The remainder of this section deals with reasons for formaliza-tion, both from the point of view of computing science and from the pointof view of linguistics.

First I will discuss a reason for formalization from the point of view ofcomputing science. When developing software a possible approach is: mak-ing an informal description of the system and then encode a program usinga programming language. In computing science it is generally accepted thatmore advanced software development techniques are essential. The utilisa-tion of formal-speci�cation languages is one possible technique.2 In thisapproach an additional step is introduced between the informal descriptionand the �nal implementation: the informal description is translated into aformal description in a speci�cation language and the formal description isthen translated into a working implementation. In this way the step frominformal to formal is made more gradually, which reduces the chance ofmistakes.

Also, when using a formal-speci�cation language, the ideas that are for-malized are possibly made more explicit than when using a programminglanguage right away. A programming language often forces the user to ap-

1See Fong [Fon91] and Stabler [Sta92b] for formalizations and implementations ofGovernment and Binding Theory [Cho81, Cho86a]. See Stabler [Sta96] and Cor-nell [Cor96, Cor97] for formalizations and implementations of the Minimalist Program[Cho93, Cho95].

2Cf. [MNB94], [MCW96] and [Gro97].

3.1. WHY FORMALIZATION? 43

ply certain data structures while the choice of a data structure for a givenconcept can be postponed when using a formal-speci�cation language. Forexample, in the Prolog implementation of our formalization trees are imple-mented as lists. The data structure `list' has a lot of properties which treesimplemented as lists inherit. In the formalization no choice is made for acertain data structure with respect to trees. By postponing the choice fora certain data structure one is forced to be more explicit.

An additional advantage of the use of a formal-speci�cation language isthat formalizations are more accessible to people without a background inprogramming in general or a certain programming language in particular.In the case of the Minimalist Program this is of major interest. The projectdescribed here not only provides a whole range of explicit de�nitions whichmight be of interest to linguists working within the minimalist theory. Italso provides a formal version of part of the theory which is easier to graspfor linguists working in other frameworks and which facilitates the detectionof consequences of, and inconsistencies in the theory.

This brings us to the attractiveness of formalization from a linguisticpoint of view. In informally stated theories it is hard to discover errors.Furthermore it is nearly impossible to determine the consequences of in-formal theories. Hence, a formally stated theory is not only attractive forcomputational linguists wanting to implement the theory, it is also veryimportant for linguists working within the theoretical framework.

When using a speci�cation language one is forced to be precise. Everynotion used in a de�nition needs to be de�ned itself. Of course, program-ming languages also o�er this advantage, but I discussed above reason forpreferring the more gradual step of formalization. The following de�nition(3.1) from Radford [Rad88, Page 110] shows that this is not necessarily thecase when using natural language.

De�nition 3.1

A node X dominates another node Y if X occurs higher up the tree than Yand is connected to Y by an unbroken set of solid lines (branches)

De�nition 3.1 contains notions like `higher up', `unbroken set' and `solidlines' that are never de�ned. These notions are assumed to be known by thereader. However, [Rad88, Page 109] claims that `any adequate descriptionof a phenomenon in any �eld of enquiry (in our present case, Syntax) mustbe maximally explicit, and to be explicit, it must be formal { i.e. make useof theoretical constructs which have de�nable formal properties'.

If we have a closer look at De�nition 3.1, we see that it is possible tointerpret the de�nition in such a way that the sister (X) of the mother of anode Y is dominating Y, which should not be true (see Example 3.1). Thisexample shows that it is advantageous to use a formal language instead of


natural language when de�nitions are needed. Naturally, formal de�nitionscan be incorrect, but then at least the mistake is explicit and therefore easierto discover.

Example 3.1

W

��X

TTZ

Y

De�nition 3.2 contains the natural language version and De�nition 3.3the formal version of the de�nition of `proper domination' that is applied inthe formalization. The notions `node' and `mother' are also de�ned in theformalization. A description of the language AFSL, which might be usefulto understand De�nition 3.3, is given in Section 3.2.

Proper domination is a type of domination where a node cannot dom-inate itself. Re exive domination is a type of domination where a nodecan dominate itself. This distinction is made because it is relevant for theformalization. Note that the De�nition 3.1 describes proper domination.

De�nition 3.2

A node nd1 properly dominates a node nd2 if and only if nd1 is the motherof nd2 or if there exists a node nd3 of which nd1 is the mother and thatproperly dominates nd2.

De�nition 3.3

AXIOM nd1 PropDominates nd2

<=> nd1 = Mother nd2

Or EXISTS nd3

( nd1 = Mother nd3

And nd3 PropDominates nd2

)

In the literature there has been a lot of discussion about what the formal-ization of grammatical theory should imply [Cho57, Pul89, Cho90, Lud92,Sta92a, Pol93]. However, broadly speaking most participants in the dis-cussion will agree on the three conditions for the adequate formalization of

3.1. WHY FORMALIZATION? 45

grammatical theory which Pullum [Pul89] formulates. The conditions areparaphrased from ideas of Stoll [Sto61] and come down to the following:

1. it must be clear whether a certain mathematical object (e.g. a tree)can represent a structural description according to the theory3

2. it must be clear whether a certain formal object represents a rule (orconstraint or principle or condition etc.) of the grammar

3. it must be clear whether a certain structural description is generatedby (or admitted by) a given set of rules

Only Ludlow [Lud92] claims that Pullum's conditions are `far too strong'.Ludlow's claim is based on the fact that he concludes that Pullum's condi-tions imply that there must be `an algorithm to determine the predictionsof the theory'. If this conclusion was right, Pullum's conditions would in-deed have been far too strong, since there is no science in which all thelogical consequences (theorems) of a theory could be determined. However,Pollard [Pol93] argues that Pullum's conditions are much more reasonablethan what Ludlow claims.

Pollard shows that in the �rst condition, Pullum expresses that the mod-els of a theory have to be de�ned. One has to be able to decide whether acertain object is a possible structural description or not. The constraints onstructural descriptions do not have to be stated in �rst-order logic. A cleardescription in natural language is enough. In the formalization a specialkind of trees, phrase markers, are the models of the theory. A tree is aphrase marker if it satis�es X-Theory and if all the movements it containsare made according to the rules of the theory as we will see in Chapter 8.A structural description carries semantic and phonetic information. Hence,in the formalization it is possible to test whether a tree is a structural de-scription by checking if it is a correct object at the interface levels LF andPF.

Pollard argues that Pullum's second condition demands that there is aclearly described �nite set of rules. It has to be possible to check whethera given constraint is actually one of the constraints of the theory. This isonly possible if all the constraints of a theory are unambiguously stated,possibly in natural language.

According to Pollard the demands of the third criterion would not havebeen reasonable if structural descriptions were in�nite objects. However,structural descriptions are always �nite (i.e. they have a �nite amount ofnodes or points), and therefore it is always possible to decide whether a

3A structural description is a representation of the certain linguistic properties of anexpression.


given structural description is licensed by the �nite set of constraints of agiven theory.

Chomsky [Cho57, Page 5] emphasizes the importance of precisely con-structed models for linguistic structure. He argues that formalized theoriesmay lead to the discovery of inconsistencies, and more positively to solutionsfor problems other than those for which the theory was designed.

Pullum [Pul89] shares this point of view with Chomsky. However, Pul-lum claims that Chomsky denied the importance of formalization on severaloccasions since 1979. On the other hand, Chomsky [Cho90] argues that thiscriticism is based on a misunderstanding.

To understand the discussion between Pullum and Chomsky, two no-tions are essential: E-language and I-language. Chomsky de�nes E-languageas the set of well-formed (grammatical) expressions [Cho86b, Cho90]. I-language is de�ned as a (generative) grammar, which is a component of thelanguage faculty of human beings [Cho86b, Cho90].

The notions E-language, I-language and structural description are inter-related in the following way. An I-language strongly generates a structuraldescription for each expression. Hence, an I-language licenses certain struc-tures and rejects others. Furthermore, an I-language weakly generates anE-language. Since an E-language is the set of all valid phonetic expres-sions, each of these expressions is assigned a structural description by theI-language. This makes the notion È-language' the less informative one.

According to Chomsky [Cho90], the misunderstanding between Pullumand him is based on confusion about the importance of the notion È-language'. Pullum [Pul89, Page 138] de�nes formal linguistics as `the studyof languages and grammars', which is interpreted by Chomsky [Cho90, Page144] as `the study of E-languages and the I-languages that weakly gener-ate them'. Pullum assumes that Chomsky denies the importance of formallinguistics in general, while Chomsky claims that he only denies the im-portance of the notion È-language' for formal linguistics in the claim thatgrammar might `characterize languages that are not recursive or even notrecursively enumerable, or even (. . . ) not generate languages at all with-out supplementation of other faculties of mind'. Chomsky argues that ìt ismeaningless to ask whether (. . . ) such an expression as misery loves com-

pany is, or is not, a member of the E-language weakly generated by [theI-language] L; and nothing would follow from a discovery (or stipulation)one way or another. These expressions have their status, determined by L;they are parsable, appropriate in certain situations, have a de�nite meaning,etc.'

Hence, in principle Chomsky recognizes the importance of formalizationof the I-language, although he does not think that `Pullum's injunction'to make à concerted e�ort' to meet `the criteria for formal theories set

3.2. THE FSA METHOD AND THE LANGUAGE AFSL 47

out in logic books' would be taken seriously by the natural sciences. Theimplicit question is then why linguistics, which is much less advanced thanthe natural sciences, should take this seriously. As we saw above, Pollard[Pol93] shows that Pullum's conditions are not much more reasonable thanChomsky claims here.

We can conclude that the formalization of linguistic theories is a rea-sonable and useful enterprise. But the availability of precise de�nitions innatural language would already be an enormous improvement. Pollard andSag [PS94, Page 9] for instance, who emphasize the importance of formal-ization, claim in their book about HPSG that their rules and principles areexpressed clearly and unambiguously, although put in natural language.

When I was collecting de�nitions for the formalization I noted that thereare a lot of notions that do not have de�nitions at all. For example, thenotion `feature checking', which is a central notion within the MinimalistProgram as we will see in the coming chapters, is not de�ned properly. Fromthe literature we can deduce that feature checking implies that the featuresof a moving element (i.e. constituent) and a node that serves as a landingsite for the moving element have to match. But we do not know, for instance,whether the moving element and the landing site must have exactly the samenumber of features or not. In Chapter 5 we will see that it is essential thatfor the de�nition of `feature checking' that the moving element contains thesame feature value pairs as the landing site, and possibly more. The wholeidea of feature checking does not work without this addition. However, thisdetail could not be found in the literature.

The formalization described in the following chapters provides precisede�nitions for parts of the Minimalist Program. Which parts of the theoryare covered is described in Section 3.4, but �rst I will give a brief descriptionof the formal-speci�cation language AFSL.

3.2 The FSA method and the language AFSL

In this section I will give a brief introduction to the speci�cation languageAFSL. The language is developed as a part of the Formal System Analysismethod. Therefore this method will also be brie y discussed below.

FSA The Formal System Analysis (FSA) method, with its formal-speci�cation language AFSL, is especially developed for the formalization ofknowledge domains. Knowledge domains have certain typical features thatimpose requirements upon a formal-speci�cation language:

� the language must be `lean and clean', as domain experts must beable to understand the formalization. Therefore AFSL is based on


�rst-order logic.

� knowledge domains often lack clear and stable de�nitions, especiallywhen the described theory is still evolving. Therefore the principleof stepwise formalization is introduced in AFSL: informal axioms canbe applied to bridge the gap between the informal de�nitions in adictionary and the formal de�nitions in the axiomatization.4

� the variety of the domain requires that the language has a wide spec-trum of possibilities. For instance, the language must be modular andprovide the possibility of typing.

The formal-speci�cation language AFSL is the result of the FSA project(cf. [Gro97], [Saa]) that has been carried out at the Department of Comput-ing Science of the University of Groningen. The method for the constructionof formal speci�cations that is developed within the scope of the FSA re-search project comprises three separate parts, of which the language AFSLis one. The other two parts are: a set of guidelines for formalization, andtool support to enable validation of a speci�cation.

Roughly we can distinguish two types of speci�cation methods:

� model-oriented speci�cation: an approach to speci�cation where asystem is speci�ed by de�ning an explicit model of it.

� property-oriented speci�cation: an approach to speci�cation where asystem is speci�ed in terms of its desired properties. Of course, thespeci�cation implicitly de�nes a model.

The FSA method applies the property-oriented method. This can be ex-empli�ed with the formalization project described here. The formalizationincludes a declarative description of trees within the Minimalist Program.Thus, the formalization describes the properties of trees that are correct ac-cording to the Minimalist Program. The type of tree (phrase marker) thatis described is the model of the minimalist theory. We de�ne which treesare legal phrase markers within the minimalist theory without referring tothe process of constructing phrase markers.

The FSA method supports the whole process of making an implemen-tation using formalization (see Figure 3.1). Firstly, the requirements ofthe relevant system are stated informally in natural language. Secondly,a formalization of the requirements is made. Thirdly, a formal implemen-tation is based on the formalization. In principle this implementation isexecutable because all de�nitions from the formalization have been made

4See further on in this section for more detailed descriptions of the notions `dictionary'and `axiomatization'.


explicit. However, a last (fourth) phase may be needed for the constructionof an actually executable program. This program is informal since it hascertain properties that di�er from their formal counterparts. For instance,a program cannot have access to all possible integer values, but only to a�nite amount of integers since programming languages must be �nite.

implementation

(formal)

(formal)

realization

specificationvalidation

formalizationdescription

(informal)

program

(informal)

programming

testing

refinement

verification

Figure 3.1: Implementing while using a formal-speci�cation language

The set of guidelines for formalization that was mentioned above consistsamong other things of a division of the formalization in three parts:

� a dictionary

� a signature

� an axiomatization

The dictionary is a list of informal descriptions of basic concepts of thedomain. The axioms in the axiomatization stage are based on the descrip-tions from the dictionary. For instance, in De�nition 3.2 we �nd the dic-tionary item for `proper domination'. In the discussion of the formalizationin the chapters about the modules of the formalization we will not giveany dictionary items. The formalization of the dictionary items and theinformal descriptions that are given to explain the formalization have com-pletely replaced the dictionary. Hence, it would be redundant to also givethe dictionary items.

The signature is the �rst step towards formalization. Names (identi�ers)and types are assigned to all the concepts from the dictionary. Identi�ersrefer to individual objects, sorts or functions. Individual objects take asort name as a type. For instance, the object Category is of the sortAtomNameS (atomic feature names, i.e feature names that take an atomic


value) which is a sub-sort of FeatureNameS (feature names). Another sub-sort of FeatureNameS is StructNameS, that is, feature names that take afeature structure as their values. For instance, the feature name Agreementrefers to an object of the sort StructNameS. Its value is a feature structurecontaining one or more of the features Person, Number and Gender. Thesignature given here is represented in the formalization in the following way:

SORT FeatureNameS

SORT AtomNameS <<< FeatureNameS

SORT StructNames <<< FeatureNameS

.

.

.

OBJ Category : AtomNameS

OBJ Person : AtomNameS

OBJ Number : AtomNameS

OBJ Gender : AtomNameS

.

.

.

OBJ Agreement : StructNameS

Functions are of the type:

A1,...,An -> B

where A1,...,An and B are sort names. For instance, LogicalForm isa function (or rather, a predicate) that is of the type TreeS -> BoolS. Atree is correct at LF if all the features that need to be checked are checked.In the formalization this is represented as follows:

FUNC LogicalForm : TreeS -> BoolS

The axiomatization is the formal counterpart of the dictionary. Allthe concepts described in the dictionary are translated into formal axioms.

The formalization process for the speci�cation of the Minimalist Pro-gram started with collecting a list of relevant notions. Then de�nitionsfor the important notions of the theory in natural language were formu-lated. It was not possible to �nd explicit de�nitions for all the notionswe collected. The de�nitions in natural language were translated into theformal-speci�cation language AFSL. The relevant notions were collected ina so-called dictionary. The dictionary contains items consisting of a descrip-tion of a notion in natural language (De�nition 3.2). When the dictionarywas su�ciently worked out, we started on the actual formalization. Theformalization process resulted in the need to reformulate some of the de�-nitions in the dictionary. It also happened that notions were removed from


the dictionary because they turned out to be irrelevant for the formaliza-tion. An example of a notion that has been removed is `branch'. Whiledeveloping the dictionary, the notion `branch' (connection between nodeswith a mother-daughter relation) seemed relevant with respect to trees. Inthe formalization the notion was not applied in any of the functions andtherefore it was removed from the dictionary.

AFSL I conclude this section with a brief description of the languageAFSL. Note that the parts of the formalization that are given in the follow-ing chapters are always described extensively in the accompanying text sothat the description of the language given here will probably be super uous.

Modules are the basic building blocks of the speci�cation-languageAFSL. In a module the names of objects (OBJ), sorts (SORT), sub-sorts(SUBSORT) and functions (FUNC) can be introduced. The introduction of thenames is also known as the signature of the formalization. Below I will givesome examples of name introductions from the formalization.

The object Agreement is de�ned as follows in the formalization:

OBJ Agreement : StructNameS

Agreement is a feature name that takes a feature structure as itsvalue (StructNameS).

De�nition 3.4 shows the name introduction of the sort FeatureValueSand its sub-sorts.

De�nition 3.4

SORT FeatureValueS

SORT AtomS <<< FeatureValueS

SORT FeatureStructS <<< FeatureValueS

<<< means `is a sub-sort of'. Hence, atoms (AtomS) and feature struc-tures (FeatureStructS) are both sorts that are sub-sorts of feature values(FeatureValueS).

The SUBSORT construction is used to de�ne an already introducedsort as a sub-sort. For instance, we could de�ne FeatureValueS fromDe�nition 3.4 as a sub-sort of the sort X by adding the following line tothe formalization:

SUBSORT FeatureValueS <<< X

An example of the introduction of a function name is:


FUNC PossibleValue : FeatureNameS, FeatureValueS -> BoolS

It can either be true or false that a given feature value is a possiblevalue for a given feature name. For instance, `�rst' is not a possible featurevalue for the feature name `number', but it is for the feature name `person'.

Sort names always end with a capital `S' (for sort) in AFSL. The languagecontains seven prede�ned sort names:

� EmptyS: the empty sort

� ObjectS: the sort of all objects (every sort is a sub-sort of ObjectS)

� BoolS: the sort of boolean values

� RealS: the sort of real numbers

� NatS: the sort of natural numbers (including 0). NatS is a sub-sort ofRealS

� StringS: the sort of strings

� CharS: the sort of strings of length 1. CharS is a sub-sort of StringS

AFSL contains two prede�ned function symbols: one for equality (=)and one for inequality (=/=).

Since AFSL is a �rst-order language, we can only quantify over objects(i.e. sort elements). Variables for quanti�cation can be introduced usingthe DECL construction. In De�nition 3.3, repeated below as 3.5, we see anexample of the use of dummies (variables) within an AFSL axiom. Thedummy for the sort NodeS is nd as is indicated in the following line fromthe formalization:

DECL nd : NodeS

Dummies can be extended with numbers (e.g. nd1, nd2) when dum-mies are needed for di�erent objects of the same sort.

De�nition 3.5



Or EXISTS nd3

( nd1 = Mother nd3


)


In De�nition 3.6 we �nd the �rst part of the parameterized moduleFeatureNameM. If this module is imported in another module in thefollowing way:

IMPORT FeatureNameM [Name]

we dispose of all the properties that are assigned to the parameterName in the module FeatureNameM. But which properties are assigned toName?

� Name is an object of the sort FeatureNameS (feature names)

� the sort ValueS[Name] is a sub-sort of FeatureValueS (feature val-ues). ValueS[Name] is the set of possible feature values for the featurename Name. For instance, the possible values for the feature name`number' are `singular' and `plural'

� the sort ValueS[Name] inherits the properties of sorts as described inthe module SortM

De�nition 3.6

MODULE FeatureNameM [Name]

OBJ Name : FeatureNameS

SORT ValueS[Name] <<< FeatureValueS

IMPORT SortM[ValueS[Name]]

.

.

.

As we see in De�nition 3.6, not only modules but also names (of objects,sorts as well as functions) can be parameterized. This is very useful incases as the following:

FUNC Value[Name] : FeatureStructS -> PARTIAL�ValueS[Name]

Value[Name] is a function from feature structures to values. In otherwords, if we want to know the value of a given feature name (Name) in agiven feature structure, the value that is yielded has to be a possible valuefor the given feature name. The PARTIAL construction indicates that notevery feature structure will always yield a feature value for a given featurename. The reason for this is the fact that not every feature name is presentin every feature structure. In fact, a feature structure can even be empty.


3.3 Verb movement

In this section I will describe a version of the Minimalist Program that wasdeveloped by Zwart [Zwa97]. This version is a combination of Chomsky's1993 version of the Minimalist Program (cf. [Cho93]), Chomsky's 1995version of the Minimalist Program (cf. [Cho95]), and some of Zwart's newideas that enable the proper description of verb movement in Germaniclanguages such as Dutch and German, that show an asymmetry with respectto the position of the �nite verb between main and subordinate clauses.

Example 3.2 shows that in subordinate clauses (a), the �nal verb appearsto the right of the subject and the direct object. In main clauses (b) on theother hand, the �nal verb appears in between the subject and the directobject.

Example 3.2

(a) dat de hond een bal vindt(that the dog a ball �nds)that the dog �nds a ball

(b) De hond vindt een balThe dog �nds a ball

This asymmetry is not straightforward for the Minimalist Program.Word order di�erences between languages are dealt with by the strong/weakparameter, but construction-speci�c word order di�erences must be ex-plained in another way. Zwart [Zwa97] provides such an explanation.

The most striking changes that Zwart introduces in relation to Chom-sky's 1993 version (of the Minimalist Program as described in Chapter 1)mainly concern feature checking and movement.

In Chomsky's 1993 version of the Minimalist Program, LF was reachedwhen all lexical constituents of a given sentence had checked all their for-mal features (such as case and tense). In Chomsky's 1995 version andin Zwart's framework functional constituents have to attract lexical con-stituents. Hence, the focus at LF switches from lexical to functional heads.A tree is an LF-representation when all functional constituents it containshave checked all their features.5

Chomsky [Cho95, Page 230] considers lexical items to be bundles of three

5This switch of focus is mainly made for reasons having to do with the principle ofGreed. This principle says that elements may only move in order to satisfy their ownfeature checking requirements. If we change the focus from lexical elements to functionalelements the principle changes accordingly: Elements may only attract other elements tosatisfy their own feature checking requirements. Hence, not the moving node but insteadthe attracting node determines when movement is needed. See [Cho95, Page 294�] and[Zwa97, Page 184] for details.

3.3. VERB MOVEMENT 55

di�erent types of features: formal (or syntactic or in ectional) features, se-mantic features and phonological features. In Chomsky's 1993 version asdescribed in Chapter 1 this distinction was not (explicitly) made. The for-mal features are the only features that have to be checked. Therefore, itwould be most natural from a minimalist point of view that only formalfeatures move. However, Chomsky [Cho95, Page 262] assumes that isolatedformal features are uninterpretable at PF. For instance, PF cannot inter-pret an isolated Wh-feature of an interrogative word. It needs the wholeconstituent (e.g. whose car), and this constituent contains more than just aWh-feature. Therefore semantic and phonological features must move alongwith the formal features.

Zwart applies an approach where phonological features are added tolexical items only after the syntactic derivation has been completed. Thisapproach is called postlexicalism (introduced as Distributed Morphology byHalle and Marantz [HM93]). Before the derivation, a universal lexicon isconsulted with only semantic and syntactic informationabout lexical items.6

After the derivation, more speci�cally at PF, a language-speci�c lexicon isconsulted to �nd the phonological features of a given lexical item on thebasis of its semantic and formal features. A consequence of the postlexicalistapproach is that features cannot be deleted after they are checked since thesyntactic information they contain, for instance that a given lexical item is�rst person singular, is needed at PF to retrieve the corresponding lexicalitem in the language-speci�c lexicon (see also Chapter 6). Note that thestrong/weak parameter still determines the moment of Spell-Out and so thePF positions of lexical constituents.

The idea that feature checking always implies deletion of features wasintroduced by Chomsky [Cho93] (see Chapter 1). Chomsky assumed thatformal features cannot be interpreted at LF and therefore these featureshad to be deleted in the course of the derivation. However, in the descrip-tion of the 1995 version of the Minimalist Program [Cho95, Page 277�],Chomsky concludes that some formal features, namely the agreement andWh-features of the noun and categorial features in general, are interpretedat LF. Hence, not all formal features are considered to be uninterpretable atLF and therefore not all formal features need to be deleted when checked.

Since the postlexicalist approach Zwart proposes is irreconcilable withthe deletion of any formal features in the course of the derivation, Zwart[Zwa97, Page 186] is forced to modify the notion of interpretability. Heproposes that a functional constituent XP is interpretable if its label con-tains only formal features that are checked by the lexical constituents that

6This fact implies that the strong/weak parameter is not represented in the lexicon.The lexicon used during the derivation is universal and therefore it cannot be used toexpress word order di�erences between languages. In Chapter 9 we will see that I formu-lated this parameter separately.


moved to XP for feature checking. Also overt movement (i.e. movementbefore Spell-Out) is driven by this `proper pairing condition' according toZwart [Zwa97, Page188], but, of course, the moment of Spell-Out is stilldetermined by the weak/strong parameter [Zwa97, Page 187].

Zwart introduces the notion `LC-features' (lexical-categorial features).The notion `LC-features' covers semantic and categorial features (such asnoun and verb). Zwart claims that LC-features only have to move alongwith the formal features in their movements if this is required by PF. Aswe saw above, isolated formal features are uninterpretable at PF.

LC-features of a given lexical constituent do not have to follow the mov-ing formal features, provided that the PF-position of this lexical constituentalready contains LC-features of another lexical constituent. If movement ofLC-features is required this is called Last Resort movement. The Examples3.3 and 3.4 respectively show a sentence where Last Resort movement is notrequired and a sentence where Last Resort movement is required.

Example 3.3 shows a tree where the LC-features of the �nal verb stay inits position of lexical insertion. The highest position of its chain with strongfeatures (the head of CP), i.e. the PF-position, contains the LC-features ofthe lexical item dat (that). Therefore PF does not require the LC-featuresof the verb to move along with its formal features.

Example 3.3

CP

C

C AgrSP

ek C DP AgrS

datl de hondi

ek TP

ei T

ek AgrOP

DP AgrO

de balj

ek VP

ei V

V ej

vindtk

3.4. THE FORMALIZATION 57

Zwart assumes that subject-initial main clauses do not necessarily con-tain a CP (see Example 3.4). The head of AgrSP becomes the PF-positionof the verb, because this is the highest position in its chain with strongfeatures. As the head of AgrS does not contain any LC-features of anotherlexical item the LC-features have to move along with the formal features.Therefore the �nal verb is spelled out in the head of AgrSP in main clauses.

Example 3.4

AgrSP

DP AgrS

de hondi

AgrS TP

T AgrS ei T

AgrO T ek AgrOP

V AgrO DP AgrO

vindtk de balj

ek VP

ei V

ek ej

Summarizing, Zwart introduces an economical kind of movement wherephonological features are never involved in movement, while LC-features areonly involved in movement as a Last Resort. Zwart's approach enables us toderive a di�erent word order for subject-initial main clauses and subordinateclauses by introducing Last Resort movement of LC-features for sentenceswhere lexical constituents at PF occur without LC-features. Last Resortmovement is necessary because isolated formal features are uninterpretableat PF.

3.4 The formalization

The formalization described in the Chapters 4 through 9 consists of two sep-arate parts, which have a great deal in common. The �rst part formalizesthe ideas of Chomsky's 1993 framework [Cho93] as described in Chapter 1.As was mentioned before, this framework does not properly describe verbmovement in Germanic languages such as Dutch and German. Therefore Idecided to make a formalization of Zwart's framework [Zwa97], as described


in the previous section, which does give a proper description of verb move-ment in Dutch. In the following chapters I only give separate descriptionsof the two frameworks if there are signi�cant di�erences. In principle onlythe formalization of Zwart's framework is discussed.

The formalization described here is not a procedural representation ofwhat Chomsky calls `the computational system'. I consider the computa-tional system to be a declarative system which represents linguistic compe-tence, that is, a grammar. On this declarative or representational systemone could base procedural systems such as parsers and generators.

The formalization described here has a lot in common with Brody'sLexico-Logical Form [Bro95].7 Brody's framework is non-derivational. Heargues that the Minimalist Program is redundant in having both move-ment derivations and chains representing movements and provides evidenceagainst movement derivations. A radically minimalist framework withoutderivations is sketched, where LF is the only level of representation. Hence,LF is the only syntactic level where conditions on representations, such asthe principle of Full Interpretation, can hold.8 According to Brody, theLF-to-PF mapping is not syntactic but purely phonological. Hence, Brodymaintains PF as an interface level but LF is the only interface level which isconsidered to be a level of representation. In Brody's framework lexical in-put is not related with the interface levels through a derivation: the lexiconand the semantic interpretation rules can access the same interface whichis called Lexico-Logical Form (LLF).

Brody's ideas relate to the formalization in the following way. The for-malization presented here de�nes conditions on LF-trees. The system canjudge whether a tree is a correct LF-tree or not. LF-trees can be consid-ered to be the trees produced in the �nal stage of the derivation, whereall features that need checking are checked. In the LF-tree all movementsof lexical constituents (from their position of lexical insertion to their LF-positions) are visualized by chains. The PF-representation, which is a listof words representing a sentence, can be derived from a correct LF-tree by�nding the highest position with strong features in a chain.

Cornell [Cor97, Page 26] de�nes PF in the same way and notes that thede�nition of PF only can be put representationally, not derivationally sinceit is based on completed chains.9 To determine the PF-position of a chain

7For representational versions of Government and Binding Theory see [Kos87] and[Riz90].

8Note that Chomsky [Cho93] considers LF and PF to be the only levels of represen-tation.

9Cornell also notes that to de�ne the PF-position as the upper strong position of thechain is not completely correct. Chomsky forbids the occurrence of strong features in thecovert component. Cornell suggests to add the requirement that a chain should consistof a `continuously strong `pre�x' followed by a continuously weak `su�x', although hedoes not apply this idea.


the whole chain needs to be �nished. A strong position is not automaticallythe PF-position of a chain since a chain can contain more than one strongposition, and there is only one PF-position per chain. Hence, the PF-position of a chain cannot be determined in the course of a derivation. Alsowithin a derivational approach to the Minimalist Program the PF-positionof chains must be determined representationally.

Cornell [Cor97] argues that both derivational and representational ap-proaches to the Minimalist Program have their value for the development ofthe �eld: derivational minimalism can provide the proof theory whereas rep-resentational minimalism can provide the model theory. Hence, accordingto Cornell, the merit of a representational approach can be the elucida-tion of syntactic structures. Derivational approaches do not do this: theyonly produce a �nal LF-PF pair. Note that Cornell's system is based on aderivational system developed by Stabler [Sta96].

The objective of the formalization project described here was to spec-ify the basic ideas of the Minimalist Program. Only a few basic types ofsentences in Dutch are dealt with:

� declarative main clauses: both transitive and intransitive (e.g. Wim

believes Tony respectively Wim speaks.)

� subordinate clauses (e.g. that Wim believes Tony)

� Wh-questions: questions starting with an interrogative word (e.g.Who believes Tony?)

� yes/no-questions: questions which can be answered with either `yes'or `no' (e.g. Does Wim believe Tony?)

The choice to represent linguistic competence as a declarative systemresulted in the fact that the operations Merge and Move have not beenformalized. The system judges completed derivation trees and does nothave any knowledge about how to construct a derivation tree.

During the formalization process the domain has been divided into sixmodules: trees, feature structures, the lexicon, X-Theory, movement andinterfaces. All the modules are discussed in detail in separate chapters.10

The content of the modules is brie y summarized in this section.

� Chapter 4: the module about trees contains basic knowledge aboutderivation trees: what is the number of mothers and daughters a nodecan have, which functions can apply to nodes etc.

� Chapter 5: the feature structure module outlines which feature names,feature values and feature structures occur in the Minimalist Program.

10See also [VS96] for a description of an earlier version of the formalization.


Furthermore, operations on feature structures such as feature checkingare de�ned.

� Chapter 6: what is the character and the format of the lexicon andhow is it integrated in the rest of the theory?

� Chapter 7: the module about X-Theory not only speci�es X-rules but,for instance, also the position of speci�ers, heads and adjuncts withina projection (XP).

� Chapter 8: the chain module describes the chains that are allowed bythe Minimalist Program. As we saw before movement is connectedwith feature checking in the Minimalist Program. Therefore featuresplay an important role in this module.

� Chapter 9: the interface module speci�es a function to determinewhether a tree is a correct representation at the interface level LF.Furthermore, a function is provided to deduce the PF-representationof a sentence from an LF-tree. A PF-representation contains not onlyphonological information about all the lexical items that occur in agiven sentence; it also represents all the lexical items in the order inwhich we read or hear them.

The formalization described here is validated by an implementation inProlog. The implementation will not be discussed in the following chapterssince the translation from AFSL to Prolog was mostly very straightforward.Furthermore I assume that the formalization in AFSL will be easier to graspfor readers without a background in programming.

Chapter 4

Trees

4.1 Introduction

The �rst module of the formalization (TreeM) contains a description of thebare structure of minimalist trees and subtrees of minimalist trees. Fur-thermore, it contains some functions on trees and nodes.1

In the Minimalist Program it is assumed that trees are binary branching,which implies that a node has at most two daughters. Furthermore it isassumed that the nodes of a tree contain features (see also Chapter 5).However, there are four exceptional kinds of nodes that do not seem tocontain any features. These four types of empty nodes are described in thefollowing paragraphs.2

The �rst kind of empty node is radically empty. It contains a completelyempty feature structure. For instance, intransitive verbs do not select com-plements. Therefore the label belonging to the sister of the verb is an emptyfeature structure and consequently the sister of the verb is an empty node.Because of the possibility that nodes are empty, trees can always be binarybranching. If a head does not select a complement, the mother of the headstill has two daughters, although one of the daughters is an empty node.

A second kind of empty node occurs when a head does not have anyphonological content. For example, in the DP girls as opposed to the DP the

girls the head of the DP is empty. This is a kind of emptiness that is di�erentfrom radical emptiness because here the feature structure connected withthe head is not empty. It contains, for instance, a category feature.

A third kind of empty node is the one that is created by Merge and

1See also [HU79, BGMV93, BRVS95].2Note that PRO [Cho81, CL93] and pro [Cho82] are left out of consideration since

they are of no importance for the fragment formalized here.

61

62 CHAPTER 4. TREES

Move as described in Section 1.6. This type does not occur in the repre-sentationally oriented formalization described in this work because it onlydescribes the result of the operations Merge and Move, and not how thoseoperations are performed. The stage where the empty node is created isan intermediate stage. Therefore the empty node is not visible in the �nalresults of Merge and Move.

A fourth kind of empty nodes is a trace. Traces are left behind inpositions fromwhich a constituent moved. In the formalization it is assumedthat traces are in fact copies of the moved constituent.3 This implies thata movement within a tree is represented by two identical copies of the sameconstituent in di�erent positions. Furthermore, we will see that there is alink between the positions where the two copies occur.

It is essential for the formalization that copies instead of traces are ap-plied to express movement, since we want to specify the characteristics ofthe �nal result of a derivation. In the representational approach chosen herethere must be a possibility to dispose over the feature structure of a lexicalconstituent in every position of a chain, as feature checking applies locallywithin functional projections. Feature checking is the matching of the fea-tures of a moving lexical constituent with the features of the functionalprojection where it lands. Since traces just are empty nodes without anyfeatures they are not appropriate for the local operation of feature checking.Copies, on the other hand, are full- edged constituents, consisting of nodeslabelled with features.


Complete trees In De�nition 4.1, we see the de�nition of complete trees(ComplTreeS). Later on in this chapter I will give the de�nition of subtrees(TreeS).

De�nition 4.1

IMPORT FeaturesM

DECL fstruct : FeatureStructS

SORT DirectionS

SORT AddressS === ListS[DirectionS]

OBJ Left : DirectionS

OBJ Right : DirectionS

3Cf. [Cho93, Page 34-35].


AXIOM Elems[DirectionS] = Set(Left,Right)

DECL dir : DirectionS

DECL addr : AddressS

SORT ComplTreeS

FUNC Addresses : ComplTreeS -> FiniteSetS[AddressS]

FUNC Features : ComplTreeS, AddressS -> PARTIAL~FeatureStructS

FUNC ConnectionTarget : ComplTreeS, AddressS -> PARTIAL~AddressS

DECL ctr : ComplTreeS

AXIOM FORALL addr

( Addresses ctr1 = Addresses ctr2

And Features(ctr1, addr) = Features(ctr2, addr)

And ConnectionTarget(ctr1, addr) = ConnectionTarget(ctr2, addr)

)

==> ctr1 = ctr2

In the �rst line of De�nition 4.1, the module FeaturesM (see Chapter 5)is imported. Therefore, the variable declaration of fstruct (next line) canbe given without de�ning the sort FeatureStructS.

Next, a de�nition of addresses to localize nodes in trees is given. Ad-dresses (AddressS) are de�ned as lists of directions (ListS[DirectionS]).Directions are of a sort (DirectionS) for which two objects are de�ned:Left and Right. These two directions are the only objects in the set ofdirections:

AXIOM Elems[DirectionS] = Set(Left,Right)

The reason that there are only two directions lies in the fact thattrees are binary branching in the Minimalist Program. In Example 4.1 theaddress of B is [Left] and the address of G is [Left,Right,Right].

Example 4.1

A

B C

D E

F G

To de�ne complete trees we need three characteristic functions:Addresses, Features and ConnectionTarget (see De�nition 4.1). These

64 CHAPTER 4. TREES

functions are characteristic for complete trees in the sense that, if two com-plete trees ctr1 and ctr2 (which are of the sort ComplTreeS) yield equalvalues for all three functions, we can say that ctr1 and ctr2 are equal.

The function Addresses takes a complete tree and yields a �nite setof addresses (FiniteSetS[AddressS]). The set of addresses must be �nitebecause trees are �nite in the Minimalist Program and therefore trees havea �nite number of nodes (which implies a �nite set of addresses of nodes).

The function Features takes a complete tree and an address andyields a feature structure, which is the feature structure associated withthe node that is indicated by the given address. The function is partial(PARTIAL~FeatureStructS) because it does not always yield a value: it isimpossible to name the features of a node at an address which does notexist in the given tree, and furthermore not all nodes contain features, aswe will see further on in this chapter.

The function ConnectionTarget expresses the existence of connectionsbetween nodes without a mother-daughter relation within trees. This func-tion is required to represent chains within derivation trees, that is, a node Xis the connection target of a node Y if and only if Y is a trace of X. There-fore the (complete) trees described in this module can be considered to bedirected graphs. They are speci�ed in such a way that they do not onlycontain arrows from mothers to daughters; it is also possible that two nodeswhich do not have a mother-daughter relation are linked with an arrow.The connection target of a node with a given address in a given tree is anode with another address in the same tree. Hence, the �rst address in thefunction de�nition of the function ConnectionTarget indicates the positionwhere the movement starts, and the second address indicates the positionthat the movement targets. I assume that movement is always leftward (seeSection 1.4) so that the �rst address always is to the right of the secondaddress. The function ConnectionTarget is partial since not all addressesin a tree have a connection to another node.

Example 4.2

A

B C

D E F G

H I

Specifying trees as a kind of directed graphs has the advantage that we donot need indexes to indicate traces. A connection between two nodes I and F


is indicated in the root of the subtree (C) which is the smallest subtree whichcontains both I and F (Hence ConnectionTarget(ctr,[Right,Right]) =

[Left], where ctr = C, see Example 4.2).Note that if we want minimalist trees to be real directed graphs we

need to de�ne a mother-of relation instead of a mother-of function plusthe function ConnectionTarget. The correct way to represent the tree inExample 4.2 would then be:

A

B C

D E G

H

F/I

Cutting subtrees As I claimed above, two complete trees are equal ifthey are equal with respect to addresses, features and connections. This iswhat is expressed in the last axiom of De�nition 4.1.

For reasons that will become clear in Chapter 8, we need a functionwhich isolates a subtree from a complete tree. The function declaration ofthis function (Cut) in De�nition 4.2 shows that if we indicate an address ina given complete tree, then the function may yield a second complete tree.This second complete tree is a subtree of the original tree with the nodewith the given address as its root.

Note that subtrees are not always of the sort TreeS which will be dis-cussed later on in this section. A subtree is of the sort ComplTreeS if itsatis�es all the constraints on ComplTreeS concerning features, addressesand connections.

De�nition 4.2

FUNC Cut : ComplTreeS, AddressS -> PARTIAL~ComplTreeS

AXIOM Cut (ctr1, addr1) = ctr2

<=> FORALL addr2, addr3

( addr2 In (Addresses ctr2) = (addr1 ++ addr2) In (Addresses ctr1)

And Features (ctr2, addr2) = Features (ctr1, addr1 ++ addr2)

And ( ConnectionTarget (ctr2, addr2) = addr3

<=> ConnectionTarget (ctr1, addr1 ++ addr2) = addr1 ++ addr3

)

)

66 CHAPTER 4. TREES

There are some constraints on the addresses, features and connections inthe tree (ctr2) that is yielded (see axiom in De�nition 4.2). The addresses,features and connections have to be equal for the original tree (ctr1) andthe tree that is the result of the function (ctr2) in the sense that for eachaddress addr2 in ctr2 we can �nd a corresponding address in ctr1. In thefollowing three paragraphs I will give examples with respect to addresses,features and connections.

If the tree in Example 4.3 is ctr1 and addr1 is [Right], then C is theroot of ctr2, and if addr2 (= [Right,Left] = H) is an address in ctr2, thenthe corresponding address in ctr1 is [Right,Right,Left] (= H), which is aconcatenation (++) of addr1 and addr2.

Example 4.3

A

B C

D E F G

H I

With respect to features, if the tree in Example 4.3 is ctr1 and addr1 is[Right], then C is the root of ctr2, and if addr2 (= [Right,Left] = H) is anaddress in ctr2 with certain features, then the same features can be foundin the corresponding address in ctr1 ([Right,Right,Left] = H), which is aconcatenation (++) of addr1 and addr2.

Regarding connections, if the tree in Example 4.3 is ctr1 and addr1 is[Right], then C is the root of ctr2, and if there is a connection in ctr2

between addr2 (= [Right,Left] = H) and addr (= [Left] = F), then thecorresponding addresses in ctr1 are respectively [Right,Right,Left] (= H)and [Right,Left] (=F), which are both concatenations of addr1 and theoriginal addresses in ctr2. It is impossible to cut a subtree ctr2 out ofctr1 that has a connection to a node outside ctr2. For instance, if thereis a connection from F to E, it is impossible to cut C out of A, since theaddress of E is not expressible from the perspective of C: we only havethe empty list and all di�erent combinations of [Left] and [Right] at ourdisposal. Hence, we have the possibility to refer to addresses that are toolow for ctr2 (for instance, [Left,Left]), but not to refer to addresses thatare above the root of ctr2.

Nodes Nodes are de�ned by the characteristic functions ComplTree andAddress, that is, a node is a part of a given complete tree and it has


an address that determines its position in the tree. Nodes are de�ned inDe�nition 4.3. The �rst axiom de�nes that two nodes nd1 and nd2 are equalif they yield the same values for the function ComplTree and Address. Thesecond axiom de�nes that if addr is an address belonging to the completetree ctr, then there must exist a node nd of which ctr is the complete treeand of which addr is the address.

De�nition 4.3

SORT NodeS

DECL nd : NodeS

FUNC ComplTree : NodeS -> ComplTreeS

FUNC Address : NodeS -> AddressS

AXIOM ComplTree nd1 = ComplTree nd2

And Address nd1 = Address nd2

==> nd1 = nd2

AXIOM addr In (Addresses ctr)

<=> EXISTS nd

( ComplTree nd = ctr

And Address nd = addr

)

Trees The characteristic function of the sort of subtrees (TreeS) is Root.Two subtrees tr1 and tr2 are equal if they have the same root (�rst axiom inDe�nition 4.4). For every tree tr there is a root nd (see second axiom). Notethat the constraints on TreeS are much less stringent than on ComplTreeS.For instance, a subtree of the sort TreeS does not have to contain bothnodes of a connection.

The �nal line of De�nition 4.4 de�nes that there is no di�erence betweennodes (NodeS) and subtrees (TreeS). Hence, all functions that are de�nedfor nodes are also de�ned for subtrees, and the other way around. Thispossibility is applied often in the modules described in the following chap-ters. In the literature some notions are de�ned on nodes while others arede�ned on trees. It is convenient to be able to refer, for instance, to theleft daughter of a node in the former case, and to the left daughter tree(meaning the left daughter of the root of the tree) in the latter case.

De�nition 4.4

SORT TreeS

DECL tr : TreeS

68 CHAPTER 4. TREES

FUNC Root : TreeS -> NodeS

AXIOM Root tr1 = Root tr2

==> tr1 = tr2

AXIOM EXISTS tr (Root tr = nd)

SUBSORT NodeS === TreeS

Some functions on nodes and trees The functions in De�nition 4.5are all based on the functions Address, ComplTree, ConnectionTarget,Cut and/or Features as de�ned above. Note that additional versions of thefunctions ConnectionTarget, Features and Cut are de�ned with di�erentarguments.

The function LeftDaughter is de�ned in the following way: the leftdaughter of a node nd1 is nd2 if and only if the complete tree belongingto nd2 equals the one belonging to nd1 (hence, if nd1 and nd2 are nodesof the same tree), and the address of nd2 is equal to the address of nd1with the direction [Left] added at the end of the list. The de�nition ofRightDaughter is equal to the de�nition of LeftDaughter except that thedirection [Right] is added to the address of nd1.

The function ConnectionTarget de�nes that there is a connection fromthe node nd1 to nd2 if and only if the complete tree belonging to nd2 equalsthe one belonging to nd1 and the address of nd2 is equal to the addressthat is yielded by the function ConnectionTarget when it is applied to thecomplete tree of nd1 and the address of nd1.4

The function Features yields the features of a node nd. The featureof nd are equal to the features that are yielded by the function Features

applied to the complete tree belonging to nd and the address of nd.The function Cut is de�ned in the following way. The result of cutting

the subtree tr1 out of a bigger tree is tr2, if and only if the address oftr2 is an empty list (Nil) and the complete tree of tr2 equals the resultof the function Cut applied to the complete tree of tr1 and the address oftr1 (see also De�nition 4.2). The address of tr2 is an empty list as tr2 isa root. Note that normally roots are nodes, but we de�ne that there is nodi�erence between nodes and trees. Hence, if we want to cut the subtree

4Note that the complete trees belonging to nd1 and nd2 by de�nition need to havethe same features. In the following chapters we will see that this is not problematic forfeature checking in the formalization. In the Minimalist Program features are deletedwhen checked. This implies that two elements in the same chain cannot be associatedwith exactly the same feature structure. In the formalization, features are not deletedwhen checked but instead a `list' is introduced, which indicates which features are checkedat a given point in a chain.


with the root B (tr1) out of the tree in Example 4.1 repeated here as 4.4,then the result tr2 is the tree in Example 4.5.

De�nition 4.5

FUNC LeftDaughter : NodeS -> PARTIAL~NodeS

FUNC RightDaughter : NodeS -> PARTIAL~NodeS

FUNC ConnectionTarget : NodeS -> PARTIAL~NodeS

FUNC Features : NodeS -> FeatureStructS

FUNC Cut : TreeS -> TreeS

AXIOM LeftDaughter nd1 = nd2

<=> ComplTree nd2 = ComplTree nd1

And Address nd2 = (Address nd1) ;; Left

AXIOM RightDaughter nd1 = nd2


And Address nd2 = (Address nd1) ;; Right

AXIOM ConnectionTarget nd1 = nd2


And Address nd2 = ConnectionTarget (ComplTree nd1, Address nd1)

AXIOM Features nd = Features (ComplTree nd, Address nd)

AXIOM Cut tr1 = tr2

<=> Address tr2 = Nil

And ComplTree tr2 = Cut (ComplTree tr1, Address tr1)

SUBSORT NodeS <<< FeatureStructS

Example 4.4

A

B C

D E

F G

Example 4.5

B

D E

F G

70 CHAPTER 4. TREES

The function Mother in De�nition 4.6 shows that the mother of a nodend1 is nd2 if and only if nd1 is one of the daughters of nd2.

The function Sister in De�nition 4.6 shows that the sister of nd1 is nd2if and only if nd1 has a mother, nd1 is not the same node as nd2, and nd1

and nd2 have the same mother.A node nd1 properly dominates nd2 if and only if nd1 is the mother of

nd2, or if there is a node nd3 of which nd1 is the mother and nd3 properlydominates nd2. Hence, B in Example 4.2 properly dominates G becausethere is a node E of which B is the mother and E properly dominates G(because E is the mother of G).

A node nd1 re exively dominates nd2 if and only if nd1 properly dom-inates nd2 or nd1 is the same node as nd2. Hence, a node can re exivelydominate itself, but it cannot properly dominate itself.

The node nd is a node of (NodeOf) the subtree tr if and only if the rootof tr re exively dominates nd.

The function ConnectionSource is based on the functionConnectionTarget speci�ed above. A subtree tr1 is the startingpoint (connection source) of a movement to tr2 if and only if tr2 is thetarget (connection target) of a movement from tr1.

The function IsLeaf de�nes that a node nd is a leaf if and only if it doesnot have any daughters.

The function EmptyLeaf de�nes that a node nd is an empty leaf if andonly if it is a leaf and it does not have a feature structure as a label.

The function NonEmptyLeaf de�nes that a node nd is an empty leaf ifand only if it is a leaf and it does have a feature structure as a label.

De�nition 4.6

FUNC Mother : NodeS -> PARTIAL~NodeS

FUNC Sister : NodeS -> PARTIAL~NodeS

FUNC PropDominates : NodeS, NodeS -> BoolS

FUNC ReflDominates : NodeS, NodeS -> BoolS

FUNC NodeOf : NodeS, TreeS -> BoolS

FUNC ConnectionSource : TreeS -> PARTIAL~TreeS

FUNC IsLeaf : NodeS -> BoolS

FUNC EmptyLeaf : NodeS -> BoolS

FUNC NonEmptyLeaf : NodeS -> BoolS

AXIOM Mother nd1 = nd2

<=> LeftDaughter nd2 = nd1

Or RightDaughter nd2 = nd1

AXIOM Sister nd1 = nd2

<=> Mother nd1 =/= Undef

And nd1 =/= nd2

And Mother nd1 = Mother nd2

4.3. SUMMARY 71



Or EXISTS nd3

( nd1 = Mother nd3


)

AXIOM nd1 ReflDominates nd2

<=> nd1 PropDominates nd2

Or nd1 = nd2

AXIOM nd NodeOf tr

<=> (Root tr) ReflDominates nd

AXIOM ConnectionSource tr1 = tr2

<=> ConnectionTarget tr2 = tr1

AXIOM IsLeaf nd

<=> LeftDaughter nd = Undef

And RightDaughter nd = Undef

AXIOM EmptyLeaf nd

<=> IsLeaf nd

And Features nd = EmptyStruct

AXIOM NonEmptyLeaf nd

<=> IsLeaf nd

And Features nd =/= EmptyStruct

4.3 Summary

In this chapter I discussed notions like tree, subtree and node, plus severalfunctions on nodes and trees. Remarkable is that there are two di�erenttypes of subtrees: those of the sort TreeS and those of the sort ComplTreeS.

For both subtrees of the former and of the latter type holds that twosubtrees are the same if their nodes have the same features and addresses.However, for a subtree ctr of the sort ComplTreeS there is an additionalconstraint: if one of the nodes nd1 of ctr is connected with another nodend2 then nd2 must also be a node of ctr.

The function ConnectionTarget represents connections between nodes.I consider minimalist trees to be a kind of directed graphs. The functionConnectionTarget is used instead of indices to indicate movements withintrees.

The function Cut which cuts subtrees out of trees, always yields subtreesof the sort ComplTreeS. In Chapter 8 we need the function Cut to be able toindicate that the constituents that are linked with each other must be exactcopies. When the function Cut is applied for this objective, it is essentialthat the subtrees that are yielded are subtrees with completed connections.

Chapter 5

Feature structures

The feature structure module outlines which feature names, feature valuesand feature structures occur in the Minimalist Program. Furthermore, oper-ations on feature structures such as checking are de�ned. Many of the ideasdescribed in this module derive from feature-based grammar [Shi86, Joh88].Furthermore, ideas from typed feature logic [Car92] are adopted.

In the minimalist framework ideas about features are not worked outin much detail. The distinction between feature and value is not made byChomsky [Cho93, Cho95]. Examples of what Chomsky calls features are:[nominative], [3 person] and [-human]. Apparently, both combinations of afeature and a value, and isolated values are referred to as features. Zwartdoes distinguish between features and values.1

The de�nition of checking is not made explicit in minimalist work. Thischapter outlines the de�nition of checking that was deduced from the min-imalist literature and from experiments with formalizations and implemen-tations.

In Section 5.1 I will give an introduction to the treatment of featureswithin the minimalist framework. Note that I sometimes refer to the for-malization in the introduction. For instance, when I sum up the featurenames that occur in the Minimalist Program, I add, for the sake of conve-nience, all the feature names that occur in the formalization which do notcorrespond to a feature name from the Minimalist Program. Linguistic mo-tivation for certain choices in the formalization is also given in this section.In Section 5.2 I will discuss the formalization of feature structures.

1See for instance [Zwa97, Page 186-187].

73

74 CHAPTER 5. FEATURE STRUCTURES

5.1 Introduction

Feature structures The notion `feature structure' is not applied in theMinimalist Program. It is assumed that the nodes of a derivation tree maycontain features, also called `feature bundles'. As I noted above in thissection, what is referred to as a feature is actually a feature-value pair. Inthe next two sections we will see that operations on features, such as featurechecking, require that the features belonging to a node can be treated asa unit. Therefore the features belonging to a node will be referred to as`feature structures'.

Feature names and feature values Within the minimalist theory themost well-known feature names are [person], [number], [gender], [case],[tense], [category] and [wh]. All the feature names, except (maybe) for[wh] speak for themselves, especially when their possible values will be pre-sented later on in this section. With the feature name [wh] we can indicatewhether a word is an interrogative word or not. The [wh] feature forces, forinstance, interrogative words like wie (who) to move to the sentence-initialposition (i.e. the speci�er of CP) in sentences such as the one in Example5.1.

Example 5.1

Wie ziet hij?(Who sees he?)Who does he see?

Furthermore, the formalization contains a number of feature names thatare less common or not common at all within the minimalist framework:[word], [sememe], [inversion], [compcat], [speccat] and [determiner].

The feature [word] represents the phonological information of a lexicalitem. The feature takes an in ected word as its value, for instance walks,which is an in ected form of the verb to walk. Hence, the feature [word]is a simpli�cation of the phonological features of a lexical item. The exactcharacter of the phonological features needed within the minimalist frame-work is not worked out yet. Therefore I applied this simpli�ed version ofphonological features.

The feature [sememe] represents the semantic information of a lexicalitem. The feature takes the stem of a word as its value, for instance walk

which is the stem (i.e. unin ected form) of the verb to walk. The MinimalistProgram is not explicit about semantic features and therefore I use the fea-ture name [sememe] to replace semantic features. A more precise approachto semantic features is not required for the formalization. Of course LF

5.1. INTRODUCTION 75

is the interface where semantic features are needed, but as the role of thisinterface has not yet been studied very intensively within the minimalistframework, this aspect of semantic features falls outside the realm of theformalization project described here.2

The feature [inversion] enables movement of the verb to the head of theCP, to obtain the right order for yes/no-questions. In Example 5.2 we seethat in yes/no-questions in Dutch, the �nite verb moves to a sentence-initialposition. The in ection of the inverted form (koop) of the verb that is re-quired in yes/no-questions is di�erent from the in ection of the non-invertedform (koopt). Hence, in the lexicon, koop and koopt are two di�erent items,with di�erent values for the feature [inversion]. The rest of the features,such as [tense] are equal for both lexical items. The analysis of inversiondescribed here is a simpli�cation of Zwart's analysis of inversion (cf. [Zwa97,Page 245�]).

Example 5.2

(a) Jij koopt het boekYou buy the book

(b) Koop jij het boek?(Buy you the book?)Do you buy the book?

The features [compcat] and [speccat] indicate respectively the category ofthe complement and speci�er that a given head may select. It is also possiblethat no complement or speci�er is selected. Note that these features are notapplied in the Minimalist Program. In Chapter 7 I will go deeper into thenecessity of the features [compcat] and [speccat].

The feature [determiner] is also a feature which does not occur in theminimalist framework. I apply it to indicate whether a noun needs a deter-miner or not. For instance, singular count nouns like meisje (girl) need adeterminer, while personal pronouns like wie (who) may not occur with adeterminer.

In the following table, all the feature names mentioned in this paragraphso far are summed up together with the possible values they received in theformalization:

feature name feature value

[person] �rst, second, third[number] singular, plural[gender] masculine, feminine, neuter[case] nominative, genitive, accusative, dative

2Cf. [Cor96, Page 3], [Cor97, Page 7] and [Sta96, Page 105] for comparable approachesto semantic and phonological features.


feature name feature value

[tense] past, present[category] N(oun), V(erb), D(eterminer),

C(omplementizer), Agrs, Agro, T(ense)[wh] yes, no[word] `string of characters'[sememe] `string of characters'[inversion] yes, no[compcat] N(oun), V(erb), D(eterminer),

C(omplementizer), Agrs, Agro, T(ense)[speccat] D(eterminer)

Besides the atomic feature names (i.e. feature names that take atomsas their values), the formalization contains three complex feature names.Complex feature names take a feature structure as their value. The threecomplex feature names in our version of the Minimalist Program are: [agree-ment], [object] and [subject].

The feature name [agreement] takes a feature structure as its value thatmay contain [person], [number] and [gender] features.

The complex feature names [subject] and [object] represent the featuresof the subject and the object of the verb respectively. The complex featurename [object] may contain [case] and [agreement] features. The complexfeature name [subject] may only contain an [agreement] feature.3

The use of the [object] feature may not be self-evident. In the MinimalistProgram it is assumed that there is both subject and object agreement,although in most languages object agreement is commonly satis�ed becausethe agreement features of the object, as opposed to the features of thesubject, do not in uence the morphology of the verb. An example of alanguage with object agreement is Mohawk (cf. Baker [Bak96]).

Operations on feature structures The most important operation onfeature structures is feature checking. Feature checking is applied when aconstituent moves in the Minimalist Program. Moreover, a constituent mayonly move when it can check one or more formal features (contained in afeature structure) in the position it moves to. In our non-derivational versionof the Minimalist Program this is put in the following way: constituents thathave a connection with a lower constituent in the same tree must check theirfeatures against the head of the functional projection they are part of. The�rst argument of the function Check, fstruct1, corresponds to the headof the functional projection; the second argument, fstruct2, correspondsto the constituent which is connected to a lower constituent. fstruct2

3The feature name [subject] may not contain a [case] feature since it occurs withinfeature structuresdescribing verbs, and verbs do not assign case to the subject. Accordingto the Minimalist Program [Cho95, Page 174], the verbs assigns case to the object whilethe functional head T assigns case to the subject. See also Chapter 8.


contains at least as many feature-value pairs as fstruct1.For instance, fstruct2 is a feature structure that contains all formal

features of the verb loopt (walks) that adjoins to AgrS in Example 5.3.The feature structure fstruct2 is represented in Example 5.4. fstruct1 isthe feature structure containing the formal features of one of the functionalprojections, say AgrSP, where the verb loopt adjoins to, to check its features.The feature structure fstruct1 is represented in Example 5.5. As not allfeatures of fstruct2 are always checked in the same functional projection,it is clear that fstruct2 must contain as many features as fstruct1 ormore. In the case of Example 5.3 fstruct2, associated with V, containsmore features than fstruct1, associated with AgrS.

Example 5.3

AgrSP

Spec AgrS

AgrS TP

T AgrS

AgrO T

V AgrO

loopt

Example 5.4

266666666664

subject

266664agreement

264person third

number singular

gender masculine

375

case nominative

377775

tense present

inversion no

377777777775

Example 5.5

2664subject

2664agreement

264person third

number singular

gender masculine

375

3775

3775


Chomsky's treatment of Wh-movement in the Minimalist Program (cf.[Cho93]) played an important role in determining how to formalize checking.According to Chomsky, Wh-words have Wh-features while other nouns donot. Wh-words have to move higher than other nouns because they needto check this extra feature (in the speci�er of CP).4 In Example 5.6 we seethat the subject DP moves to the speci�er of CP (to check its Wh-feature).

In the formalization we allow that all feature structures belonging towords of the category noun may have a Wh-feature. Hence, the lexicalitem referring to Wh-words contains the feature-value pair WhWord Yes.Non-Wh-nouns, on the other hand, should not contain a Wh-feature. Ifwe assume that checking is a uni�cation operation (see Appendix) thenthe feature could check with any possible value (either Yes or No), sincethe uni�cation of two feature structures fstruct1 and fstruct2 yields(if it exists) the smallest feature structure fstruct3 that is subsumed byboth fstruct1 and fstruct2. A feature structure A subsumes anotherfeature structure B if B contains all the feature-value pairs that A containsand possibly more (cf. [Shi86]). fstruct1 and fstruct2 unify if featurenames that occur in both feature structures have compatible feature values.If a feature name only occurs in one of the two feature structures thatare uni�ed, this feature name (together with its feature value) is part offstruct3.

Yes is de�nitely the wrong value for a non-Wh-noun. Therefore we couldchoose an approach in which all non-Wh-words get the value No for the fea-ture WhWord. But this approach also causes problems. The idea behindchecking in Chomsky's framework is namely that if a certain formal featureis present, it must be checked. Hence, a constituent with a feature-valuepair WhWord No should check its features. But movement to the speci�er ofCP is only desirable for DPs containing a Wh-word, not for DPs contain-ing a non-Wh-word. It is of course possible to de�ne that all in ectionalfeatures except for WhWord No have to be checked, but making checking anasymmetric variant of uni�cation is more elegant. In that case Yes can beconsidered the only possible value for the feature WhWord. If the feature thenis not present in a feature structure belonging to a non-Wh-word this reallymeans that the word does not have a WhWord feature. Hence, no featureneeds to be checked in the speci�er of CP.

The formalization of Zwart's framework is di�erent. As lexical heads nolonger need to check all their features, it is possible to introduce a secondvalue for the Wh-feature. Besides the value Yes we can introduce the valueNo since the feature-value pair WhWord No may remain unchecked withoutcausing the derivation to crash. Nevertheless, we maintain the de�nition ofchecking as it was developed for Chomsky's framework. Namely, in Zwart's

4Cf. [Cho93].


framework we need to verify that all features of the functional heads arechecked before LF. This can be done by requiring the moved element tocontain at least the features contained by the functional head serving as alanding site.

Example 5.6

CP

DP C

whoi

ek AgrSP

ei AgrS

AgrS TP

T AgrS ei T

AgrO T ek AgrOP

V AgrO ej AgrO

foundk

ek VP

ei V

ek DP

the ballj

Furthermore the feature structure module contains two operations thatcan modify a given feature structure: the operations Remove and Keep.These two operation take a feature structure fstruct1 and a set of featurenames nset as their argument and yield a new feature structure fstruct2

by removing or keeping nset from fstruct1. We will come across theseoperations several times in the coming chapters. For instance, the operationKeep is used to get rid of all the non-formal (i.e. phonological and semantic)features in a feature structures if we want to check the formal features of alexical constituent against those of a functional constituent.


Feature structures In the Minimalist Program it is assumed that thenodes of derivation trees may contain feature-value pairs, often simply calledfeatures. I assume that with each node of the �nal LF-tree a feature struc-ture is associated. A feature structure is a set of zero or more feature-value


pairs. In the Minimalist Program the notion `feature structure' is not ascommon as it is in other linguistic frameworks such as feature-based gram-mar [Shi86, Joh88]. However, feature structures are applied in the formal-ization, because, if the feature-value pairs of a node are treated as a unit,it is easier to refer to the features of a node. Furthermore, this approachfacilitates de�ning operations on the features of a node, such as featurechecking.

In the formalization, feature structures are de�ned as `functions fromfeature names to feature values', as we see in De�nition 5.1. Thereare three sorts de�ned in this example: FeatureNameS (feature names),FeatureValueS (feature values) and FeatureStructS (feature structures).Feature structures are de�ned as a sub-sort of feature values, which meansthat complex feature values are allowed (see also Section 5.1). The functionValue is a function from feature structures and feature names to featurevalues. This means that given a feature structure and a feature name, thefunction yields the feature value belonging to the feature name in the givenfeature structure. The function is partial (PARTIAL) because not every fea-ture structure contains every possible feature name. It is even possible thata feature structure does not contain any feature name at all. In this casethe feature structure is an empty feature structure (see also Section 4.1).

The fact that Value is a function implies that it is impossible that afeature name can occur more than once per feature structure with di�erentfeature values, since functions may only yield one result.

The function Value is crucial to the formalization of equality in featurestructures: if for all feature names name in the feature structures fstruct1and fstruct2 applies that the feature values val are equal (i.e. of thesame value), then fstruct1 and fstruct2 are equal. The feature structuresfstruct1 and fstruct2 do not have to be in the same order in order for thestructures to be equal. The only requirement is that they contain exactlythe same feature-value pairs. If fstruct1 does not contain a given featurename name, then fstruct2 may not contain the feature name name either(i.e. partiality).

De�nition 5.1

SORT FeatureNameS

SORT FeatureValueS


DECL name : FeatureNameS

DECL val : FeatureValueS


FUNC Value : FeatureStructS, FeatureNameS -> PARTIAL~FeatureValueS


AXIOM FORALL name

( Value (fstruct1, name) = Value (fstruct2, name) )

==> fstruct1 = fstruct2

Feature names and feature values The feature module of the formal-ization contains feature names, among other things. Some of those takeatomic values, namely: Category, Person, Number, Case, Gender, WhWord,Determiner, CompCat, SpecCat, Tense, Inversion, Sememe and Word.

Atomic feature names are referred to as AtomNameS in the formalization.De�nition 5.2 shows that AtomNameS are a sub-sort (<<<) of FeatureNameS.

De�nition 5.2

SORT FeatureNameS

SORT AtomNameS <<< FeatureNameS

SORT StructNameS <<< FeatureNameS

The rest of the feature names (Agreement, Subject and Object) takecomplex values (that is, feature values that are feature structures). Complexfeature names are referred to as StructNameS in the formalization. De�ni-tion 5.2 shows that StructNameS is a sub-sort (<<<) of FeatureNameS.

Together with feature values, feature names build feature-value pairs. Inthe formalization a type is assigned to each feature value.5 For example, allperson values are of the type ValueS[Person]. In this way it is impossibleto assign, for instance, a number value such as Plural to the feature namePerson, as number values are of the type ValueS[Number] and Person

needs a value of the type ValueS[Person]. As we saw in Section 3.2, indi-vidual objects such as the feature value Plural take a sort name as a type:ValueS[Number] in the case of Plural (OBJ Plural : ValueS[Number]).

In the formalization, feature values are of the sort FeatureValueS (seeDe�nition 5.3). This sort has two sub-sorts: AtomS and FeatureStructS.The former sub-sort represents atomic feature values (such as Plural); thelatter represents complex feature values (i.e. feature values that are featurestructures, such as the value of the feature name Agreement, which is afeature structure that may contain person, number and gender features).

De�nition 5.3

SORT FeatureValueS

SORT AtomS <<< FeatureValueS


5Cf. [Car92].


Complex values are not only assigned a type, for instanceValueS[Agreement]. For complex values it is also speci�ed which typesof feature-value pairs can form part of the feature structure.6 A featurestructure that serves as a value for the feature Agreement contains zeroor more of the features Person, Number or Gender as its value. A featurestructure that serves as a value for Subject or Object contains zero ormore of the features Agreement or Case. Note that not all of the possiblefeature names for a certain type of feature structure must be present ineach occurrence of that type. Hence, a feature structure does not need tobe well-typed in Carpenter's sense [Car92, Page 88]. For example, the func-tional projection T has a Subject feature which has a value only containinga Case feature as only the case feature of the subject must be checked here.Hence, the subject agreement features of T are underspeci�ed.

For each type of lexical item (i.e. noun, verb etc.) it is also speci�edwhich type of feature-value pairs it may contain. For example, a featurestructure that represents a lexical item describing a noun, contains di�erentfeatures from a feature structure belonging to a complementizer. Theabove is summarized in the following table:

complex feature name feature names

Agreement Person, Number, GenderSubject Agreement, CaseObject Agreement, Case

The following table shows which features-value pairs a given lexicalitem may contain:

Lexical item Features

N Word, Sememe, Agreement,Case, Determiner, WhWord,CompCat and SpecCat

D Word, Sememe, Agreement,Case, Determiner, WhWord,CompCat and SpecCat

V Word, Sememe, Subject,Object, CompCat, SpecCat,Inversion and Tense

AgrO Object, CompCat and SpecCatAgrS Subject, CompCat and SpecCatT Subject, Tense, CompCat and SpecCatC Word, Sememe, Inversion, Tense,

WhWord, Agreement, CompCat and SpecCat

In Chapter 8 I will argue why certain lexical items contain certain fea-tures.

6Cf. type signature [Car92].


Operations on feature structures The feature module de�nes an im-portant operation on feature structures, namely Check. Check de�nes theminimalist operation feature checking. Furthermore, two less central oper-ations Remove and Keep are de�ned here.

The operation Check is a boolean function that checks whether twofeature structures, fstruct1 and fstruct2, match.7 The feature struc-tures need to match in the sense that any feature name that occurs infstruct1 must occur in fstruct2. For feature-value pairs that occur inboth fstruct1 and fstruct2 that have a feature structure as a value,those feature structures will also have to be checked against each other. If afeature name occurs in fstruct1 and not in fstruct2 checking fails, or, toput it di�erently, checking succeeds only if fstruct1 subsumes fstruct2.

De�nition 5.4 shows the formal de�nition of checking. The �rst conjunctof the de�nition says that each atomic feature name aname that occurs infstruct1 with the atomic feature value atom must also occur in fstruct2

with the same feature value. The second conjunct says that for all thecomplex feature names sname in fstruct1 that have a complex featurevalue fstruct3, fstruct3 must be checked against the value of the featuresname in fstruct2.

De�nition 5.4

FUNC Check : FeatureStructS, FeatureStructS -> BoolS

AXIOM fstruct1 Check fstruct2

<=> FORALL aname, atom

( Value (fstruct1, aname) = atom

==> Value (fstruct2, aname) = atom

)

And FORALL sname, fstruct3

( Value (fstruct1, sname) = fstruct3

==> fstruct3 Check Value(fstruct2,sname)

)

Furthermore the module about feature structures contains two opera-tions that can change a given feature structure.

Remove is a function that given a feature structure fstruct1 and a set offeatures nset returns the value fstruct2 where for all feature names namethe following holds: if name is not a member of nset then the value of namefor fstruct2 equals the value of name for fstruct1, and else the value ofname for fstruct2 is unde�ned (see De�nition 5.5).

The function Keep has the opposite e�ect of the function Remove: ifname is not a member of nset then the value of name for fstruct2 is unde-

7Cf. [Cho93, Page 30].


�ned, and else the value of name for fstruct2 equals the value of name forfstruct1 (see De�nition 5.5).

De�nition 5.5

FUNC Remove : FeatureStructS, SetS[FeatureNameS] -> FeatureStructS

FUNC Keep : FeatureStructS, SetS[FeatureNameS] -> FeatureStructS

DECL nset : SetS[FeatureNameS]

AXIOM fstruct1 Remove nset = fstruct2

==> ( Not (name In nset)

==> Value (fstruct2, name) = Value (fstruct1, name)

)

And ( name In nset

==> Value (fstruct2, name) = Undef

)

AXIOM fstruct1 Keep nset = fstruct2

==> ( Not (name In nset)

==> Value (fstruct2, name) = Undef

)

And ( name In nset

==> Value (fstruct2, name) = Value (fstruct1, name)

)

5.3 Summary

In this chapter I outlined why I introduced the notion `feature structure'in the formalization, although this notion does not occur in the MinimalistProgram. The main reason is that it is convenient to be able to treat thefeatures of a node in a tree as a unit. I also described how feature structuresare formalized in the formalization. Furthermore, I described the featurenames that occur in the formalization, plus their possible values. Not allthe feature names used in the formalization are present in the minimal-ist framework. Finally, I introduced some operations on feature structuresof which the most important is the operation `feature checking'. I arguedthat the features of a lexical constituent can only be checked against thefeatures of a functional head if the feature structure belonging to the lexi-cal constituent contains at least as many feature-value pairs as the featurestructure belonging to the functional head.

Chapter 6

Lexicon

The role of the lexicon in the Minimalist Program is to serve as input forthe structure-building operation Merge. The structure-building operationsMerge and Move take two trees � and � to construct a tree with � and �

as its left and right subtrees. The input trees for the operation Merge caneither be lexical items or trees already built by Merge and Move (see alsoSection 1.6).

The formalization, which is representational instead of derivational, en-ables to judge if trees are correct according to the Minimalist Program.The structure-building operations Merge and Move do not play a role. Theformalization de�nes the requirements an LF-tree must meet, not the wayit is built up. The lexicon is linked with the rest of the formalization viaX-Theory (see Chapter 7). Within the X-module of the formalization, itis de�ned that heads must be associated with a feature structure that is amember of the lexicon. Note that also in the derivational version the lexi-con and X-Theory are closely related, since the operations Move and Mergebuild structures that are permitted by X-Theory.

In Section 6.1 I will outline the ideas on the lexicon on which the for-malization is based. The formalization itself is discussed in Section 6.2.

6.1 Introduction

Phonological, semantic and formal features In the Minimalist Pro-gram, the lexicon is considered to be a set of lexical elements representedby bundles of features. In Chomsky's 1995 framework [Cho95] features aredivided into three categories: phonological, semantic and formal (or syntac-tic) features. Phonological features are interpreted at PF, semantic featuresare interpreted at LF, and formal features trigger the movements that take

85

86 CHAPTER 6. LEXICON

place during overt and covert syntax.As we saw in Chapter 5, what are called bundles of features in the min-

imalist framework are treated as feature structures in the formalization.Hence, lexical items are represented as feature structures in the formaliza-tion. And furthermore, in our framework formal features do not triggermovements. Since the formalization is non-derivational, movements aremodelled by declaratively de�ned `licensing chains'. A chain may have acopy in a given position within a functional projection if the formal fea-tures of the copy can be checked against the formal features of the relevantfunctional head.

Formal features are split up in two categories according to Chomsky[Cho95]: optional and intrinsic. Optional features are called variable fea-tures by Zwart [Zwa97] for reasons that will be explained later in this sec-tion.

According to Chomsky [Cho95, Page 236], formal features are intrinsicif they are idiosyncratic or if they can be predicted from other properties(semantic features) of the lexical item.

An example of an idiosyncratic feature is grammatical gender for theDutch word klok (clock). The fact that klok is feminine is not predictablefrom any semantic feature of the word and therefore this [gender] featuremust be listed explicitly in the lexicon. Note that Dutch does not have afeminine/masculine distinction with respect to the selection of determiners.Both feminine and masculine nouns select the de�nite article de while neuternouns select the de�nite article het.

An example of a predictable feature is [person]. The fact that klok isthird person is predictable from the semantic feature [artifact]. Therefore[person] is also considered to be intrinsic to klok, like [gender]. Chomskyassumes that features such as [person], that can be determined by semanticfeatures, are not listed explicitly in the lexical entry. These features areadded to the lexical item when it enters the derivation.

Zwart's view di�ers from Chomsky's view at this point. Zwart assumesthat both types of intrinsic features (idiosyncratic features and featuresderivable from semantic features) should be listed explicitly in the lexicalitem.

Furthermore Zwart does not consider the [category] feature to be a for-mal feature. This feature is grouped together with semantic features in acategory of features that is referred to as lexical-categorial features (hence-forth LC-features). The reason for calling the [category] feature an LC-feature is that it is derivable from semantic features. For instance, we donot need to stipulate a formal feature [category noun] since we know thatall lexical items with the semantic feature [artifact] automatically are nouns[Zwa97, Page 169].


Optional features are all formal features that are not intrinsic. Zwart[Zwa97, Page 170-171] claims that `optional' is the wrong name for this typeof feature. It suggests that the presence of the feature is optional whereasits presence is no more optional than the presence of intrinsic features. Thereal di�erence between intrinsic features and what Chomsky calls optionalfeatures is that optional features have a variable value whereas the valuesof intrinsic features are �xed.1 Therefore Zwart prefers to refer to optionalfeatures as variable features. Examples of variable (or optional) features fora noun are [case] and [number]. For instance, the [case] of the Dutch wordstoel (chair) can either be nominative or accusative.

Traditionally the lexicon is the location for everything in a languagethat is unpredictable.2 In the same spirit, Chomsky claims that variable(optional) features are �rst added to the lexical entry as it enters the deriva-tion, since those features are predictable from other properties of the lexicalentry (see earlier in this section). Zwart reformulates this idea in the follow-ing way: the value of a variable feature is �xed as it enters the derivation,i.e. at this point a choice from the possible values is made. The di�erencebetween the two approaches is that in Zwart's point of view the lexicon con-tains both intrinsic and variable formal features, whereas it only containsintrinsic formal features in Chomsky's point of view.

Postlexicalism There is also a di�erence between Chomsky's approachand Zwart's approach in the presence of phonological features in the lexicon.Chomsky assumes that lexical entries contain phonological, semantic andintrinsic formal features. Zwart assumes that lexical entries only containsemantic and formal features. This approach is called postlexicalism. Inpostlexicalism (introduced as Distributed Morphology by Halle and Marantz[HM93]) phonological features, which determine how a lexical item is pro-nounced, are added after the syntactic derivation has been completed (cf.also [Bea66, Aro76, Bea91, And92, Aro92]).

Zwart [Zwa97, Page 162-165] advances several arguments (of which, forthe sake of simplicity, only one will be described here) to adopt this ap-proach. One of the arguments is connected with Economy of Representa-tion. Because phonological features are not relevant to syntax it is moreeconomical if phonological features are absent during the syntactic deriva-tion. In the postlexicalist approach as opposed to the lexicalist view that isadopted by Chomsky [Cho93], phonological features are added after Spell-Out.3 Therefore postlexicalism is more economical than lexicalism, in which

1There are exceptions to this rule. For example, the Dutch word �ets (bicycle) caneither be masculine or feminine, although [gender] is an intrinsic feature.

2Cf. [Blo33, Page 274] and [Aro92].3In the lexicalist approach, lexical items enter the derivation in fully in ected form.

The syntax cannot manipulate in ectional a�xes of words.


phonological features are present throughout the syntactic derivation (cf.[Zwa97, Page 160-165]).

Zwart assumes that in the morphological component after Spell-Out, thefeatures of the morphosyntactic object determine the phonological featuresof the object, i.e. the actual word as it appears at PF. It is claimed that themorphological component can be considered as a kind of lexical insertionthat takes place after the derivation [Zwa97, Page 161]. After syntax, achoice (based on morphosyntactic objects) is made from a postsyntacticlexicon. On the basis of semantic features (such as [artifact]) and formalfeatures (such as [person] and [number]) the phonological features of themorphosyntactic object are selected.

Possibly there will be more than one match between the morphosyntac-tic object and the postsyntactic lexicon. In such a case the most speci�centry will be selected. Zwart [Zwa97, Page 164] clari�es this idea with thewords in Example 6.1 and 6.2. Example 6.1 gives a possible lexical repre-sentation for singular forms of the Dutch verb kussen (to kiss). Example6.2 gives the representation of the forms in Example 6.1 as they appear inthe underspeci�ed postsyntactic lexicon.

Example 6.1

[number singular], [person 1] kus[number singular], [person 2] kust[number singular], [person 3] kust

Example 6.2

[number singular], [person 1] kus[number singular] kust

The lexical entries in the postsyntactic lexicon are underspeci�ed becausethis is the most economical way of representing morphological paradigms (cf.[Kip73] and [HM93]). If the relevant morphosyntactic object is �rst person,both kus en kust in Example 6.2 will match. As noted above, the closestmatch is the right match. Therefore kus is selected from the postsyntacticlexicon.

In the formalization two di�erent lexicons are de�ned: one on which theinput of the LF-tree are based (henceforth: the prelexicon) and one whichis consulted at PF (henceforth: the postlexicon).

Disjunctive feature values In the lexicon we apply feature values thatare disjunctions (of either atomic values or feature values that are featurestructures).4 This implies that what looks like a feature structure in the

4Cf. [Shi86, Page 14].


lexicon might actually be a description of a set of feature structures. I willclarify this with the help of the simpli�ed feature structure representing alexical item for the Dutch noun boek (book) in Example 6.3.

Example 6.3

26666666664

word boek

category noun

agreement

264person third

number singular

gender neuter

375

case nominative OR accusative

37777777775

At �rst sight Example 6.3 seems to represent a feature structure. How-ever, the fact that the feature name [case] has two possible values (eithernominative or accusative) implies that it represents two feature structures,or to put it di�erently, a set of feature structures. The two feature struc-tures are identical, except for their case values: the �rst has a nominativecase, the second an accusative case.

The reason for using disjunctive feature values is conciseness. By apply-ing one or more disjunctive feature values per lexical item, the number ofitems in a lexicon can be reduced considerably.


The formalization of Zwart's framework as described in this section formal-izes Zwart's ideas on postlexicalism:

� the prelexicon will contain intrinsic as well as variable formal features

� the prelexicon will contain only semantic and formal features (nophonological features)

� a postlexicon containing phonological features `simulates' morpholog-ical processes

� semantic and categorial features form a complex that is referred to asLC-features

Phonological, semantic and formal features In the formalization,phonological features are represented by the feature Word and semantic fea-tures are represented by the feature Sememe. Word takes a fully in ected


word form as its value, while Sememe takes a stem as its value (see alsoChapter 5). The reason for this simpli�ed treatment of phonological andsemantic features is that the exact character of these features is not workedout in much detail in the minimalist literature. Furthermore, the chosenapproach is e�ective in the formalization.

The formal features in the formalization are: Agreement, Subject,Object, Person, Number, Gender, Case, Tense, Inversion, WhWord andDeterminer.

Features that do not belong to any of the above three types of featuresare: Category, CompCat and SpecCat. In Zwart's framework the Categoryfeature is grouped together with the semantic features. This type of featureis called LC-feature (lexical categorial) by Zwart.

Postlexicalism In the formalization Zwart's postlexicalism is imple-mented by de�ning two di�erent lexicons. The �rst lexicon, which accordingto Zwart is consulted when a lexical item enters the derivation, is called theprelexicon. The second lexicon, which according to Zwart is consulted afterthe derivation (at PF), is called the postlexicon.

Disjunctive feature values Before I turn to the treatment of disjunctivefeature values, I will deal with the way feature structures are built up inthe formalization. The function Add is the central function with respect tofeature structures.

The function Add, which adds feature-value pairs to feature structures,is an indexed function. The index is given between square brackets. Eachindex stands for a di�erent kind of Add. For instance in De�nition 6.1, whichcontains the lexical item for the Dutch word for book, Add[Sememe] adds avalue of the type Sememe to a feature structure yielding a feature structure,Add[Agreement] adds a value of the type Agreement to a feature structureyielding a feature structure etc.

The function Add is speci�ed in such a way that adding the same featurename twice to a feature structure makes the whole lexicon unde�ned. Afeature-value pair can only be added to a feature structure if the relevantfeature name has an unde�ned value until then.

The feature structures in the formalization are built by starting with anempty feature structure and adding feature-value pairs to it. In De�nition6.1 we start with an empty feature structure of the category noun (N). Thisis relevant information because feature structures belonging to nouns docontain other features than, for example, feature structures belonging toverbs. As we saw in Chapter 5 the formalization indicates which lexicalitems may contain which feature-value pairs.

Also the permitted feature-value pairs for the complex feature values


of the feature names Agreement, Object and Subject are indicated inthe formalization. For instance, the agreement value is a feature struc-ture that is built in a way that is comparable with building a main featurestructure (representing the entire noun): feature-value pairs are added toan empty feature structure. The only di�erence with the main featurestructure is the name of the empty feature structure. Main feature struc-tures are always introduced by EmptyCatStruct[N], EmptyCatStruct[V],EmptyCatStruct[Agro] etc., called after the category of the lexical item.Complex feature values are introduced by EmptyStruct. The feature name(such as the feature name Cat for Category above) need not be includedbecause Agreement is already mentioned outside of the feature structure.The features in the feature structure that can be referred to as the agree-ment features are all permitted because Person, Number and Gender arede�ned as agreement features in the feature module (see Chapter 5).

The shared properties of di�erent types of feature structures indicatethe redundancy of the lexicon. However, the formalization does not con-tain inheritance principles as in feature-based theories (see [PS94], [PS87],[FPW85],[FN92]) since Zwart assumes that the lexicon contains both vari-able and intrinsic features. Chomsky's idea that the lexicon only containsunpredictable material resembles the idea of inheritance principles. By in-heritance principles the amount of idiosyncratic information that needs tobe stipulated in individual lexical items is reduced by grouping lexical itemsinto di�erent types. For instance, all nouns share a considerable amount ofinformation. Of course they share the same category (N) and often (inthe case of artifacts but not always in the case of personal pronouns) theyhave third person. Furthermore, a considerable amount of other featuresare shared, which may have di�erent values for di�erent nouns.

Now we know how feature structures are built up, we can turn to thetreatment of disjunctive feature values in the formalization. There are twodi�erent ways to express sets of values in the formalization: one is a dis-junction of values represented by ++ (cf. `OR' in predicate logic), the otheris in principle also a disjunction represented by Any[Name] which indicatesthe set of possible values for the feature name Name.

The AFSL-function ++ represents set theoretical joining. In the lexiconsin our formalization the function ++ both joins the di�erent lexical items(which themselves may be sets, as we saw above) and feature values (seeDe�nition 6.1).

In the line ++ ( EmptyCatStruct[N] the function ++ joins the lexicalitem for book with all the preceding lexical items, which are not representedhere for the sake of simplicity. This is the same concept of the lexiconused in feature-based grammars: the lexicon is a disjunction of all its items[PS87, Page 44].


In lines such as Add[Number] (Singular ++ Plural) and Add[Case]

(Nominative ++ Accusative) the function ++ joins two feature values.

De�nition 6.1

.

.

.

++ ( EmptyCatStruct[N]

Add[Sememe] "boek"

Add[Agreement] ( EmptyStruct

Add[Person] Third

Add[Number] (Singular ++

Plural)

Add[Gender] Neuter

)

Add[Case] (Nominative ++ Accusative)

Add[Determiner] (Yes ++ No)

Add[WhWord] No

)

.

.

.

A lexical itemwith only singleton sets as its feature values is a descriptionof a set of feature structures with only one element, which can also be calleda feature structure. All feature values that do not contain the function ++

are sets as well: they are singleton sets.The line Add[Number] (Singular ++ Plural) and the line

Add[Determiner] (Yes ++ No) in De�nition 6.1 can be replaced byAny[Number] and Any[Determiner] respectively, as is shown in De�nition6.2. Any[Name] is applied for the disjunction of all the possible values of agiven feature name. Both the feature name Number and the feature nameDeterminer have only two possible values, Singular and Plural, andYes and No respectively. Since for both the feature name Number and thefeature name Determiner all possible feature values are applied, De�nition6.1 can be replaced by De�nition 6.2.

De�nition 6.2

.

.

.


Add[Sememe] "boek"


Add[Person] Third


Add[Number] Any[Number]

Add[Gender] Neuter

)


Add[Determiner] Any[Determiner]

Add[WhWord] No

)

.

.

.

Any[Name] is needed because of the nature of checking. In standarduni�cation-based grammar the fact that a certain feature is not representedmeans that it can take any possible value, because uni�cation succeeds whenjust one of the two feature structures contains a certain feature. However,checking is only possible if a certain feature is present in a given functionalhead as well as in the lexical constituent that checks its features against it(i.e. the lexical constituent adjoined to the functional head and/or the lexi-cal constituent in the speci�er position of the functional head) (see Chapter5). Hence, the approach of indicating that any possible value for a givenfeature name can be chosen by not representing the feature-value pair atall is fatal for a theory where checking plays a role: if a feature-value pairis not visibly represented on a lexical head, the feature cannot be checkedagainst a functional head. In Zwart's framework all functional heads needto have checked all their features against those of a lexical constituent byLF. If lexical heads might miss certain features to indicate that the featurecan take any possible value, there will be a functional head that cannotcheck all its features, and hence LF will never be reached.

For instance, if in the sentence in Example 6.4 (Bill reads the newspaper)krant (newspaper) is represented by the feature structure in De�nition 6.3then the tree in Example 6.4 is not an LF-tree. AgrO cannot check itsagreement number feature since the lexical item for krant does not containthis feature.

De�nition 6.3

.

.

.


Add[Sememe] "krant"


Add[Person] Third

Add[Gender] Neuter

)



)

.

.

.

Example 6.4

AgrSP

DP AgrS

Billi

AgrS TP

T AgrS ei T

AgrO T ek AgrOP

V AgrO DP AgrO

leestk de krantj

ek VP

ei V

ek ej

Any[Name] and ++ occur only in lexical items in the lexicon; thereforethe de�nition of checking in De�nition 5.4 on Page 83 does not deal withsets of feature values. If a lexical item is integrated in a tree, a choicehas to be made between the disjuncts. Both Any[Name] and ++ are ap-plied to avoid requiring that a new lexical item has to be written down foreach of the disjuncts. Hence, lexical items are not always feature struc-tures: if they contain disjunctive values (i.e. sets of values) they representsets of features structures. We assure that a derivation tree can never con-tain a set of feature structures by requiring that nodes contain labels ofthe type FeatureStructS (feature structure) and not labels of the typeSetS[FeatureStructS] (sets of feature structures).

Any[Name] resembles the atomic value ANY described in [Shi86, Page43] and introduced by Kay [Kay85]. ANY is a kind of variable because ituni�es with anything, just like Any[Name]. In a �nal functional structureANY has to have been uni�ed with something else. In our formalizationsomething similar is the case. Only the lexicon may contain disjunctions;successful derivation trees may not.

prelexicon The de�nition of the prelexicon, including only the �rst lexicalitem for the sake of conciseness, is given in De�nition 6.4.


De�nition 6.4

MODULE PreLexiconZW

IMPORT FeaturesM

IMPORT SetM[FeatureStructS]

OBJ PreLexicon : SetS[FeatureStructS]

= ++ ( EmptyCatStruct[N]

Add[Sememe] "boek"


Add[Person] Third

Add[Number] Any[Number]

Add[Gender] Neuter

)


Add[Determiner] Any[Determiner]

Add[WhWord] No

)

.

.

.

END MODULE

In De�nition 6.4 we see that, �rstly, the module where all features andtheir values are introduced is imported: IMPORT FeaturesM. Of course, thisis done because a prelexicon is a set of feature structures with feature namesand feature values as its main building blocks. Next, we import all the spec-i�ed information about sets by the line: IMPORT SetM[FeatureStructS].Finally, it is declared that the prelexicon is an object existing of sets offeature structures: OBJ PreLexicon : SetS[FeatureStructS].

The prelexicon is connected with the rest of the formalization via thefunctions XFeatures in the module on X-Theory (see Chapter 7). Thisaxiom says that leaves with BarLevel 0 have a feature structure that is amember of the lexicon. What has to be taken into account is that nodesof trees may never contain disjunctive feature values. In the formaliza-tion typing takes care of this: nodes of trees contain feature structures(FeatureStructS), not sets of feature structures (SetS[FeatureStructS]).As we said earlier in this section, we must distinguish between a descriptionof a set of feature structures (which contains disjunctive feature values) anda single feature value (which may not contain disjunctive feature values).Nodes of trees may not contain sets of feature structures, as they are not ofthe right type.


The fact that sets of feature structures are not appropriate in nodes oftrees is a consequence of the necessity of feature checking. Checking cannottake place if, for instance, it is not clear if a lexical item has nominative oraccusative case. When a feature is checked it must have a singleton featurevalue.

By the application of the prelexicon in the formalization, we simulateZwart's �xation of variable features when the lexical element enters thederivation. Namely, elements from the prelexicon do not contain multiplevalues once they are applied in an LF-tree.

Postlexicon Since we apply postlexicalism in the formalization we needtwo di�erent lexicons. The �rst lexicon (prelexicon) contains one lexicalentry per stem (sememe). We will see that the lexicon that is consulted atPF (postlexicon) contains one item per in ected form, for instance one forzij (she) and one for haar (her). The prelexicon does not contain Word fea-tures as opposed to the postlexicon. This is because Zwart argues that theprelexicon is a more or less language independent lexicon, with only formal(intrinsic as well as variable) and semantic features. In our formalizationthe Sememe feature represents the semantic features, as the literature is notspeci�c enough about the nature of semantic features. The application ofthe Sememe feature instead of semantic features causes the prelexicon to beless language independent than it would be if actual semantic features wereused, as the Sememe feature takes a language speci�c stem as its value. TheWord feature in the postlexicon replaces phonological features. The Mini-malist Program is not explicit about phonological features. Therefore, wedecided to apply the Word feature instead of phonological features, as theword is a representation of how to pronounce a lexical item.

The postlexicon is the more extensive of the two lexicons, because itoften contains more than one form of the same paradigm. For instance, thestem zij (she) appears in two di�erent forms: once as zij and once as haar(see De�nition 6.5).

De�nition 6.5

MODULE PostLexiconZW

IMPORT FeaturesM

IMPORT SetM[FeatureStructS]

OBJ PostLexicon : SetS[FeatureStructS]

AXIOM PostLexicon

= .


.

.


Add[Stem] "zij"

Add[Word] "zij"


Add[Person] Third

Add[Number] Singular

Add[Gender] Feminine

)

Add[Case] Nominative

Add[Determiner] No

Add[WhWord] No

)


Add[Stem] "zij"

Add[Word] "haar"


Add[Person] Third


Add[Gender] Feminine

)

Add[Case] Accusative

Add[Determiner] No

Add[WhWord] No

)

.

.

.

END MODULE

The part above the axiom in De�nition 6.5 is comparable with the be-ginning of the prelexicon module.

The postlexicon is connected with the rest of the formalization at PFby the function LookUpWord (see Chapter 9): when a tree is spelled out,the postlexicon is consulted. In a tree that is spelled out there are nophonetic/word features to be found, as the prelexicon, on which the LF-tree is based, does not contain Word features. However, the prelexicondoes contain Sememe features. At PF, entries that can be uni�ed withthe features of the heads of the tree are selected from the postlexicon. Asentence that is spelled out is a list of words that is based on the Word valuesof those elements. Sometimes more than one entry per head is selectedfrom the postlexicon. In such a case the most speci�c entry is chosen. Themost speci�c entry is the entry with most features that can still be checkedagainst the features of the head from the tree that is spelled out. Forexample, the paradigm kus (kiss) has two occurrences that can be checkedagainst a feature structure with a �rst person singular form. The �rst hasthe word feature kus and contains an explicit person feature with the value�rst. The second has the word feature kust and does not contain a person


feature, which means that it uni�es with any person value (cf. Examples6.1 and 6.2). The most speci�c occurrence of the two is, of course, the �rst.Namely, the second does not have a person feature at all. Therefore the �rstoccurrence of the Sememe kus with the word value kus is spelled out. Hence,if more than one matching feature structure is found in the postlexicon, themost speci�c feature structure is selected by the function LookUpWord.

In the postlexicon, the Any-value is not applied when a feature can occurwith any possible value. Not listing the feature at all is more economicalaccording to Zwart. Moreover, it would be incorrect to use the Any-valuefor this objective. If we would apply Any-values in the case of the aboveexample, the postlexicon would contain three occurrences of the word kust,of which one is �rst person. This is a form that does not occur in Dutch: Ikkust hem (I kisses him) is not a grammatical Dutch sentence. If this formdid exist it would be impossible to select the most speci�c form from thepostlexicon because kus and kust are equally speci�c: they both contain aperson feature with the value �rst.

Therefore Zwart's idea of not giving a person feature at all for the formkust is preferred here. If an LF-tree includes a head with a feature structurecontaining a stem kus and a person value �rst, the form that is spelled outis kus. The reason for this is that the postlexicon contains two matchingfeature structures, one with the word value kus and the other with the wordvalue kust, of which the former is the more speci�c because it contains aperson feature with the value �rst, while the latter has no person feature.

The idea of selecting the most speci�c form is well-known in linguisticliterature. Arono� [Aro76] describes the principle of Morphological Block-ing, which implies that the existence of a more highly speci�ed form in thelexicon excludes the selection of a less highly speci�ed form. MorphologicalBlocking is considered to be a consequence of the Elsewhere Condition. TheElsewhere Condition requires that rules with more speci�c constraints applybefore rules with more general constraints (cf. [And69, Kip73, And86]).

What is problematic is that it is not always possible to indicate whichfeature structure is the more speci�c of two. For instance, two featurestructures that both consist of three feature-value pairs might share twofeature-value pairs while the third is di�erent for both. Such cases do notoccur in the fragment that our formalization describes. However, theoreti-cally it might happen that it is impossible to indicate which of two featurestructures is the most speci�c.

Note that the use of the postlexicon more or less denies the role of in ec-tional morphology. In ectional morphology enables us to derive in ectedforms from a stem on the basis of in ectional features such as [number],[person] and [tense]. In the approach chosen here the paradigm belongingto a stem consists of a group of postlexical items in the lexicon from which

6.3. THE LEXICON IN CHOMSKY'S 1993 FRAMEWORK 99

we can make a choice.

6.3 The lexicon in Chomsky's 1993 frame-

work

In the formalization of Chomsky's 1993 framework there only is one lexicon.As we saw earlier this lexicon contains semantic, formal and phonologicalfeatures. As in the formalization of Zwart's framework the lexicon is con-nected with the rest of the formalization via X-Theory. The Word featuresin the lexicon represent the phonological features of the lexical items. AtPF these are the features that are spelled out.

6.4 Summary

In this chapter I discussed the treatment of the lexicon in the formalization.There are di�erences between the treatment of the lexicon in Zwart's frame-work and in Chomsky's 1993 framework. These di�erences are caused by thepostlexicalist approach chosen by Zwart. In this approach, the main idea isthat phonological features are �rst introduced after the derivation. The lex-icon only contains semantic and formal features. In Chomsky's frameworkthe lexicon contains semantic and formal as well as phonological features.In Zwart's framework an extra lexicon is introduced which is consulted atPF and which does contain phonological features. The selection from theextra lexicon (which is called postlexicon in the formalization) is based onthe formal and semantic features from the lexical heads in the LF-tree. Theidea behind Zwart's postlexicalism is that it is more economical to intro-duce the phonological features, which are not needed in the course of thederivation, after the derivation.

Chapter 7

X-Theory

7.1 Introduction

X-Theory is a part of Chomskyan linguistics that is intended to simplifyphrase structure rules. Phrase structure rules are rewrite rules that indicatehow trees that represent phrase structure can be built.

In Section 1.2 we saw that X-Theory was based on proposals by Chomsky[Cho70]. He removed lexical properties from phrase structure rules. Thespeci�c phrase structure rules such as in Example 7.1 are replaced by moregeneral rules such as in Example 7.2, where X and Y are used as variablesfor lexical categories such as noun (N), verb (V) and preposition (P).1

Example 7.1

(a) V ! V, NP(b) P ! P, NP(c) N ! N, PP

Example 7.2

X ! X, YP

Chomsky [Cho93] considers X-Theory to be an independent set of prin-ciples, which the operations Merge and Move should consult. These twooperations, also known as Generalized Transformations, create phrase struc-ture. Both Merge and Move combine two trees (� and �) into one ( ) byprojecting one of the two trees (say �). is the mother of � and � and

1For applications and revisions of X-Theory: cf. [Jac77], [Stu85] and [Muy82].

101

102 CHAPTER 7. X-THEORY

has the same category as �. The newly constructed tree must obeyX-Theory.

X-Theory as Chomsky [Cho93] applies it is given in Example 7.3. Rule(a) introduces the speci�er (YP), rule (b) introduces the complement, andrule (c) introduces the head adjoined element (W), which we will refer toas adjunct in the following. Following Kayne [Kay94] I assume that theorder of the constituents in the right-hand side of the rules is �xed (see alsoSection 1.3). Hence, the speci�er always precedes the head, the head alwaysprecedes the complement and the adjunct (if present) precedes the head, asis represented in Example 7.4.

Example 7.3

(a) XP ! YP, X(b) X ! X, ZP(c) X ! W, X

Example 7.4

XP

YP X

(Speci�er)

X ZP

(Complement)

W X

(Adjunct) (Head)

More recently, Chomsky [Cho95, Page 241�] no longer presupposes X-Theory. The properties of X-Theory are derived from minimalist assump-tions. This resulted in a major revision of X-Theory, and Chomsky [Cho95,Page 249] even assumes that `one goal of the Minimalist Program seems tobe within reach: phrase structure can be eliminated entirely'. But for themoment X-Theory is still a vital component of the Minimalist Program.

Following Muysken [Muy82], Chomsky [Cho95, Page 242] takes [+max-imal] and [-maximal] to be properties that depend on relations betweennodes. Within a phrase XP, the head X is [- maximal] and [-projection].XP is [+maximal] and [+projection], since it is the highest level of the XPand since its features are projected from the head X. The intermediate level,X, is [-maximal] and [+projection], since it is not the highest level of theXP but it is a projection of the head X. Chomsky now assumes that itis possible that a head only projects once. In that case the node directly


dominating that head is [+maximal] and [+projection]. Hence, if the nodedirectly dominating a head is [+maximal] or [-maximal] depends on whetherits mother is a projection of the same head or not. This idea is illustrated inExample 7.5 and 7.6. Example 7.5 shows a tree where the node dominatingthe head X is [+maximal] since this node in its turn is dominated by Y(where X and Y stand for two distinct bundles of features). Example 7.6,however, shows a tree where the node dominating the head X is [-maximal]since this node in its turn is dominated by XP.

Example 7.5

YP

ZP Y

Y XP

WP X

Example 7.6

YP

ZP Y

Y XP

WP X

X UP

Note that the intermediate bar-level X is not present in Example 7.5since the head X has no complement. The head X in Example 7.6 doeshave a complement (UP). X has a speci�er (WP) both in Example 7.5 andin Example 7.6. Since Chomsky wants to derive X-Theory rather thanstipulating it as a set of independent principles, it is impossible to let ahead X project when it has no complement or no speci�er. The operationsMerge and Move always take two trees � and � and combine them intoone tree by projecting either � or �.2 If a head X has no complement

2See Kayne [Kay94] for the argument that trees must be binary branching.


or speci�er, there is no reason for the operations Move and Merge to applyand consequently there is no possibility for X to project. A head X whichdoes not project is at the same time [+maximal] and [-maximal].3

According to Chomsky the label of a node, which is the feature bun-dle belonging to a node, may only contain features that represent inherentproperties such as [case] and [person]. Therefore the features [maximal] and[projection] are not appropriate as a part of a label of a node. The features[maximal] and [projection] are not inherent but relational. Their values fora given node can be computed with respect to the tree (the representation)the node is part of, that is, their values are determined representationally.The inherent (non-relational) features in the labels of nodes are the samefor every projection of a given head and therefore they can be determinedderivationally. This means that the label is �xed once the node it belongsto is formed by the operations Merge or Move.

Zwart [Zwa97, Page 174] prefers considering phrase structure level asproperty that is part of the label of a node. Hence, also the phrase struc-ture level of a node must be determined derivationally. As we saw above,Chomsky uses the features [maximal] and [projection] to express the phrasestructure level of a node. The values of these features for a given nodeare determined representationally according to Chomsky, that is, they aredetermined on the basis of the position of the node in relation to the othernodes in the representation (i.e. tree) it is part of. Zwart argues that ifthe phrase structure level of a node is considered to be part of the label ofa node, the feature [maximal] is problematic. A node is always [+maxi-mal] when it is created as the root of a tree by Merge or Move. But in thenext step of the derivation the features of could be projected again, whichmakes [-maximal]. Since the features of are determined derivationally,its features cannot be changed afterwards. Zwart assumes that the feature[maximal] is super uous. By just applying the feature [projection] to in-dicate the phrase structure level of a node, we obtain an X-structure withonly two levels instead of three, which has been proposed before (see forinstance [Stu85, Hel91, Hoe91, Zwa92, Kay94]). In this structure phrasesare [+projection] and heads are [-projection].

Zwart [Zwa97, Page 175] summarizes the possible phrase structures inthe following law (where � and � are categorial features and m, n = [+/-projection]):

Example 7.7

3Chomsky [Cho95, Page 249] does not expect this assumption to cause any problems.As an illustration of items that must be both [+maximal] and [-maximal] Chomsky[Cho95, Page 249] mentions clitics.


�m + �n = �n

The law presented in Example 7.7 yields the phrases in Example 7.8, nottaking into account the relative order of the daughters.

Example 7.8

(a) XP

X YP

(b) X

X Y

(c) XP

YP XP

(d) X

Y XP

In practice the law in Example 7.7 predicts one phrase, (d), that doesnot seem to occur. Zwart claims that (d) is ruled out independently. It issupposed that (d) is either a complementation or an adjunction structure.In the �rst case, Y is the head and XP is the complement. Y, being a head,should project its categorial features. This is not the case and therefore (d)is excluded as a complement structure. In the second case, XP is supposedto be the head. Y should check its features against the head X of XP. For achecking relation we need Y to be adjoined to X like in (b). This is not thecase in (d) and consequently (d) is excluded as an adjunction structure.

In the next section, I will present X-Theory as it is formalized in theformalization. Note that neither Chomsky's [Cho95] nor Zwart's [Zwa97]version of X-Theory as presented in this section is formalized. The reasonsfor preferring the traditional X-Theory (where heads always project from Xto X to XP, independent of the presence of complements or speci�ers) overthe newer versions presented in this section are described in Section 7.3.


In this section I will outline the formalization of X-Theory. Mainly, we aredealing here with X-Theory as described by Chomsky [Cho93]. Only atsome points I decided to apply ideas from Chomsky's 1995 framework orZwart's 1997 framework if this made the formalization more elegant.

The X-module describes, among other things, which binary branchingtrees are allowed with respect to the bar-levels (i.e. phrase structure levels)of the nodes of trees. In this module, restrictions on trees rather than phrasestructure rules are de�ned. A tree tr satis�es X-Theory if the boolean func-tion Xbar tr (see De�nition 7.1) yields True. The functions XBarLevels,XFeatures and XRestrictions which are consulted in the function XBar

will be discussed in detail below. Here it will be su�cient to explain whythese three functions are consulted in the function XBar.


In the function XBarLevels the traditional X-rules (for instance, X !

X, YP) are formalized. Remarkable is here that the category variables Xand Y are not mentioned in XBarLevels. This part of the X-rules is dealtwith in the function XFeatures.

The function XFeatures formalizes feature percolation within projec-tions of heads. Heads come from the lexicon as a feature structure. Allnon-heads receive their features from the heads they belong to. The tradi-tional X-rules only (implicitly) deal with the percolation of category featuresby always mentioning one category value (e.g. X) twice in an X-rule: onceat the left-hand side and once at the right-hand side of the arrow. Featuresother than category features were left out of consideration. In the formal-ization it turned out that it is convenient that all the features from the head(not only the category feature) are available at all levels. In this way it is,for instance, possible to refer to the features of an XP or to the features ofthe mother of any particular node in a tree, and not only to the features oflexical heads.

The signi�cance of separating the features that describe the phrase struc-ture level of a node (here represented by the feature BarLevel, and inChomsky's 1995 framework represented by the features [maximal] and [pro-jection]) from all the other features was discovered independently of Chom-sky [Cho95]. As we saw in Section 7.1, Chomsky considers phrase structurelevel to be relational, while he considers all other features such as [number],[gender] and [tense] to be inherent. In the formalization BarLevel turnedout to be an exceptional feature since it was the only feature that projec-tions did not seem to inherit from their head. Furthermore, the featureBarLevel proved to be essential to describe the way features percolate fromheads to their projections.

The function XRestrictions speci�es a residue. It describes a kind offeature checking which is not invoked by movement. In the Minimalist Pro-gram feature checking and movement are intimately linked. Movement ofconstituents is only allowed if it is required for purposes of feature checking.During the formalization process there turned out to be a type of featurechecking which is not only linked with the operationMove, but in some casesalso with the operation Merge. This type of feature checking is described inthe function XRestrictions. The kind of feature checking I am referring tohere is required in order to let a head, lexical or functional, select the rightarguments. These arguments can either manifest themselves as speci�ers orcomplements, as we will see below.

After the more extensive description of the functions XBarLevels,XFeatures and XRestrictions I will discuss the functions in which spec-i�ers, heads etc. are given a position within projections. This is not ano�cial part of X-rules, but I will argue that the X-module is the suitable


module for this type of information.

De�nition 7.1

FUNC XBar : TreeS -> BoolS

AXIOM XBar tr

<=> XBarLevels tr

And XFeatures tr

And XRestrictions tr

Bar-levels In the function XBarLevels the bar-levels of nodes are givenon the basis of the bar-level of their mother. The function is based on thefollowing de�nition I formulated (see De�nition 7.2 for an exerpt from theformalization and Example 7.9 for a picture of a tree):

� If the bar-level of a node nd is not unde�ned, then the bar-level of ndis either 0, 1 or 2 (�rst axiom in De�nition 7.2). The bar-level of anempty leaf is unde�ned.

� If the bar-level of a node nd is 2, then the bar-level of its left daughteris 2 or its left daughter is empty. Furthermore, the bar-level of theright daughter of nd is 1 (second axiom in De�nition 7.2). Note thatthe implication can also be read in the other direction.

� If the bar-level of a node nd is 1, then the bar-level of its left daughteris 0. Furthermore, the bar-level of the right daughter of nd is 2 or theright daughter nd is empty (third axiom in De�nition 7.2). Note thatthe implication can also be read in the other direction.

� If the bar-level of a node nd is 0, then nd is a nonempty leaf, or theleft daughter of nd has bar-level 0 and the right daughter of nd hasbar-level 0 and is a nonempty leaf (fourth axiom in De�nition 7.2).Note that the implication can also be read in the other direction.

De�nition 7.2

FUNC BarLevel : NodeS -> PARTIAL~NatS

AXIOM BarLevel nd =/= Undef

==> (BarLevel nd) In Set(0,1,2)

AXIOM BarLevel nd = 2

<=> ( EmptyLeaf LeftDaughter nd

Or BarLevel LeftDaughter nd = 2


)

And BarLevel RightDaughter nd = 1


<=> BarLevel LeftDaughter = 0

And ( EmptyLeaf RightDaughter nd

Or BarLevel RightDaughter nd = 2

)


<=> NonEmptyLeaf nd

Or ( BarLevel LeftDaughter nd = 0

And NonEmptyLeaf RightDaughter nd

)

FUNC XBarLevels : TreeS -> BoolS

AXIOM XBarLevels tr

<=> BarLevel tr =/= Undef

Example 7.9

2

2 or < empty > 1

0 2 or < empty >

0 0

0 0

Note that the illustration in Example 7.9 is just a possible tree. Moreor fewer adjunctions than the depicted amount of two are permitted. Andof course it is possible to have a head with no adjunctions at all.

Because a head X requires two projections (X and XP), the predicateEmptyLeaf is required. For instance, even if a phrase does not contain acomplement, we need an X-projection, and this projection can only ariseby applying one of the structure-building operations. Since the operationsMerge and Move combine two trees into one, we need a substitute for thenon-existing complement. The predicate EmptyLeaf is used as a substitute.

The feature Category does not occur in the function BarLevel. Thisis not necessary because the three rules (axioms) of the function BarLevel

are mutually exclusive without referring to the feature Category: there areno nodes nd that could be described by two di�erent rules.


The need to refer to left and right daughters emerges since I acceptKayne's [Kay94] conclusion that there is only one possible way to arrangespeci�ers, heads, complements and adjuncts (see Section 1.3). For instance,the speci�er must precede the head. Therefore, a node with BarLevel 2

must have a node with BarLevel 2 or an EmptyLeaf (the speci�er) as itsleft daughter, and a node with BarLevel 1 (which dominates the head) asits right daughter.

The de�nition of BarLevel is recursive. If we want to compute the bar-level of the root of a tree, we have to compute the bar-levels of all thenodes of the tree. It is possible to compute the bar-level of a node of a treebecause trees are �nite, as is speci�ed in the tree module. In the fourthaxiom of the function BarLevel we see that lexical heads always adjoin tothe left.4 Namely, the bar-level of the left daughter is 0, which accordingto the same axiom means that it can either be a nonempty leaf or a nodewith a left and a right daughter. The latter possibility is required becauseadjuncts themselves can have an adjunct as a daughter.5 Therefore theright daughter in the fourth axiom can never be an adjunct: it must be anonempty leaf.

The �rst axiom in De�nition 7.2 implies that all nodes nd that do nothave a bar-level 0, 1 or 2 do have a bar-level that is unde�ned. For instance,if it is impossible to compute the bar-level of a certain node or if a node isan empty leaf, then its bar-level is unde�ned. It is impossible to computethe bar-level of a node nd which is inconsistent with respect to the X-rulesde�ned in the �rst four axioms in De�nition 7.2. Therefore the bar-levelsof nd and all the nodes that dominate nd are unde�ned.

The function XBarLevels at the bottom of De�nition 7.2 accounts forthe bar-level of the root of a tree tr. This boolean function fails if thebar-level of the root of tr is unde�ned. The bar-level of the root of tr isunde�ned (as we saw in the above paragraph) when the root of tr is anempty leaf or if the root of tr is inconsistent with respect to the X-rules orif it dominates a node which is inconsistent with respect to the X-rules.

Features The X-module also describes the distribution of features intrees. The function XBar tr in De�nition 7.1 calls the function XFeatures

(see De�nition 7.3) to ensure that the features in tr are correctly percolated.Features have such a prominent role in the Minimalist Program because ofthe importance of feature checking for deriving word order variation, and sothey need to be connected with X-Theory. Therefore features are percolated

4An illustration of a lexical head (V) which adjoins to another head (AgrO) is givenon Page 20 in Example 1.15). V is called the adjunct in this example.

5An illustration of an adjunct which has an adjunct as its daughter can be found inExample 1.17 on Page 22, where the adjunct AgrO has the adjunct V as its daughter.


up from the head in the formalization described here, so that features areavailable at all levels of the projections. This is desirable because we canthen retrieve the features of both trees with BarLevel 0 and BarLevel 2

that move for feature checking in their root.The X-module is the appropriate module to deal with the distribution

of features because features are connected with the units that X-Theorydescribes (XPs). In every XP the head is the node from which the pro-jections inherit their features. Within a tree tr with BarLevel 2 featurespercolate up from the head of tr to its mother (with BarLevel 1) and itsgrandmother (with BarLevel 2).6

In `traditional' X-Theory Category was the only feature that was per-colated up from the head to the head's mother and grandmother. This wasdone by always mentioning the same category variable (for example: X)twice in every X-rule, once on the left-hand side and once on the right-handside (for example: X �! X Complement). In the version of X-Theory for-malized here, on the other hand, the percolation of more features than onlycategory features is proposed, because this is a requirement for the successof the rest of the formalization. Namely, features need to be available at alllevels of a projection.

De�nition 7.3 shows the formalization of feature percolation. The nodesnd of a tree tr are divided into two groups: leaves and non-leaves. Thefeatures of a non-leaf nd are equivalent to the features of its head.7 Thefeature structure belonging to a leaf nd (if it is nonempty) must be a memberof the lexicon.

The requirement that the features of a nonempty leaf must be a lexicalitem is our equivalent of lexical insertion. The formalization can judgewhether a tree is built according to the Minimalist Program. It cannotbuild trees with the operations Merge and Move in combination with lexicalinsertion. The formalization deals with abstract trees that might have beenconstructed by Merge and Move. The only way to check whether lexicalinsertion took place correctly is by determining if all heads from the treeare taken from the lexicon.

The fact that BarLevel is not considered to be an inherent feature is veryadvantageous for the readability of the function XFeatures. If the featureBarLevel had been a part of the feature structure belonging to a node, thenthe features of the head would not have been equal to the features of itsprojections. Namely, the BarLevel of the head is 0 while the BarLevel of a

6In GeneralizedPhrase StructureGrammar this is called the Head Feature Convention[Gaz82] and in Head-driven Phrase Structure Grammar this is called the Head FeaturePrinciple (see [PS94]). These theories share with the current formalization the percolationof features connected with lexical heads.

7The de�nition of the notion `head' is given further on in this section, together withthe de�nitions of complements, speci�ers and adjuncts.


projection is either 1 or 2, dependent on the projection being intermediate(X) or maximal (XP). Therefore, the feature BarLevel would have beenseparated from the rest of the features if we treated it as an inherent feature,and this would imply an operation of removing the BarLevel feature fromthe rest of the features within the function XFeatures.

Something similar holds for the feature Word if we treat it according toChomsky's 1993 framework. In this framework only leaves carry the featureWord, because leaves are the only nodes of trees where words are depicted.In Chomsky's 1995 framework we see that words are present in all theprojections of a head. The ideas with respect to the feature Word fromthe 1995 framework are preferred over those in the 1993 framework sincethe former ideas simplify the function XFeatures. If the Word feature wouldhave been present in the head of a phrase, it would have to be separated fromthe rest of the features when the features of the head are percolated up tothe projections. In the way the feature Word is treated in this formalization,this extra operation is not necessary.

De�nition 7.3

FUNC XFeatures : TreeS -> BoolS

AXIOM XFeatures tr

<=> FORALL nd

( nd NodeOf tr

==> ( Not IsLeaf nd

==> Features nd = Features Head nd

)

And ( NonEmptyLeaf nd

==> (Features nd) In Lexicon

)

)

In a construction such as the tree in Example 7.10 all the right daughters,except for TP, are heads (see further on in this section) and therefore themothers inherit their features. For instance, the higher AgrO inherits thefeatures of the lower AgrO since the latter is a head.

Example 7.10

AgrS

AgrS TP

T AgrS

AgrO T

V AgrO


Additional restrictions In the minimalist framework the term `fea-ture checking' is associated with movement. In the boolean functionXRestrictions a kind of feature checking is formalized which cannot bereferred to as `feature checking', because it is not always associated withmovement (see De�nition 7.4).

De�nition 7.4

FUNC XRestrictions : TreeS -> BoolS

AXIOM XRestrictions tr

==> FORALL nd

( nd NodeOf tr

And BarLevel nd = Two

==> ( Value[Category] Complement nd

= Value[CompCat] nd

And Value[Category] Specifier nd

= Value[SpecCat] nd

)

)

The axiom in De�nition 7.4 indicates that all nodes nd in a tree tr thathave BarLevel 2 must have:

� a complement that has the same category as the value of the featureCompCat (if the complement is unde�ned, the value of the featureCompCat must also be unde�ned)

� a speci�er that has the same category as the value of the featureSpecCat (if the speci�er is unde�ned, the value of the feature SpecCatmust also be unde�ned)

Only nodes with BarLevel 2 are taken into account because these arethe only nodes that can have a complement as well as a speci�er. As wewill see further on in this section, nodes with BarLevel 1 do not have aspeci�er because the position of the speci�er is not dominated by the nodewith BarLevel 1 (see Example 7.13). A node with BarLevel 0 neitherhas a speci�er nor a complement because the complement and the speci�erpositions are not dominated by the node with BarLevel 0 (see Example7.13).

The features CompCat and SpecCat respectively indicate the categoryof the complement and the speci�er a given head selects. The featuresCompCat and SpecCat, as all other features of the head, are percolatedup to the projections of the head. Therefore it is possible to check thecategory features of the complement and the speci�er of nd (with BarLevel

2) against its CompCat and SpecCat values, respectively.


The phenomenon described in the above paragraph could be referred toas subcategorization. In Chomskyan linguistic theory, subcategorization islinked with the assignment of thematic roles (cf. [Cho95], [HK93]). Forinstance, whether a verb is transitive or intransitive is not a primitive prop-erty: it follows from the meaning of the verb. The verb see expresses anactivity that involves two participants: one active participant who sees, andan inactive object or participant that is looked at. The thematic roles (�-roles) that are assigned by the verb see are Agent (for the active participant)and Patient (for the inactive object or participant).

In the Minimalist Program [Cho95, Page 312�], the role of �-Theory isto make sure that derivations where not all arguments are assigned �-roleswill not converge (succeed). �-roles are not associated with movement butwith merger because they are assigned to a lexical item when it is insertedin a structure, and consequently lexical insertion is always merger and nevermovement. Because �-role assignment is connected with lexical insertion,�-roles are always assigned in the lowest position of a chain. For instance,a subject always receives its �-role when it is in the speci�er position ofthe VP, not when it is in the speci�er position of T or AgrS, or in aneven higher position. If the subject entered a derivation in the speci�erposition of, for instance, T, this derivation would be more economical thana derivation where the subject enters the derivation in the speci�er positionof VP, because the latter derivation involves more steps. However, theformer derivation would not converge because the object never occurred ina con�guration where it was assigned a �-role.

Subcategorization frameworks are not described within the MinimalistProgram. However, subcategorization turns out to be vital for the formal-ization. We need a way to represent what kind of complement or speci�era certain head may select, otherwise the formalization would for instanceallow transitive verbs to behave like intransitive verbs, by not forcing in-transitive verbs to select both a subject and an object. This is especiallyessential in Zwart's version since in this version the derivation is not guidedby the features of the lexical heads in a sentence. In Chomsky's 1993 ver-sion all lexical heads need to check all their formal features. Therefore theobject features of the verb will require the verb to select an object to checkagainst. Furthermore it proved to be essential for the word order of sen-tences that functional projections always appear in the same order. Hence,also functional heads must contain the features CompCat and SpecCat. Forinstance, if the formalization allowed the functional head AgrS to selecta CP complement instead of allowing the functional head C to select anAgrSP complement, the word order of a subordinate clause like the one inExample 7.11 would end up with the complementizer (that) in the wrongposition as in Example 7.12.


Example 7.11

that she kisses him

Example 7.12

she kisses that him

Therefore the function XRestrictions is applied to both lexical andfunctional projections. Most functional projections (AgrOP, CP etc. butnot DP) take DP speci�ers which arrive there by movement. Furthermore,functional heads are always `united' with their complements by the op-eration Merge, since, as we saw in Chapter 2, movement to complementpositions is impossible. In the lexical domain, that is within the VP, boththe speci�er and the complement are created by the operation Merge, sincein the lexical domain lexical insertion takes place. Of course lexical insertionis Merger by de�nition.

Summarizing, we can say that the function XRestrictions speci�es akind of feature checking which is not exclusively associated with movement,but which we need in order to approve only of sentences with a correct wordorder, and a correct meaning (in the sense that, for instance, intransitiveverbs never select a complement).

Stabler [Sta96, Page 108] proposes a comparable approach to the se-lection of complements and speci�ers. Both functional and lexical headsare associated with a list of features which may contain either zero, one ortwo selection features. The selectional features indicate the category of thespeci�er and/or complement the head selects. If a feature list contains twoselectional features, the �rst represents the complement and the second thespeci�er.

Speci�ers, heads, complements and adjuncts The X-module alsoidenti�es speci�ers, heads, complements and adjuncts within XPs (if theyexist). This module is a natural location to represent this information be-cause X-rules in the literature often contain these notions (for instance: XP�! Spec(i�er) X).8 Sometimes the information is not given in the rules (forinstance: XP �! YP X). In such cases the positions of speci�ers, heads,complements and adjuncts are discussed elsewhere, or this is supposed tobe familiar to the reader.

De�nition 7.5 consists of four di�erent axioms: one for each bar-level (2,1 and 0) plus one for cases in which the bar-level is unde�ned. The functionsSpecifier, Complement, Head and Adjunct are all partial functions. Thisimplies that the functions are unde�ned for certain trees. For instance:

8cf. [Hae91, Page 95]


� For a tree tr with BarLevel 2, the speci�er can only be unde�ned ifthe speci�er position (see the tree in Example 7.13) is `occupied' byan empty leaf (see the second conjunct in the �rst axiom in De�nition7.5). If the speci�er position is not occupied by an empty leaf, tr hasa speci�er because the root of tr dominates the speci�er position (seethe �rst conjunct in the �rst axiom in De�nition 7.5).

� A tree with BarLevel 1 does not contain a speci�er because the nodewith BarLevel 1 (i.e. X) does not dominate the speci�er position(see Example 7.13). This phenomenon is accounted for by the �rstconjunct of the second axiom in De�nition 7.5.

� Both the head and the adjunct in the tree in Example 7.13 do haveunde�ned heads and adjuncts because neither of the two dominates ahead or adjunct. In De�nition 7.5 this phenomenon is accounted forby the third conjunct of the third axiom: for leaves with BarLevel 0

adjuncts and heads are unde�ned.

� A tree with an unde�ned bar-level, i.e. an empty leaf, does not have aspeci�er nor a complement nor a head nor an adjunct for the obviousreason that it does not dominate a speci�er position or a complementposition etc. (see the fourth axiom in De�nition 7.5).

De�nition 7.5

FUNC Head : TreeS -> PARTIAL~TreeS

FUNC Complement : TreeS -> PARTIAL~TreeS

FUNC Adjunct : TreeS -> PARTIAL~TreeS

FUNC Specifier : TreeS -> PARTIAL~TreeS

AXIOM BarLevel tr = 2

==> ( Not EmptyLeaf LeftDaughter tr

==> Specifier tr = LeftDaughter tr

)

And ( EmptyLeaf LeftDaughter tr

==> Specifier tr = Undef

)

And Complement tr = Complement RightDaughter tr

And Head tr = Head RightDaughter tr

And Adjunct tr = Adjunct RightDaughter tr



And ( Not EmptyLeaf RightDaughter tr

==> Complement tr = RightDaughter

)

And ( EmptyLeaf RightDaughter tr


==> Complement tr = Undef

)

And ( IsLeaf LeftDaughter tr

==> Head tr = LeftDaughter tr

And Adjunct tr = Undef

)

And ( Not IsLeaf LeftDaughter tr

==> Head tr = Head LeftDaughter tr

And Adjunct tr = Adjunct LeftDaughter tr

)



And Complement tr = Undef

And ( IsLeaf tr

==> Head tr = Undef


)

And ( Not IsLeaf tr

==> Head tr = RightDaughter tr

And Adjunct tr = LeftDaughter tr

)

AXIOM BarLevel tr = Undef


And Complement tr = Undef

And Head tr = Undef


Example 7.13

XP

YP X

(Speci�er)

X ZP

(Complement)

W X

(Adjunct) (Head)

The de�nitions of speci�ers, complements, heads and adjuncts are re-cursive. For instance, if the root of a certain tree (say tr with BarLevel

2) does not have a daughter that is a complement position, but if the rootdoes dominate a complement position, then the complement is de�ned as


the complement of one of the daughters (see the third conjunct of the �rstaxiom in De�nition 7.5). If the right daughter of tr is an empty leaf, thebar-level of the right daughter is unde�ned and therefore the complementof tr is unde�ned (see fourth axiom).

Sometimes the de�nitions seem to allow incorrect trees. For instance:

� In the �rst axiom in De�nition 7.5 the left daughter of tr can either bean empty leaf (second conjunct) or not an empty leaf (�rst conjunct).If the left daughter is not an empty leaf this can either imply that it isa nonempty leaf or a non-leaf (i.e. a tree with more than just a root).If the left daughter is a nonempty leaf, tr would not be a correct treein a theory where it is assumed that all heads should project. We alsoassume that only XPs can serve as speci�ers and complements, andXPs can never be (nonempty) leaves. Still we leave the de�nition asit is because this is not the place to prohibit speci�ers that are leaves.Speci�ers that are leaves are excluded by the function BarLevel. Inthis function (second axiom in De�nition 7.2) we claim that speci�ers(left daughters of trees with BarLevel 2) must be trees with BarLevel2. And from the same axiom we can deduce that trees with BarLevel

2 can never be leaves as their roots must always have a left daughter(possibly empty) and a right daughter (with BarLevel 1).

� The left daughter of a tree tr with BarLevel 1 can either be an emptyleaf, a nonempty leaf or a non-leaf (i.e. a tree with more than justa root). However, only two of the three possibilities are correct ac-cording to the Minimalist Program: nonempty leaves and non-leaves.An empty left daughter of a tree with BarLevel 1 is incorrect as isspeci�ed in the function BarLevel (see De�nition 7.2), and thereforewe do not have to worry here about the incorrectness of empty nodesas a left daughter of trees with BarLevel 1 (see last two conjuncts ofthe �rst axiom of De�nition 7.5).

A projection can be either deeper or shallower than the tree in Example7.13. The di�erence occurs at BarLevel 0.

The projection is deeper in the case of branching adjuncts. An adjunct,which always is the left daughter of a tree with BarLevel 0 and which has asister that is a head, can itself also have an adjunct as a left daughter (and ahead as its right daughter) etc. This structure is needed for head movement.For instance, if the head of the VP moves to AgrOP to check its features,it adjoins to AgrO. If the head moves further to TP the whole adjunctionconstruction from AgrOP, that is, the whole phrase that is dominated bythe highest node with BarLevel 0, adjoins to T. Again, if the head movesfurther, the whole left daughter of T adjoins to AgrS. In Example 7.10 thedepth of the adjunct in AgrSP is shown. Heads never branch. In the fourth


axiom in De�nition 7.2 we see that right daughters of nonempty heads withBarLevel 0 always are empty leaves.

The projection is shallower than the tree in Example 7.13 when the leftdaughter of a tree with BarLevel 1 is a nonempty leaf. The third axiom inDe�nition 7.5 shows that trees with BarLevel 0 can be nonempty leaves.The second axiom in the same example shows that if the left daughter of atree with BarLevel 1 is a nonempty leaf, then this nonempty leaf must bea head.

Except for being able to refer to the speci�er, complement, head oradjunct of a certain tree, it is sometimes necessary to refer to a certaintree as a speci�er, complement, head or adjunct. Therefore the functions inDe�nition 7.6 are de�ned. The functions are rather straightforward: a treetr1 is a speci�er if there is a tree tr2 of which tr1 is the speci�er etc.

We need the function IsAdjunction to be able to refer to the mothersof adjuncts. This is convenient with respect to head movement where themoving element grows with each step (see Example 7.10), because in thesecond move it takes along the construction it adjoined to in the �rst move,etc. Because an adjunction is the mother of an adjunct it can never be aleaf (see �fth axiom in De�nition 7.6).

De�nition 7.6

FUNC IsSpecifier : TreeS -> BoolS

FUNC IsComplement : TreeS -> BoolS

FUNC IsHead : TreeS -> BoolS

FUNC IsAdjunct : TreeS -> BoolS

FUNC IsAdjunction : TreeS -> BoolS

AXIOM IsSpecifier tr1

<=> EXISTS tr2 (Specifier tr2 = tr1)

AXIOM IsComplement tr1

<=> EXISTS tr2 (Complement tr2 = tr1)

AXIOM IsHead tr1

<=> EXISTS tr2 (Head tr2 = tr1)

AXIOM IsAdjunct tr1

<=> EXISTS tr2 (Adjunct tr2 = tr1)

AXIOM IsAdjunction tr

<=> BarLevel tr = 0

And Not IsLeaf tr

7.3. TWO-LEVEL X-THEORY 119

7.3 Two-level X-Theory

In this section, I will discuss why I prefer to apply Chomsky's 1993 versionof X-Theory instead of the later versions by Chomsky [Cho95, Page 241�]or Zwart [Zwa97, Page 171�], which I discussed in Section 7.1. As wasmentioned in Section 7.1, X-Theory is no longer presupposed in the laterversions of the Minimalist Program. X-Theory is now derived from mini-malist assumptions. The main idea behind the new versions of X-Theoryis that X-Theory may no longer force us to build a tree in a way that isnot natural with respect to the lexical material the tree is based on. Theoperations Move and Merge are the only structure-building operations inthe Minimalist Program. They both construct trees by combining two othertrees. If we do not want X-Theory to be independent, we do not want toassume an empty tree when a given head does not select a speci�er or acomplement just to be able to derive the right number of projections, asin the case of the speci�er of X in Example 7.14. If X-Theory is not inde-pendent there is no `right' number of projections. For instance, if a head Xselects a complement YP and no speci�er, the head X only projects once,as in Example 7.15.

Example 7.14

XP

< empty > X

X YP

Example 7.15

XP

X YP

In the rest of this section we will see that the idea that heads onlyproject if they select a speci�er and/or a complement is problematic. Fortwo di�erent reasons we will come to the conclusion that we have to assumethat a head always selects at least one speci�er or one complement, possiblyan empty one. This makes the new version of X-Theory so little di�erentform the earlier three-level version, that I decided not to implement the newversion of X-Theory.

The �rst reason why we have to assume that a head always selects at leastone speci�er or complement is caused by the fact that we have to be able


to point out all the speci�ers, adjuncts and complements in a tree. Thesepositions are vital for the theory of movement, which says that movement isonly possible from the complement domain of a given head to the checkingdomain of that same head. The complement domain consists of all thenodes that are re exively dominated by the complement of a head X. Thechecking domain consists of the speci�er position and the adjunct positionof a head X.

The fact heads do not always have to project, namely not in case theydo not select a complement nor a speci�er, prevents us from making thenotions `complement', `speci�er' and `head' deterministic. Since heads donot always project, complements and speci�ers may appear in a tree as aleaf (see for instance the complement in Example 7.16). Of course, heads arealways leafs. From the above facts we can deduce the following problematicX-rule:

[+projection] �! [-projection], [- projection]9

The above rule is problematic, because it both describes a tree withspeci�er as a left daughter and a head as a right daughter (see Example7.17), and a tree with a head as a left daughter and a complement as a rightdaughter (see Example 7.18). In the formalization described in Section 7.2,we could unambiguously point out speci�ers and complements in a tree onthe basis of the bar-levels of their mothers in combination with their beinga left or a right daughter:

� a speci�er is the left daughter of a node with BarLevel 2

� a complement is the right daughter of a node with BarLevel 1

If we apply the same idea to the X-rules of the new version of X-Theory,the head position gets mixed up with both the speci�er position and thecomplement position:

� a speci�er is the left daughter of a node which is [+projection]

� a complement is the right daughter of a node which is [+projection]

� a head is the left or the right daughter of a node which is [+ projection]

9I use Zwart's equivalent of BarLevel here, because in the formalization the X-rulesare also solely based on bar-levels.


Example 7.16

DP

D N

the woman

(head) (complement)

Example 7.17

XP

Y X

(speci�er) (head)

Example 7.18

XP

X Y

(head) (complement)

To compensate for the fact that the head cannot be unambiguously de-�ned, categorial features are needed to formalize X-rules (see for instanceDe�nition 7.7, second axiom, second and fourth conjunct). It is possible todistinguish heads from complements and speci�ers because heads have thesame category as their mother, while speci�ers and complements do not.However, in this way we start a circular reasoning which is avoided whenwe apply X-Theory as it is described in Section 7.2. The circular reasoningoriginates because the function IsProjection (see De�nition 7.7) is basedon the feature Category while the function XFeatures (see De�nition 7.3)which takes care of the percolation of features (such as Category) relies onbar-levels. In the traditional type of X-rules (e.g. X ! X, YP) there alsowas a variable present for the feature Category but we were able to bancategorial features from the function BarLevel (see De�nition 7.2) in theformalization which we based on these X-rules.

Another reason for categorial information in the function IsProjection

is the fact that without this information we cannot determine which nodeis the highest node of a certain projection. What formerly was an XPcould now appear as an X (if it does not have a speci�er or a complement).The only way of determining whether a certain node is the top level of a


projection is by looking at its mother (see �rst and second conjunct of thesecond axiom of De�nition 7.7). If the mother has a di�erent category weknow that it is the top level. However, this solution is not adequate becauseit might result in a head of category X taking a complement of the categoryX.10 For instance, Example 7.19 shows a Larsonian structure where a verbtakes a verb complement.11

De�nition 7.7

FUNC IsProjection : NodeS -> PARTIAL~NatS

AXIOM IsProjection nd =/= Undef

==> (IsProjection nd) In Set(0,1)

AXIOM IsProjection nd1 = 1

<=> EXISTS nd2

( nd1 = Mother nd2

And Value[Category] nd1

=/= Value[Category] nd2

And ( IsProjection nd2 = 1

Or IsProjection nd2 = 0

)


= Value[Category] Sister nd2

And ( IsProjection Sister nd2 = 1

Or IsProjection Sister nd2 = 0

)

)

AXIOM IsProjection nd1 = 0

<=> IsLeaf nd1

Or EXISTS nd2

( nd1 = Mother nd2


=/= Value[Category] nd2

And IsProjection nd2 = 0


= Value[Category] Sister nd2

And ( IsProjection Sister nd2 = 0

And IsLeaf Sister nd2

)

)

FUNC XProjections : TreeS -> BoolS

AXIOM XProjections tr

<=> IsProjection tr =/= Undef

10Generally, this is not supposed to be the case (see [Hoe84]).11The Larsonian structure is an analysis of multi-argument verbs [Lar88].


Example 7.19

VP

DP V

she

< empty > VP

DP V

him

V DP

gives

books

A solution to the problem sketched above would be to make the di�erencebetween heads on the one hand and speci�ers and complements on the otherhand unambiguous. This could be accomplished by requiring speci�ers andcomplements to project even though their heads do not select a speci�er ora complement.

Another reason why we have to assume that a head always selects at leastone speci�er or complement is caused by the fact that I adopt the linearordering of speci�ers, adjuncts, heads and complements that Kayne [Kay94]proposes in his Linear Correspondence Axiom (LCA). Kayne derives thislinear ordering from the hierarchical structure of trees: if two subtrees Aand B of a tree C, occur in C in a certain hierarchical relation (namely, Aasymmetrically c-commands B), then A linearly precedes B. However, theLCA puts some requirements on X-Theory, among which the requirementthat complements cannot be bare heads, since otherwise a head cannotasymmetrically c-command its complement.12

Since one of the basic ideas behind X-Theory was to make phrase struc-ture rules category-independent, we do not want to construct a special X-rule for categories which can serve as a complement. Hence, we must con-clude, again, that all categories must project before they can be selected asa speci�er or a complement.

Now we have concluded, for two di�erent reasons, that heads mustproject before they can be selected by another head as a speci�er or a com-plement, we will have a closer look at the nature of this vacuous projection.Below we will see that the assumption of a null-complement is preferredover the assumption of a null-speci�er.

12See [Kay94, Page 7�] for an explanation.


Hale and Keyser [HK93] argue that also intransitive verbs take a com-plement. For instance, the verb to dance is actually an abstract V, in whichthe nominal head of its NP-complement (dance) is incorporated, hence: todance a dance. This idea is applied by Stabler [Sta96, Page 108] in hisderivational formalization of some minimalist ideas.

In Stabler's formalizations, intransitive verbs are represented as projec-tions in the lexicon (see Example 7.20 for a simpli�ed version of the lexicalitem for the verb to dance). This is remarkable because, of course, normallythe lexicon only contains heads. Stabler needs this solution since, as we sawin Section 7.2, he assumes that heads have a list of selectional features inthe order object-subject. Since intransitive verbs only select a subject (i.e.speci�er), Stabler needs intransitive verbs to be represented in the lexiconwith the complement already included, so that the �rst (and only) elementon the list of selectional features (D) will be interpreted as a speci�er. Ex-ample 7.21 shows a simpli�ed version of the lexical item for the transitiveverb to love. The �rst feature on the list of selectional features representsthe object (or complement), the second represents the subject (or speci�er).

Example 7.20

V

V < empty >

[D]

dance

Example 7.21

V

[D;D]

love

For nouns Stabler has a di�erent solution. Nouns do not contain a null-complement in the lexicon. Stabler does not give a reason for this di�erencein treatment of verbs and nouns, but the reason might be that it is notnecessary for the simple type of DPs he deals with in his formalization,which only contain determiners and nouns. Another reason might be thatnouns never seem to select a speci�er, so there is no risk of confusing theelement on the list of selectional features.13

The fact that unprojected complements do not cause problems for Sta-bler's formalization lies in the fact that his approach is derivational and

13See for instance [Lat97].


not representational. At the moment that the head D and the unprojectedN-complement merge, an arrow (<) is put in the label of their mother asin Example 7.22.14 The arrow indicates that the features of the label arepercolated from the left daughter (D). Therefore, complements can be de-�ned as the right daughter of a node with the label `< ', and heads as theleft daughter of a node with the label `<'. Speci�ers can be de�ned as theleft daughter of a node with the label `>'. The mother of the speci�er is anode with the label `>' because the features of the mother are percolatedfrom the right daughter (see Example 7.23).

Example 7.22

<

D N

[N ] []

the car

Example 7.23

>

< <

D N V <

[N ] [] [D;D]

the girl loves

D N

[N ] []

her car

The fact that Stabler can apply (category) features to distinguish com-plements and speci�ers from heads and projections of the head, and I can-not, lies in the fact that Stabler's approach is derivational and my approachis representational. In a representational approach one wants to preventincorrect structures from being approved of, while in a derivational ap-proach incorrect X-structures are prevented from being built. In Stabler'sapproach, incorrect feature percolation can be prevented by requiring thatMerge and Move always project one of the two trees they combine. In my

14Note that Stabler cancels (i.e. deletes) the selectional feature N of the determiner atthe stage of the derivation Example 7.22 represents. I maintain it here for the sake ofclarity.


approach, it is possible that we have to judge a structure where no daugh-ter percolates its features since Merge and Move do not play a role, andhence it is impossible to impose requirements on the structure via Mergeand Move. Therefore it is impossible to rely on (category) features whende�ning X-rules, as we already saw in this section.

Although we concluded that one of the reasons for requiring heads toproject before they are selected as complements and speci�ers is the rep-resentational nature of the formalization, it still seems advizable to obeythe projection requirement in both representational and derivational ap-proaches. The fact that Kayne's LCA requires complements to project isnamely of great importance for both derivational and representational ap-proaches, especially if we want to eliminate X-Theory entirely, as Chomsky[Cho95, Page 249] proposes. If we want to eliminate X-Theory we needto derive the linear order of speci�ers, adjuncts, heads and complements,which is now simply given in X-Theory. Since it is possible to derive thislinear ordering applying Kayne's LCA, we need to obey the requirementsthe LCA poses on the structure. Assuming projected complements is oneof those requirements.

The most important goal of the new versions of X-Theory is to avoidvacuous projections. I argued that it is impossible to avoid vacuous projec-tions since each head seems to need a complement, which causes the needfor null-complements in some cases. Therefore I decided not to formalizeone of the new versions of X-Theory.

7.4 Summary

The module on X-theory is identical for Chomsky's and for Zwart's frame-work. The latest ideas about X-theory, as described by Chomsky [Cho95,Page 241�] and Zwart [Zwa97, Page 171�], appear not to be suitable forformalization and therefore the original X-theory is applied in the formaliza-tion of Zwart's framework. The reason why the new ideas are not suitable isthat speci�ers, heads and complements cannot be made mutually exclusive.

Features have such a prominent role in the minimalist framework thatthey have to be connected with X-theory. In the original X-rules, [cat-egory] is the only feature that is percolated. In the formalization, I de-scribe the percolation of category features and other features in the func-tion XFeatures. Therefore the function XBarLevels, which is closest to theoriginal X-rules, does not contain category features.

The module on X-theory deals with subcategorization. The functionXRestrictions de�nes that the speci�ers and complements of a phrasemust be licensed by the head of the phrase.

The positions of speci�ers, heads, complements and adjuncts are explic-itly de�ned in the X-module. It is necessary to de�ne these positions in

7.4. SUMMARY 127

order to be able to use the notions `speci�er', `head', `complement' and `ad-junct' in the formalization. This module seems to be the correct place torepresent this knowledge, because in the literature X-rules are often used tode�ne notions such as `speci�er' and `complement'.

Chapter 8

Chains

8.1 Introduction

Chains in the formalization represent what is called movement in the Min-imalist Program. There, movement is connected with feature checking. Aconstituent moves only if it is forced to do so because of the need of featurechecking. A moving constituent is `attracted' to the constituent it moves towhen the both constituents have similar features. The moving constituentis always a lexical projection or a lexical head. The landing site is always anode within a functional projection (such as the speci�er of AgrSP or theposition adjoined to the head of TP). Features are divided into three classes:formal, semantic and phonological. The formal features are the only classof features that require feature checking. A lexical constituent may checkits formal features in di�erent functional projections, so that it can movemore than once. In each functional projection where it lands, it must checkat least one feature. The overlap in features of the moving constituent andthe landing side must therefore concern at least one joint feature-value pair.The process of movement of lexical constituents to functional projectionswith overlapping features is called feature checking.

The feature checking requirement described above can be derived fromthe Economy of Derivation [Cho91]. Zwart [Zwa96, Zwa97] considers it tobe a consequence of the Economy of Derivation that the derivation mustinvolve as few steps as possible. A way to restrict the number of movementsis to allow only movements which involve feature checking.

There are more constraints on movement in the minimalist theory:

� Movement is only allowed to speci�er positions of functional heads andpositions adjoined to heads of functional projections (i.e. the checkingdomain).

129

130 CHAPTER 8. CHAINS

� The moving element must originate from a position re exively domi-nated by the complement (i.e. the complement domain) of the func-tional head whose checking domain the element moved to.

� XPs are only allowed to move to speci�er positions, since the speci�erposition is the position where the type of formal features (NP-features,cf. [Cho93, Page 28�]) that XPs are associated with can be checked.Xs are only allowed to move to positions adjoined to heads, since thespeci�er position is the position where the type of formal features (V-features, cf. [Cho93, Page 28�]) that Xs are associated with can bechecked.1

Chomsky [Cho93] assumes that the Economy of Derivation not onlyimplies that the derivation involves as few steps as possible, but also thatthe steps in the derivation are as short as possible. That subjects mustmove from the speci�er of the VP to the speci�er of the AgrSP skippingthe speci�er of AgrOP is problematic from this point of view. Therefore,Chomsky [Cho93, Page 17] introduces the notion `equidistance', of whichthe de�nition will not be given here for the sake of simplicity. The notion`equidistance' makes it possible to consider the movement from positionP3 to position P1 in Example 8.1 to be the shortest possible movement,even though a possible candidate landing site (P2) which is closer to P3 isskipped. Namely, if two positions are equidistant according to Chomsky'sde�nition, a movement to either the higher or the lower position of the twocan be referred to as the shortest move.

Example 8.1

.

P1 .

. .

P2 .

. P3

Zwart [Zwa96] considers the `shortest steps and fewest steps requirement'to be contradictory, since shorter steps in a derivation will result in moresteps and fewer steps in a derivation will result in longer steps. Zwarttherefore argues that Economy of Derivation only involves the fewest stepsrequirement. As we saw earlier in this section, the fewest steps requirementis connected with the feature checking requirement.

1Cf. Uniformity of Attachment [Cor97, Page 18].


The fact that there is no shortest steps requirement in Zwart's 1997framework makes the notion `equidistance' (which turns out to be problem-atic in many cases, see for instance [Zwa97, Page 238�]) super uous. Butstill one needs a way to prevent the subject (i.e. the speci�er of the VP)from moving to the speci�er of AgrOP, and the object (i.e. the complementof the VP) moving to the speci�er of TP and AgrSP as in Example 8.2. Al-though the PF-representation of the structure is correct, this is not the kindof structure we want to be described by the formalization (because of theconfused indices). Since no satisfying solutions to this problem have beenpresented for Dutch, I solved this problem in a trivial way in the formaliza-tion: all the movements that are needed are given and all other movementsare considered to be incorrect (see Section 8.2).2

Example 8.2

CP

C

C AgrSP

ek C DP AgrS

datl jiji

ek TP

ei T

ek AgrOP

DP AgrO

hemj

ek VP

ej V

V ei

kustk

In the next section I will give the formalization which is a representa-tional interpretation of the derivational constraints given above. Ratherthan describing movements that build chains, I describe connections be-tween two nodes that build chains.

As we saw in Chapter 3, the choice of a representational approach forcesus to apply copies instead of traces to indicate that an element moved from

2For a solution regarding English see Stabler [Sta96, Page 115], who applies a simpleversion of an idea from Ferguson and Groat [FG94] in one of his formalizations.


one position to another. It is crucial that we check that all the copies withina chain are in fact copies of the original that was introduced in the structureby lexical insertion.3 Whether two positions in a tree may be connected bya chain is given in the formalization. But we need an extra constraint whichonly allows chain links between exact copies. This constraint is not neededin a derivational approach since movement already implies that the linkedpositions are associated with the same content.


In Section 8.1 I mentioned that movement is connected with feature checkingin the Minimalist Program. In the formalization, which is a representationalversion of the Minimalist Program, movements are represented by chains,that is, sequences of connected nodes. Feature checking is represented bya constraint which concerns all the copies in a chain, that is all elementsthat build the chain except for the original in the lowest position of thechain where lexical insertion takes place. This constraint implies that acopy must have formal features which can be checked against the formalfeatures of the functional projection it is part of.4 Feature checking succeedsif the lexical constituent contains at least the same formal features as thefunctional projection it is part of. The reason why only the copies (and notthe original) in a chain are associated with feature checking lies in the factthat only the copies in a chain can be compared with moved elements inthe Minimalist Program.

At this point I give a brief overview of the functions speci�ed in thechain module of the formalization. After that I will give the formalizationof the di�erent functions in combination with a more detailed description.

To be able to check the formal features of the lexical constituent againstthose of the functional projection, we have to separate the formal featuresfrom the rest of the features (i.e. semantic and phonological features) in afeature structure. The formal features of lexical constituents are isolatedby the function FFLexical nd (where `FF' stands for `formal features'); theformal features of the functional projection are isolated with the functionFFFunctional nd.

In the Minimalist Program the formal features of the functional headsare split up in two categories: NP-features and V-features. NP-features arechecked by movement to the speci�er of the functional head, and V-featuresare checked by movement to the position adjoined to the functional head.In the formalization presented here, NP-features and V-features are not ex-

3See also Brody [Bro95, Page 139].4As we saw in the previous section, the copy may either stand in the speci�er position

of the functional head or in the position adjoined to the functional head.


plicitly de�ned as NP-features and V-features. The function FFFunctional

nd yields feature structures that represent what is referred to as NP-featuresand V-features within the Minimalist Program. The type of features thatare checked in a position nd depends on whether nd is a speci�er positionor a position adjoined to a head.

The actual feature checking is performed by the boolean functionFeaturesChecked tr. With this function we can determine whether ev-ery lexical constituent in the tree tr, which is part of a chain and which isnot the lowest position of that chain, can check its formal features againstthose of the functional projection it is part of.

Whether or not a constituent is part of a chain, and, if so, whether ornot it is the lowest element in the chain, can be determined by the functionLinkSource nd1. This function indicates links between nodes in a tree.LinkSource nd1 = nd2 means that there is a link from a node nd2 (thesource) to the node nd1 (the target) as we see in Example 8.3. Hence,both nodes are the roots of an element in a chain. Since movement inthe Minimalist Program is always upward and leftward, the source (nd2) isalways lower than and to the right of the target (nd1). If LinkSource nd

is unde�ned, we know that either nd is the root of the lowest element of achain (since it has no source, see for instance nd3), or the constituent thathas nd as a root is not an element of a chain at all.

Example 8.3

.

nd1 .

. .

. .

nd2 .

. .

. nd3

. .

As we saw in Section 8.1, the requirement that feature checking must oc-cur is not the only constraint on movements. Further constraints are, �rstly,that the source of the movement is in the complement domain, while thetarget of the movement is in the checking domain of a given functional head,and secondly, that XPs only can move to speci�ers while Xs only can move


to positions adjoined to a head. In Section 8.1 I argued that I need an addi-tional constraint to prevent subjects from moving to the speci�er of AgrO.All these constraints, plus the boolean function FeaturesChecked tr whichI mentioned earlier this section, are united in the function CorrectChains

tr, which guarantees that all chains in the tree tr are built according tothe Minimalist Program, as the name of the function already suggests.

Now I will proceed to the more elaborate descriptions of the functionsgiven above.

The function FFLexical nd (see De�nition 8.2) yields a feature structurethat contains the formal features that the node nd inherited from the lexicon.All other features, such as semantic features, are left aside. For instance,the lexical item for the Dutch verb form ziet (sees), given in De�nition8.1, is a feature structure containing a Category feature, a Sememe feature,a Subject feature (which contains the agreement features for the subjectselected by the verb), an Object feature (which contains the agreement fea-tures for the object selected by the verb), a Tense feature, a CompCat feature(for subcategorization with respect to the complement) and a SpecCat fea-ture (for subcategorization with respect to the speci�er). The only featuresending up in the feature structure that FFLexical nd yields are the formalfeatures Object, Subject, Tense and Inversion.

De�nition 8.1

MODULE Lexicon

IMPORT LexiconCommon

AXIOM Lexicon

= .

.

.

++ ( EmptyCatStruct[V]

Add[Sememe] "zien"

Add[Subject] ( EmptyStruct


Add[Person] Third


Add[Gender] Masculine

)

)

Add[Object] ( EmptyStruct


Add[Person] First

Add[Number] Plural

Add[Gender] Neuter

)

Add[Case] Accusative

)


Add[Tense] Present

Add[Inversion] No

Add[CompCat] D

Add[SpecCat] D

)

.

.

.

END MODULE

It would have been possible to split up the features in the formalization intwo di�erent types: formal and nonformal (i.e. phonological and semantic).In that case the function FFLexical nd (see De�nition 8.2) would havelooked more elegant than it does now, as it would not have been necessaryto sum up all features that have to be checked. Just referring to the formalfeatures of the node nd would have been su�cient. The reason why thissolution is not preferred is that the formalization in De�nition 8.2 makesexplicit which features have to be checked if they are present in the relevantlexical item. The formalization never literally refers to formal, semanticor phonological features. But in the description of the formalization I willalways be explicit about the types of features we are dealing with in a givenfunction.

FFLexical nd only yields a nonempty feature structure for nodes thatare verbs of bar-level 0, nouns of bar-level 0, and determiners of bar-level 2,as these represent the lexical constituents that may move for feature check-ing. De�nition 8.2 de�nes that only the tense, inversion, subject and objectfeatures of a verb are formal features. The �rst axiom in De�nition 8.2literally says that for a node nd with bar-level 0 and category V, FFLexicalnd yields the features of nd of which we obtain only the tense, inversion,subject and object features. For instance, a verb may adjoin to AgrO tocheck its object agreement, then to T to check its tense feature, then toAgrS to check its subject agreement, and �nally to C to check its inversionfeature.

Determiners (Ds) of bar-level 2 must check their agreement, case andWh-features, as we see in the second axiom. For instance, the subject DPmay move to the speci�er of T to check its case feature, then to the speci�erof AgrS to check its agreement feature, and �nally to the speci�er of C tocheck its Wh-feature.

In the third axiom we see that nouns of bar-level 0 must check theirdeterminer, agreement, case and Wh-features. Later on in this section Iwill argue why and how nouns must check these features.

Certain verbs, nouns and determiners do not have all the features thatare named in the function FFLexical. For instance, intransitive verbs do nothave an object feature. In that case the feature structure that FFLexical


nd yields only contains subject, inversion and tense features.In the fourth axiom we see that if nd is an adjunction (i.e. the mother of

an adjunct), FFLexical nd yields the same feature structure as its adjunct.In this way the formal features of a moving head can percolate up to the rootof the adjunction structure the moving head is part of. Hence, FFLexicalnd, where nd is for instance the upper AgrS in Example 8.4, yields theformal features of the V at the bottom of the structure. Since nd (AgrS) isan adjunction, FFLexical nd equals FFLexical Adjunct nd. The adjunctof AgrS is T, which in its turn is also an adjunction. Eventually, via AgrO,we �nd that FFLexical nd yields the formal features of V.

Example 8.4

AgrS

AgrS TP

T AgrS

AgrO T

V AgrO

For all the remaining nodes nd in a tree, FFLexical nd yields an emptyfeature structure as we see in the �fth axiom.

De�nition 8.2

FUNC FFLexical : NodeS -> FeatureStructS


And Value[Category] nd = V

==> FFLexical nd

= (Features nd) Keep Set(Subject, Object, Tense, Inversion)


And Value[Category] nd = D

==> FFLexical nd

= (Features nd) Keep Set(Agreement, Case, WhWord)


And Value[Category] nd = N

==> FFLexical nd

= (Features nd)


Keep Set(Determiner, Agreement, Case, WhWord)

AXIOM IsAdjunction nd

==> FFLexical nd

= FFLexical Adjunct nd

AXIOM Not ( BarLevel nd = 0

And Value[Category] nd = V

)

And Not ( BarLevel nd = 2

And Value[Category] nd = D

)

And Not ( BarLevel nd = 0

And Value[Category] nd = N

)

And Not IsAdjunction nd

==> FFLexical nd

= EmptyStruct

The function FFFunctional nd yields a feature structure containing thefeatures that can be checked by movement to nd. As we saw earlier, featurechecking can only take place in positions within functional projections (suchas AgrSP and TP). De�nition 8.3 shows that only the adjuncts and speci�ersof functional projections (i.e. the checking domain) are available for featurechecking. Hence, the formal features of functional heads can only be checkedin their checking domain.

At this point I will give a brief explanation of the axioms in De�nition8.3. Next, a more elaborate description will be given of some unusual cases.

In the speci�er position of C (nd is a speci�er and the category of itsmother is C), the Wh-feature of the subject or object DP can be checkedagainst the Wh-feature of the head of CP since FFFunctional nd yieldsthe Wh-feature (WhWord)) of the functional head C (�rst axiom).5 In theadjunct position of C, tense, inversion and subject agreement features ofthe verb can be checked (second axiom). In the speci�er position of AgrSPthe agreement feature of the subject DP can be checked against the subjectagreement feature of the head of AgrSP (third axiom). In the adjunct po-sition of AgrSP the subject agreement features of V can be checked againstthe subject agreement features of the head of AgrSP (fourth axiom). In thespeci�er position of TP the case feature of the subject DP can be checkedagainst the case feature of the head of TP (�fth axiom). In the adjunct po-sition of TP the tense feature of V can be checked against the subject casefeatures and the tense feature of the head of TP (sixth axiom). In the spec-i�er position of AgrOP the case and agreement features of the object DPcan be checked against the object feature (including case and agreement) of

5Note that the function Keep takes a feature structure and a set of feature names,and yields another feature structure which is the �rst feature structure of which thefeature-value pairs of which the feature names are mentioned in the set are kept.


the head of AgrOP (seventh axiom). In the adjunct position of AgrOP theobject feature (including case and agreement) of V can be checked againstthe object features of the head of AgrOP (eighth axiom). In the speci�erposition of DP no features are checked (ninth axiom), but it is mentionedexplicitly since the speci�er position of DP in principle is a checking posi-tion because D is a functional category. In the adjunct position of DP thedeterminer, case, agreement and Wh-features of N can be checked againstthe determiner, case, agreement and Wh-features of the head of DP (tenthaxiom). All non-checking positions, which also yield an empty feature struc-ture, are dealt with in the eleventh axiom (i.e. the closure of the functionFFFunctional).

De�nition 8.3

FUNC FFFunctional : NodeS -> FeatureStructS

AXIOM IsSpecifier nd

And Value[Category] Mother nd = C

==> FFFunctional nd

= (Features Head Mother nd) Keep Set(WhWord)

AXIOM IsAdjunct nd


==> FFFunctional nd

= ( Features Head Mother nd)

Keep Set(Inversion,Tense,Subject)


And Value[Category] Mother nd = Agrs

==> FFFunctional nd

= (Value[Subject] Head Mother nd)

Keep Set(Agreement)

AXIOM IsAdjunct nd


==> FFFunctional nd


Keep Set(Agreement)


And Value[Category] Mother nd = T

==> FFFunctional nd


Keep Set(Case)

AXIOM IsAdjunct nd

And Value[Category] Mother nd = T

==> FFFunctional nd

= (Features Head Mother nd)

Keep Set(Tense)



And Value[Category] Mother nd = Agro

==> FFFunctional nd

= (Value[Object] Head Mother nd)

AXIOM IsAdjunct nd


==> FFFunctional nd


Keep Set(Object)


And Value[Category] Mother nd = D

==> FFFunctional nd

= EmptyStruct

AXIOM IsAdjunct nd

And Value[Category] Mother nd = D

==> FFFunctional nd


Keep Set(Determiner,Case,Agreement,WhWord)

AXIOM ( Value[Category] =/= C

And Value[Category] =/= Agrs

And Value[Category] =/= T

And Value[Category] =/= Agro

And Value[Category] =/= D

)

Or ( Not IsAdjunct nd

And Not IsSpecifier nd

)

==> FFFunctional nd = EmptyStruct

Now we move on to the more elaborate description. I will start withthe second axiom. Zwart [Zwa97, Page 204], following Den Besten [Bes78],assumes that the tense of T is checked against C. The reason for this typeof feature checking is the fact that complementizers are connected with thetense of a clause. Some complementizers, such as dat (that), introduce a�nite embedded clause, whereas others, such as om (to), introduce non�niteembedded clauses (see Example 8.5). In the formalization I check the tensefeature of C against the tense feature of V instead of the tense feature of T.Extensionally this is the same, as V and T must have identical tense valuessince V must check its tense feature against T. The features that have to bechecked against the feature of C are yielded by the function FFLexical. Ifwe apply this function to the upper T in Example 8.6, all the formal featuresof V are yielded. T namely is an adjunction, and, as we saw earlier section,


FFLexical applied to an adjunction yields the same feature structure asFFLexical applied to its adjunct.

Example 8.5

(a) Ik vertel haar dat jij het boek koopt(I tell her that you the book buy)I tell her that you buy the book

(b) Ik vraag haar om het boek te kopen(I ask her to the book to buy)I ask her to buy the book

Example 8.6

C

C AgrSP

AgrS C

T AgrS

AgrO T

V AgrO

Agreement is also checked in C. The reason for this type of featurechecking is the fact that many Germanic languages and dialects that showan asymmetry in verb movement between main and embedded clauses alsoshow complementizer agreement. Example 8.7 gives two embedded clausesin Frisian that show complementizer agreement. The form in which thecomplementizer dat (that) appears depends on the subject by which it isfollowed. Therefore, the agreement features of the complementizer (C) arechecked against the agreement features of the verb, which must equal theagreement features of the subject.

Example 8.7

(a) datsto (datAGR do) him sjochst(thatyou (thatAGR you) him see)that you see him

(b) dat hy him sjocht(that he him sees)that he sees him


The following mainly concerns the �fth axiom of the functionFFFunctional. According to the Minimalist Program [Cho95, Page 174] Vand T are responsible for case assignment. The case feature of the subjectand the object are respectively checked against T (in the speci�er positionof AgrSP) and V (in the speci�er position of AgrOP).6 Case feature check-ing takes place in AgrSP and AgrOP respectively because V moves to AgrOand T moves to AgrS.

In the formalization it is assumed that the verb moves from AgrO toT to AgrS and that case feature checking of the subject takes place in thespeci�er position of TP. This solution is preferred because feature checkingof the subject DP against the case feature of T within AgrSP (see Example8.8) would be an exceptional kind of feature checking. Usually, a speci�eror an adjunct within a projection � checks its features against the head of�, which is AgrS in this case. Hence, in Example 8.8 V and DP check theirfeatures against AgrS, not against T or AgrO. Therefore, the checking ofthe case feature of the subject DP must take place within TP.

Example 8.8

AgrSP

DP AgrS

AgrS TP

T AgrS

AgrO T

V AgrO

loopt

Now we turn to the tenth axiom of the function FFFunctional. I amaware of the fact that there have been various proposals within Chomskyanlinguistics with respect to the internal structure of NPs and DPs. Theseproposals deal with agreement between determiners and nouns on the onehand, and adjectives and nouns on the other hand (cf. [Abn87], [Cor91],

6Note that therefore the object feature of the verb includes a case feature, while thesubject feature of the verb does not include a case feature (see for instance De�nition8.1).


[Lat97]). In the formalization only very simple DPs, which contain a nounand possibly a determiner (D), are dealt with. D, which possibly is anempty head (i.e. a head without a word value), directly takes an NP as itscomplement, without any intermediate functional projections, as we can seein Example 8.9. The only type of movement that takes place within the DPis head movement of N to D. The features that N checks in D are given inthe ninth axiom. The determiner, case and agreement features are checkedto obtain determiner noun agreement.

The determiner feature is a feature that does not occur in the MinimalistProgram. It is applied here to be able to distinguish the treatment ofpronouns such as zij (she) and interrogative words such as wat (what) onthe one hand from nouns such as jongen (boy) on the other hand withrespect to the selection of determiners. Pronouns and interrogative wordscan only check their features against those of an empty D (i.e. a D withno phonological content), while nouns, except for the plural forms, can onlycheck their features against those of a D with lexical content such as de

(the).The fact that D has case features is not very surprising. For instance, in

German there are di�erent determiners for each case-gender combination.Gender and number features also may in uence the choice of determiners.For example, in French there are di�erent determiners for neuter and mas-culine on the one hand (le) and feminine on the other hand (la). All pluralforms, neuter, feminine as well as masculine, have the determiner les inFrench.

The Wh-feature is a feature which the DP wants to check against theWh-feature of CP. Therefore it is convenient that D has a Wh-feature sothat we do not have to go into the NP to �nd the Wh-feature. The noun andthe determiner must have the same value for the Wh-feature. Therefore, Nadjoins to D to check its Wh-feature, and other features. For instance, inthe DP who we have an empty D with a feature-value pair WhWord Yes anda noun who with the same feature-value pair.

Example 8.9

DP

< empty > D

D NP

< empty > N

N < empty >


In the following, I will describe the function LinkSource nd which Ialready mentioned above, together with its counterpart LinkTarget nd. Inderivational terms: LinkTarget nd yields a node where the constituent innd moved to; LinkSource nd yields a node where the constituent in nd

moved from. In representational terms: LinkTarget nd1 = nd2 impliesthat the constituents in nd1 and nd2 are part of the same chain and thatnd1 is a node that is located lower and to the right of nd2; LinkSourcend1 = nd2 implies that the constituents in nd1 and nd2 are part of thesame chain and that nd1 is higher and to the left of nd2. Of course, bothfunctions are partial as not each node in a tree is the root of a constituentthat is part of a chain. The formalization of both functions can be found inDe�nition 8.4.

The function LinkTarget is based on the function ConnectionTarget

from the tree module. ConnectionTarget just indicates a connection be-tween one node and another. LinkTarget takes into account that headmovement involves a tree that grows with each movement (see Example8.4 and 8.6).7 For instance, V adjoins to AgrO, the adjunction structurewith AgrO as a root adjoins to T etc. Therefore the second axiom dealswith adjuncts: if nd is an adjunct, then we can say that it moved to thenode its mother moved to (for instance, the V adjoined to AgrO movesto the position its mother (AgrO) moves to (i.e. the adjunct position ofT)). LinkTarget nd simply is the reverse case of LinkSource nd (see thirdaxiom).

De�nition 8.4

FUNC LinkTarget : NodeS -> PARTIAL~NodeS

FUNC LinkSource : NodeS -> PARTIAL~NodeS

AXIOM Not IsAdjunct nd

==> LinkTarget nd = ConnectionTarget nd

AXIOM IsAdjunct nd

==> LinkTarget nd = ConnectionTarget Mother nd

AXIOM LinkSource nd1 = nd2

<=> LinkTarget nd2 = nd1

7Note that head movement is considered to be problematic for representational ver-sions of generative syntactic theory (for instance, Rizzi [Riz90] and Brody [Bro95]), sincechains rather than movements are central in representational approaches. Movementsare subject to locality conditions, and those locality conditions are impossible to expressfor head chains, where the target of adjunction for a head can itself subsequently move.Considering traces to be copies is a possible solution here.


CorrectChains tr is a boolean function that ensures that no impossiblechain links occur within tr and that each link in the chain is associatedwith feature checking (see De�nition 8.5). The possible links are speci�edby the functions PossibleLinkA (nd1, nd2) and PossibleLinkB (nd1,

nd2). The solution given in those functions is rather trivial for reasons Ispeci�ed in Section 8.1.

The functions PossibleLinkA, PossibleLinkB and FeaturesChecked

will be described in more detail below. The function PossibleLink is splitup into two parts (A and B) for the sake of perspicuity. PossibleLinkA

speci�es the general rules for movement within the Minimalist Program:always move from the complement domain of a functional head to its check-ing domain. PossibleLinkB speci�es the category-speci�c rules which weneed to avoid certain impossible movements which are not ruled out by theMinimalist Program.

De�nition 8.5

FUNC CorrectChains : TreeS -> BoolS

AXIOM CorrectChains tr

<=> FORALL nd1, nd2

( nd1 NodeOf tr

And ConnectionTarget nd1 = nd2

==> PossibleLinkA (nd1, nd2)

And PossibleLinkB (nd1, nd2)

)

And FeaturesChecked tr

The predicate tr1 InComplementDomainOf tr2 is applied within thefunction PossibleLinkA to de�ne the notion `complement domain'. tr1

is in the complement domain of tr2 if the complement of tr2 re exivelydominates tr1 (see De�nition 8.6).

De�nition 8.6

FUNC InComplementDomainOf : TreeS, TreeS -> BoolS

AXIOM tr1 InComplementDomainOf tr2

<=> (Complement tr2) ReflDominates tr1

As was said above, the function PossibleLinkA (tr1, tr2) speci�escertain general rules for possible links. The �rst conjunct of the axiom inDe�nition 8.7 shows that links must always connect two identical trees. Inthe formalization, which is static because it only formalizes which trees are


built according to the Minimalist Program and not how those trees are built,movement is indicated by connections between identical trees. We need thefunction Cut because we cannot say that two di�erent subtrees tr1 andtr2 of a tree are equivalent, this because they have di�erent mothers, aswe saw in Chapter 4. If the subtrees are cut out of the bigger tree wecan say they are equivalent. The second conjunct says that if tr1 is ahead or an adjunction structure, it may not be too deep in the structure(i.e. it must be the sister of a complement). If tr2 is an adjunct, it maynot be to deep either (�fth conjunct). Its mother must be the sister of acomplement. According to the third and the fourth conjunct, tr1 must bein the complement domain of the functional projection it moves to. If tr2is a speci�er (Not IsAdjunct tr2) we look at the complement domain ofthe maximal projection (XP: Mother tr2). If tr2 is an adjunct we look atthe intermediate projection (X: Mother Mother tr2).

De�nition 8.7

FUNC PossibleLinkA : TreeS, TreeS -> BoolS

AXIOM PossibleLinkA (tr1, tr2)

<=> Cut tr1 = Cut tr2

And ( IsHead tr1

Or IsAdjunction tr1

==> IsComplement Sister tr1

)

And ( Not IsAdjunct tr2

==> tr1 InComplementDomainOf (Mother tr2)

)

And ( IsAdjunct tr2

==> tr1 InComplementDomainOf (Mother Mother tr2)

)

And ( IsAdjunct tr2

==> IsComplement Sister Mother tr2

)

The function PossibleLinkB(nd1,nd2) speci�es the trivial, category-speci�c rules (see De�nition 8.8). All possible movements are listed in theformalization: movement from the speci�er of VP to the speci�er of TP (forintransitive sentences), movement from the speci�er of TP to the speci�erof AgrSP, movement from the complement of VP to the speci�er of AgrOP,movement from the head of VP to the adjunct of AgrOP, movement fromthe head of NP to the adjunct of DP, movement from the head of VP tothe adjunct of TP, movement from the adjunction of AgrOP to the adjunctof TP, movement from the adjunction of TP (i.e. the highest adjunctionas is speci�ed in the function PossibleLinkA) to the adjunct of AgrSP,movement from the adjunction of AgrSP to the adjunct of C, and �nally,


movement from the speci�er of AgrO or AgrS to the speci�er of C. De�nition8.8 contains just a selection of the possible movements I summed up above.

De�nition 8.8

FUNC PossibleLinkB : TreeS, TreeS -> BoolS

AXIOM PossibleLinkB (tr1, tr2)

<=>

( IsSpecifier tr1

And IsSpecifier tr2

And Value[Category] Mother tr1 = V

And Value[Category] Mother tr2 = T

)

Or ( IsSpecifier tr1

And IsSpecifier tr2


And Value[Category] Mother tr2 = Agrs

)

Or ( IsComplement tr1

And IsSpecifier tr2


And Value[Category] Mother tr2 = Agro

)

Or ( IsHead tr1

And IsAdjunct tr2



)

.

.

.

Or ( IsAdjunction tr1

And IsAdjunct tr2



)

.

.

.

The function FeaturesChecked tr describes the actual feature checkingwithin a tree tr (see De�nition 8.9). Each node nd of tr that has been thetarget of movement (LinkSource nd =/= Undef) may not yield an emptyfeature structure for the function FFFunctional nd. Furthermore it mustbe possible to check FFFunctional nd against FFLexical nd, that is, thefeature structure that is yielded by FFLexical nd contains at least all thefeatures yielded by FFFunctional nd and possibly more.

8.3. SUMMARY 147

De�nition 8.9

FUNC FeaturesChecked : TreeS -> BoolS

AXIOM FeaturesChecked tr

<=> FORALL nd

( nd NodeOf tr

And LinkSource nd =/= Undef

==> FFFunctional nd =/= EmptyStruct

And (FFFunctional nd) Check (FFLexical nd)

)

In the next chapter the interface levels (LF and PF) of the MinimalistProgram are dealt with. PF yields a list of words (a sentence) which is basedon a tree representing LF. In our formalization an LF-tree must be a phrasemarker. A tree tr is a phrase marker if and only if it satis�es X-Theory,and if every chain that occurs in tr is formed correctly (see De�nition 8.10).This is not a de�nition which I literally found in the literature but I assumethat X-Theory and the movements within a tree determine whether a tree isa correct phrase marker because the functions XBar tr and CorrectChains

tr formalize all allowed external characteristics of a tree according to theMinimalist Program. It seems useful to be able to distinguish correct treesfrom other trees with the notion `phrase marker'.

De�nition 8.10

FUNC PhraseMarker : TreeS -> BoolS

AXIOM PhraseMarker tr

<=> XBar tr

And CorrectChains tr

8.3 Summary

The main objective of this chapter was to de�ne which chains are correctaccording to the Minimalist Program. An important constraint on chainsis that each link in a chain must be connected with feature checking. Butthe feature checking requirement is not the only constraint on links. Thereare also constraints on the link source and the link target (i.e. `landing site'in derivational terms). The link target must be in the checking domain of afunctional head. The link source must be in the complement domain of thatsame functional head. I was also forced to formulate some trivial constraintson links to prevent subjects from checking their features in AgrOP andobjects from checking theirs in AgrSP.

Chapter 9

Interfaces

9.1 Introduction

The language faculty is a set of capacities realized by the human brain. Onecomponent of the language faculty enables people to express themselves ina language. The expressions generated are called structural descriptions(SDs). Each SD contains several linguistic properties, such as semantic andphonetic properties. Universal Grammar (UG) is the theory of the initialstates of all languages. SDs (or expressions) are part of the theory of a givenlanguage. UG speci�es di�erent linguistic levels for the di�erent types oflinguistic properties in SDs.

As the language faculty includes performance systems, it is possible touse linguistic expressions for actions such as inquiring, interpreting andarticulating. Each SD contains information for these performance systems.There are two types of performance systems: articulatory-perceptual (A-P) and conceptual-intentional (C-I). Chomsky refers to the level A-P asPhonetic Form (PF), while the level C-I is referred to as Logical Form(LF).

A derivation consists of a sequence of applications of the operationsMerge and Move, and if it converges it yields legitimate LF and PF ob-jects. A derivation tree is legitimate at LF if all features that have to bechecked are checked by applications of the operation Move; a derivation treeis legitimate at PF if all strong features are checked by applications of theoperation Move.

The de�nitions of LF in the formalization of Chomsky's 1993 frameworkand Zwart's framework di�er slightly. The di�erence is mainly due to theshift from lexical constituents to functional constituents as indicators forconvergence at LF.

149

150 CHAPTER 9. INTERFACES

In Chomsky's 1993 framework the formal features (such as tense and casefeatures) of lexical heads and lexical projections must be checked againstfeatures associated with functional heads before LF. A derivation crashesif it does not yield at least one LF-object in which all formal features oflexical constituents are checked.1 Features that are checked are removedfrom functional heads, as they are not interpretable at LF.

In the Chomsky's 1995 framework it is required that each functionalhead checks its formal features before LF. A derivation crashes if it doesnot yield at least one object (i.e. phrase marker) of which all functionalheads that host formal features, `attracted' lexical constituents for featurechecking.2 Zwart adopts this approach in his 1997 framework.

The de�nition of PF is also di�erent in Chomsky's 1993 framework andZwart's framework. This is due to the fact that Zwart [Zwa97] partly adoptsideas from Chomsky's 1995 framework about feature checking: isolated for-mal features are uninterpretable at PF and therefore movement that takesplace before PF (i.e. overt movement) must include movement of phonolog-ical and semantic features.3 Zwart applies this idea in the following way tohead movement: in principle only formal features of lexical heads are movedfor feature checking, and movement of LC-features (i.e. semantic plus cate-gorial features) is a Last Resort for interpretability at PF.4 For instance, insubject-initial main clauses in Dutch the verb must be spelled out in AgrS.If only the formal features of the verb move to AgrS, the PF-representationof the sentence is incorrect since isolated formal features are uninterpretableat PF. Therefore the LC-features of the verb move directly to AgrS as aLast Resort, that is, without moving to the intermediate landing sites inTP and possibly AgrOP. The word order at PF is now SVO (subject, verb,object), which is correct for Dutch main clauses. In subordinate clauses, theverb's formal features move to C. If there is a complementizer in C, thereare LC-features of the complementizer in C, and no Last Resort movementof LC-features of the verb is required. Therefore the verb is spelled out insitu (i.e. within the VP) in Dutch subordinate clauses. The word order atPF is now CSOV, which is correct for Dutch subordinate clauses (see forinstance the examples in Section 3.3).

In the formalization, formal features and LC-features are not movedseparately, as this is problematic for copy theory. More speci�cally, LastResort movement of LC-features skips intermediate positions (i.e. positionsbetween the lowest position of the chain and the PF-position of the chain)and consequently not all the copies within a chain are identical. As we saw

1Cf. [Cho93, Page 29].2Cf. [Cho95, Page 297].3Cf. [Cho95, Page 262].4Zwart assumes that semantic and categorial features belong to the same class since

categorial features are derivable from semantic features [Zwa97, Page 169].


in the previous chapter a requirement on chains is that all its copies areidentical. Therefore I present a new solution, which is equivalent to Zwart'ssolution (see Section 9.2).

As opposed to Chomsky, Zwart proposes that phonological features areadded after Spell-Out (i.e. postlexicalism [HM93]). Morphology is a post-syntactic (PF) component, and it involves a function mapping bundles ofsemantic and formal features onto (in ected) forms from a paradigm in thelexicon. The entries selected from the lexicon on the basis of formal andsemantic features contain phonological features which represent words thatform the sentence associated with the structure that is spelled out.

In the formalization of Zwart's framework, a notion that does not occurin Chomsky's 1993 framework is formalized: the numeration. The idea ofthe numeration is introduced by Chomsky [Cho95, Page 225]. A numerationis applied to assure that a semantic representation at LF and a phonologicalrepresentation at PF are based on the same lexical items. A numeration isa set of pairs (LI,i), where LI is a lexical item and i is an index indicatingthe number of times a lexical item is selected. When a lexical item isselected by the derivation the index is reduced by 1. At the end of thederivation all indices of the numerationmust be reduced to zero. A semanticrepresentation and a phonological representation are based on the samelexical choices if and only if they are based on the same numeration. In theformalization it was necessary to formulate constraints on numerations (seeSection 9.2).

The formalization of Chomsky's 1993 framework with respect to theinterfaces LF and PF di�ers considerably from the formalization of Zwart'sFramework. Therefore I give a description of the formalization of interfaceswithin Chomsky's framework in Section 9.3.


In the interface module, LF and PF are the key notions, and thereforeLogicalForm tr and PhoneticForm tr are the key functions of the in-terface module. The function LogicalForm tr yields a boolean value toindicate whether or not a tree tr is a correct representation at the interfaceLF. The function PhoneticForm tr yields a list of words.

In Zwart's framework, LF is reached when all functional heads checkedtheir formal features.5 The de�nition of the function LogicalForm can befound in De�nition 9.1. As we see in the �rst conjunct, tr must be a phrasemarker, which implies that tr must be built according to X-Theory andthat tr must have correct chains as we saw in the previous chapter. The

5Cf. [Cho95, Page 297] and [Zwa97, Page 184].


second conjunct deals with numerations. I will return to this conjunct aftera more elaborate description of the use of numerations in the formalization.

De�nition 9.1


AXIOM LogicalForm tr

<=> PhraseMarker tr

And EXISTS num

( num in NumerationLexicon

And num Check (FuncHeadFeat tr)

)

And FORALL nd

( nd NodeOf tr

And LocalCheck nd =/= EmptyStruct

==> LinkSource nd =/= Undef

)

In the formalization numerations are applied in a way di�erent fromthe way Chomsky [Cho95] and Zwart [Zwa97] apply them (see Section 3.3).Zwart and Chomsky apply numerations to assure that LF and PF are basedon the same lexical choices. In the formalization, as we will see below,numerations are mainly applied to make the boolean function LogicalForm

work.In Chomsky's 1993 framework, lexical constituents are forced to check

all their features before LF. In order to do so, lexical constituents requirefunctional projections to move to. The lexical constituents determine theselection of functional heads. For instance, if a Wh-noun is selected, thestructure that is built must contain a C-head to check the Wh-feature ofthis noun.

In Zwart's framework, functional heads as opposed to lexical heads re-quire feature checking before LF. If the numeration was not a compulsorycomponent of the framework, structures without any functional heads couldmake correct sentences, as such a structure does not contain functional headsand hence the LF-requirement is met by de�nition. This is undesirable be-cause in such a framework it is, for instance, possible to approve of sentenceswithout subject-verb agreement. Namely, if a tree does not contain a headAgrS, it is not possible to move the verb and the subject to check subject-verb agreement. Therefore the formalization requires the numeration tomeet certain requirements.

The formalization of Zwart's framework contains an additional lexiconbesides the prelexicon and the postlexicon, which contains abstract repre-sentations of possible numerations. The representations are abstract in thesense that they only indicate which functional heads with which feature-value pairs must be present in a numeration for a given type of sentence, for


instance a yes/no-question or an embedded clause. A selection of four of theeight items from the numeration lexicon is given in De�nition 9.2. The eightitems represent the four sentence types that are dealt with in the formal-ization: subject-initial main clauses, embedded clauses, Wh-questions andyes/no questions. For each type there are two items: one for the transitiveand one for the intransitive version. In De�nition 9.2 we �nd respectively:the transitive version of a subject-initial main clause, the intransitive ver-sion of an embedded clause, the intransitive version of a Wh-question andthe intransitive version of a yes/no-question. The items in the numerationlexicon are built up in a way that is similar to the way items in a regularlexicon are built up.

De�nition 9.2

OBJ NumerationLexicon : SetS[NumerationS]

AXIOM NumerationLexicon

= ( EmptyNumerations

Add ( EmptyCatStruct[Agrs]


Add[Agreement] Any[Agreement]

)

)

Add ( EmptyCatStruct[T]


Add[Case] Any[Case]

)

Add[Tense] Any[Tense]

)

Add ( EmptyCatStruct[Agro]

Add[Object] Any[Object]

)

)

.

.

.

++ ( EmptyNumerations

Add ( EmptyCatStruct[C]


Add[Sememe] Any[Sememe]



)

)




)


)



Add[Case] Any[Case]

)


)

)

.

.

.




Add[WhWord] Yes

)




)

)



Add[Case] Any[Case]

)


)

)

.

.

.




Add[Inversion] Yes

)




)

)



Add[Case] Any[Case]

)


)

)

In the �rst item we see that transitive main clauses need three functionalheads. For both the subject and the object we need to check case and


agreement features. The agreement features of the verb and the subjectare both checked in AgrSP. The case features of the subject are checkedin TP, and so is the tense feature of the verb. Both the verb and theobject check their case and agreement features in AgrOP. Zwart argues thatsubject-initial main clauses do not need a C. Therefore C is not added tothe items representing main clauses. Example 9.1 contains a phrase markerrepresenting the main clause De pers volgt de ster (The press pursues thestar) according to Zwart's ideas.

Example 9.1

AgrSP

DP AgrS

de persi

AgrS TP

T AgrS ei T

AgrO T ek AgrOP

V AgrO DP AgrO

volgtk de sterj

ek VP

ei V

ek ej

In the case of a transitive embedded clause (see Example 9.2), there isno functional head with object case and agreement features. The item doescontain the functional head C, as embedded clauses need a complementizer.The tense feature of C forces verb movement to C. As we see in Example9.2 (dat de pers zwijgt: that the press keeps silent), the verb is not spelledout in C in embedded clauses since C already contains LC-features of thecomplementizer (Add[Sememe] Any[Sememe]).

In the third item (see Example 9.3), Wh-questions are represented.Movement of the subject or the object with Wh-features to the speci�erof CP is caused by the Wh-feature of C. Verb movement to the adjunctposition of C is caused by the tense feature of C. In Example 9.3 the in-transitive Wh-question Wie zwijgt? (Who keeps silent?) is represented.


Example 9.2

CP

C

C AgrSP

ek C DP AgrS

datl de persi

ek TP

ei T

ek VP

ei V

V

zwijgtk

Example 9.3

CP

DP C

wiei

C AgrSP

AgrS C ei AgrS

T AgrS ek TP

V T ei T

zwijgtk

ek VP

ei V

ek

In the fourth item (see Example 9.4), intransitive yes/no-questions arerepresented. The tense and the inversion features of C force the invertedverb to move to the adjunct position of C. Movement to the speci�er positionof C is not allowed as C does not contain a feature that causes this type ofmovement. In Example 9.4 the yes/no-question Zwijgt de pers? (Does thepress keep silent?) is represented.


Example 9.4

CP

C

C AgrSP

AgrS C DP AgrS

de persi

T AgrS ek TP

V T ei T

zwijgtk

ek VP

ei V

ek

Now we can return to the second conjunct of De�nition 9.1. There we�nd that there must be a numeration num for tr that is an item in thenumeration lexicon, and that it must be possible to check num against theset of feature structures that is built by joining the feature structures of thefunctional heads of tr (FuncHeadFeat tr), which is also a numeration.6

Checking numerations against each other is comparable with checking fea-ture structures against each other (see Chapter 5): the second argumentmust contain the same functional heads as the �rst argument and possiblymore.

The function FuncHeadFeat tr is de�ned in 9.3. In this de�nition wesee that only the features of heads that are not of the category D, V orN, are added to the numeration (see second axiom). In the last axiom wesee that trees with BarLevel 2 that were moved from a lower position arenot taken into consideration. The reason for this is that it is redundantto consider all the copies of a given constituent, as copies are by de�nitionthe same as their original. Therefore only the lowest element of a chain istaken into account (see fourth axiom: LinkSource = Undef). For heads(with BarLevel 0) we do not have to make the distinction between originaland copies, as copies are always subtrees of functional heads. As we sawabove, functional heads are dealt with in the second axiom. As soon asa functional category with BarLevel 0 is found, its features are added to

6Note that while Chomsky emphasizes the lexical items in the numeration, our nu-merations only contain functional heads, as functional heads determine the selection oflexical heads. For instance, if a numeration contains an AgrO, the sentence must containat least two DPs.


the numeration, and the tree it is the root of is not considered any further.Therefore, the function FuncHeadFeat will never have to deal with copiesof lexical heads.

De�nition 9.3

FUNC FuncHeadFeat : TreeS -> NumerationS

AXIOM BarLevel tr = Undef

==> FuncHeadFeat tr

= Nil


And Value[Category] tr =/= D

And Value[Category] tr =/= V

And Value[Category] tr =/= N

==> FuncHeadFeat tr

= (Features tr) :: Nil


==> FuncHeadFeat tr

= (FuncHeadFeat LeftDaughter tr)

++ (FuncHeadFeat RightDaughter tr)


And LinkSource tr = Undef

==> FuncHeadFeat tr

= (FuncHeadFeat LeftDaughter tr)

++ (FuncHeadFeat RightDaughter tr)


And LinkSource tr =/= Undef

==> FuncHeadFeat tr

= Nil

Within generative grammar and other linguistic theories abstract treesmodel phrases. I introduce a lexicalist approach to the modelling of phrases:di�erent types of phrases are described by di�erent feature structures, in away comparable to the description of lexical items by feature structures. Asimilar approach to phrases is introduced in HPSG (cf. [Hud90, FK, Kat95,Sag97].

Finally, we can return to the function LogicalForm in De�nition9.1. The third conjunct says that for every node nd of tr for whichFFFunctional nd yields a nonempty feature structure, LinkSource nd

must be de�ned. That is, if a given node nd is a position where lexicalconstituents can move for feature checking, then this position nd must be�lled by movement (of a lexical constituent). This conjunct deals withthe requirement that all functional heads must attract lexical constituents


to check their features before LF, as only certain positions within func-tional projections yield a nonempty feature structure for the functionFFFunctional. Note that the same requirement in reverse order can befound in the de�nition of the function FeaturesChecked (see De�nition 8.9on Page 147). This function is applied within the function LogicalForm

the same way as it is applied in the function CorrectChains which in itsturn is applied within the function PhraseMarker (see �rst conjunct inDe�nition 9.1). The requirement

LinkSource nd =/= Undef ==> FFFunctional =/= EmptyStruct

is completely di�erent from the requirement made in the third con-junct of De�nition 9.1. The former is a requirement on phrase markers. Itimplies that if a constituent moves, its landing site must contain formalfeatures to check against. Hence, movement is impossible without featurechecking.

For determining the phonetic formof a tree, the functions StrongPos andSpellOutPos are relevant. Furthermore we need three additional functions(IsSpecialAdjunct, IsSpecialLeaf and LookUpWord) in the formalizationof Zwart's framework because of the postlexicalism that is applied in Zwart'sapproach.

The words that are yielded by PF must in general be related to positionswith strong features. Which features are strong di�ers from language tolanguage. Thus, strength is a parameter determining word order di�erencesbetween languages. In Zwart's framework, the features of both the speci�erand adjunct position of all functional projections except for TP are strong(see De�nition 9.4).

De�nition 9.4

FUNC StrongPos : NodeS -> BoolS

AXIOM StrongPos nd

<=> ( IsSpecifier nd


)

Or ( IsAdjunct nd


)

Or ( IsSpecifier nd


)

Or ( IsAdjunct nd


)

Or ( IsSpecifier nd



)

Or ( IsAdjunct nd


)

Before we have a closer look at the de�nition of Spell-Out positionswe will consider the de�nition of the function ChainedTo, since this func-tion is applied within the de�nition of Spell-Out positions. The functionLinkTarget described in the previous chapter only covers one link of achain. In the de�nition of Spell-Out we need to be able to talk about biggerdistances within chains. A chain is a sequence of links, and therefore thefunction ChainedTo is the transitive closure of the function LinkTarget.Both ChainedTo and LinkTarget are de�ned in the chain module. Thefunction LinkTarget is described in the chapter dealing with the chainmodule (Chapter 8). The function ChainedTo is described here because theinterface module is the only module where this function is applied.

In De�nition 9.5 we see that a node nd1 is not only `chained to' the nexthighest node in its chain nd2; it is also `chained to' all other higher nodesof the same chain.

De�nition 9.5

FUNC ChainedTo : NodeS, NodeS -> BoolS

AXIOM nd1 ChainedTo nd2

<=> LinkTarget nd1 = nd2

Or EXISTS nd3

( LinkTarget nd1 = nd3

And nd3 ChainedTo nd2

)

The positions where words can be spelled out are given by the booleanfunction SpellOutPos nd (see De�nition 9.6). These positions are not al-ways equivalent to positions that are strong. If a chain contains more thanone strong position, the Spell-Out position of that chain is the highest po-sition with strong features, as all strong features must be checked beforePF. If a chain contains no positions with strong features, it is spelled out insitu, that is in the lowest position of the chain. For instance, complementiz-ers enter the derivation by lexical insertion in C. They are not involved inmovement for feature checking. Therefore complementizers are spelled outin the lowest position of their chain, which is in this case the only positionof its chain.


The �rst conjunct of the axiom in De�nition 9.6 de�nes that if the nodend1, which is a Spell-Out position, is `chained to' the node nd2, then nd2 isnot a node with strong features.

The second conjunct of the axiom in De�nition 9.6 de�nes that the nodend1, which is a Spell-Out position, is either a strong position, namely thehighest strong position of the chain (see also Section 3.4), or nd1 is thelowest position of the chain.

Note that nodes nd, which are not part of a chain, are always Spell-Outpositions, since for these nodes holds that LinkSource nd1 = Undef.

De�nition 9.6

FUNC SpellOutPos : NodeS -> BoolS

AXIOM SpellOutPos nd1

<=> FORALL nd2

( nd1 ChainedTo nd2

==> Not StrongPos nd2

)

And ( StrongPos nd1

Or LinkSource nd1 = Undef

)

The boolean function IsSpecialAdjunct nd (see De�nition 9.7) de�nesa node nd that is an adjunct and a Spell-Out position. The Sememe valueof its sister must be de�ned. In this formalization D and C are the onlyfunctional heads that can have Sememe features. The Sememe feature isan LC-feature. Verbs or nouns that are adjoined to C respectively D arenot spelled out in this position, even though it is a Spell-Out position (seethe de�nition (9.8) of special leaves) as no Last Resort movement of theLC-features of the verb or the noun is required by PF, this because theSpell-Out position already contains LC-features, namely those of C or D.

De�nition 9.7

FUNC IsSpecialAdjunct : NodeS -> BoolS

AXIOM IsSpecialAdjunct nd

<=> IsAdjunct nd

And SpellOutPos nd

And Value[Sememe] Sister nd =/= Undef

The function IsSpecialLeaf nd (see De�nition 9.8) de�nes a head thatremains in situ as its Spell-Out position is already occupied by anotherSememe (LC-)feature (see the de�nition of special adjunctions (9.7)).


A node nd1 has to meet two requirements to be a special leaf. Firstly,nd1 must be a leaf. Secondly, nd1 must be in one chain with a specialadjunct nd2. Hence, a lexical head is spelled out in situ, if its Spell-Outposition is occupied by the LC-features of a functional head. Therefore, wecan conclude that the Phonetic Form of a given tree does not only depend onSpell-Out positions in the formalization Zwart's framework. The presenceof special leaves and special adjuncts also plays an important role, as wewill see in the de�nition of the function PhoneticForm in De�nition 9.10.

De�nition 9.8

FUNC IsSpecialLeaf : NodeS -> BoolS

AXIOM IsSpecialLeaf nd1

<=> IsLeaf nd1

And EXISTS nd2

( nd1 ChainedTo nd2

And IsSpecialAdjunct nd2

)

Before we take a closer look at the function PhoneticForm we will con-sider the function LookUpWord in De�nition 9.9. The function LookUpWord

takes a feature structure and yields a string, i.e. a word. This function isapplied to consult the postlexicon at PF. In Zwart's framework, the postlex-icon must be consulted after the derivation because the regular lexicon doesnot contain phonological features. Hence, during the derivation no phono-logical features are present in the tree. As phonological features determinethe word that is spelled out at PF, the function LookUpWord is indispensablewithin the function PhonologicalForm.

In De�nition 9.9 fstruct1, fstruct2 and fstruct3 are feature struc-tures. str is a string, or rather a word. If we want to look up the wordbelonging to a feature structure fstruct1 in a given tree, there must be afeature structure fstruct2 in the postlexicon which can be checked againstfstruct1, if we remove the word feature from fstruct2. This impliesthat fstruct1 contains the same feature-value pairs as fstruct2 and pos-sibly more. If there is a feature structure fstruct3 in the postlexiconwhich also can be checked against fstruct1 (if we remove the word featureof fstruct3), then it must be possible that fstruct3 is checked againstfstruct2. The word feature does not have to be removed from fstruct2

and fstruct3 in the latter case, as both feature structures contain a wordfeature since they both come from the postlexicon. fstruct1 comes fromthe regular lexicon, and therefore it does not contain a word feature.

The function LookUpWord e�ects that we will always select the mostspeci�c lexical item from the postlexicon. If there are two feature structures


fstruct2 and fstruct3, that can be checked against fstruct1, we willselect the feature structure (fstruct2) that contains most feature-valuepairs.

De�nition 9.9

FUNC LookUpWord : FeatureStructS -> PARTIAL~StringS

AXIOM LookUpWord fstruct1 = str

<=> EXISTS fstruct2

( Value[Word] fstruct2 = str

And fstruct2 In PostLexicon

And (fstruct2 Remove Set(Word)) Check fstruct1

And FORALL fstruct3

( fstruct3 In PostLexicon

And (fstruct3 Remove Set(Word))

Check fstruct1

==> fstruct3

Check fstruct2

)

)

The function PhoneticForm tr in De�nition 9.10 yields phrases. Thetree tr is searched from left to right and, in principle, all leaves that areSpell-Out positions (and have a Sememe value) are spelled out by picking theright feature structure fstruct from the postlexicon and putting its wordvalue at the end of the phrase. Thus, Zwart's postlexicalism is representedin the function PhoneticForm tr. The phonological features, which arenot present in the derivation (i.e. in the tree), are added after Spell-Out byselecting the most speci�c feature structure from the postlexicon.

The third and the �fth axiom in Example 9.10 are the only two that addwords to the phrase that PhoneticForm tr yields. Conditions for addingwords are:

� tr must be a Spell-Out position or a special leaf (i.e. a leaf whichoccurs in one chain with an adjunct that has a sister with LC-features).

� tr must be a leaf (possibly a special leaf).

� If tr is a Spell-Out position, tr may not be a special adjunct and tr

must have a Sememe feature.

The only way for a tree tr to yield words is by being a Spell-Out positionor by being a special leaf. Hence, for trees that are not Spell-Out positions orspecial leaves we do not add any words to the phrase (see �rst axiom). Butthere are more reasons not to add any words to the phrase for a given treetr. Firstly, trees which are Spell-Out positions but also special adjuncts


are not spelled out (see second axiom). Secondly, trees which are Spell-Out positions and leaves but which do not have a Sememe feature are notspelled out for the obvious reason that they cannot be connected with aword feature (see fourth axiom).

In the �fth axiom we see that trees which are Spell-Out positions, butwhich are not a special adjunct or a leaf, are spelled out by applying thefunction PhoneticForm to their left and right daughters.

De�nition 9.10

FUNC PhoneticForm : TreeS -> PhraseS

AXIOM Not SpellOutPos tr

And Not IsSpecialLeaf tr

==> PhoneticForm tr = Nil

AXIOM IsSpecialAdjunct tr


AXIOM IsSpecialLeaf tr

==> PhoneticForm tr

= (LookUpWord Features tr) :: Nil

AXIOM SpellOutPos tr

And IsLeaf tr

And Value[Stem] tr = Undef



And Not IsSpecialAdjunct tr

And IsLeaf tr

And Value[Stem] tr =/= Undef

==> PhoneticForm tr

= (LookUpWord Features tr) :: Nil


And Not IsSpecialAdjunct tr

And Not IsLeaf tr

==> PhoneticForm tr

= (PhoneticForm LeftDaughter tr) ++ (PhoneticForm

RightDaughter tr)

9.3 Interfaces in Chomsky's framework

In the interface module of the formalization of Chomsky's 1993 frameworkboth the de�nitions of LF and PF di�er considerably from those in theformalization of Zwart's framework,

9.3. INTERFACES IN CHOMSKY'S FRAMEWORK 165

There are two aspects that determine whether a tree tr is a correct LF-representation. These two aspects are represented in the formalization ofLF given in De�nition 9.11.

Firstly, the tree in question must be a phrase marker, i.e. it must obey X-Theory and its chains must be correct according to the Minimalist Program(see De�nition 8.10). Secondly, all features that need to be checked beforeLF must be checked.

The second aspect needs some discussion. As we saw earlier in thischapter, an LF-representation may not contain lexical constituents withunchecked features. That is, all lexical constituents with root nd that are thehighest constituent of the chain they belong to (LinkTarget nd = Undef)need to have checked all their features that had to be checked (FFLexicalnd = Checked nd). This also holds for nodes that do not have to check fea-tures (FFLexical nd = Undef), as these nodes cannot move and thereforedo not check features (Checked nd = Undef). The function Checked is notapplied within Zwart's framework. This function is given in De�nition 9.12.

De�nition 9.11


AXIOM LogicalForm tr

<=> PhraseMarker tr

And FORALL nd

( nd NodeOf tr

And LinkTarget nd = Undef

==> FFLexical nd = Checked nd

)

According to Chomsky [Cho93] features are deleted when they arechecked, and LF is reached when there are no formal features left. Thefunction Checked nd which yields a structure containing the features thathave been checked via movement of the constituent of which nd is theroot (see De�nition 9.12). In the lowest position of a chain (LinkSourcend = Undef), no features are checked (Checked nd = EmptyStruct). Forevery other position nd in the chain holds that checked features arethe features that were checked until the preceding position in the chain(Checked LinkSource nd) uni�ed with the features that are checked in nd

(FFFunctional nd).7

7See Appendix for the de�nition of Unify. This de�nition is a part of the featurestructure module, but it is only discussed here because this is the only place in theformalization where this function is applied.


De�nition 9.12

FUNC Checked : NodeS -> FeatureStructS

AXIOM LinkSource nd = Undef

==> Checked nd

= EmptyStruct

AXIOM LinkSource nd =/= Undef

==> Checked nd

= (Checked LinkSource nd) Unify (LocalCheck nd)

The function PhoneticForm tr searches tr and yields a list of words.The positions that are strong in Dutch are indicated by the boolean functionStrongPos nd (see De�nition 9.13). In the formalization of Chomsky's 1993framework the features in the speci�er position of AgrS and AgrO are strong.There are no adjunct positions with strong features.

In Chapter 3 we saw that Chomsky's framework is not adequate to coververb movement in Dutch. The parameters given in De�nition 9.13 only yielda correct word order for embedded clauses in Dutch. Main clauses and Wh-questions as in Example 9.5 ((a) respectively (b)) do not get the right wordorder in Dutch. Yes/no-questions are not dealt with in the formalization ofChomsky's framework.

De�nition 9.13

FUNC StrongPos : NodeS -> BoolS

AXIOM StrongPos nd

<=> ( IsSpecifier nd


)

Or ( IsSpecifier nd


)

Example 9.5

(a) *De politieagent de politicus arresteertThe policeman the politician arrests

(b) *Wie de politicus arresteertWho the politician arrests

The function SpellOutPos nd (see De�nition 9.6 in the previous section)is the same as in the formalization of Zwart's framework.

9.4. SUMMARY 167

The function PhoneticForm tr yields a phrase ph. The tree tr issearched from left to right and all leaves that are Spell-Out positions arespelled out by putting the word values of those positions (if they have any)in a list.

In the �rst axiom in De�nition 9.14 it is de�ned that trees that are notSpell-Out positions do not yield a word. Spell-Out positions that are leaveswithout a word value, for instance the functional head AgrS, do not yielda word either, as we see in the second axiom. Spell-Out positions that areleaves with a word value yield a word which is concatenated to the list ofwords yielded so far, as we see in the third axiom. In the fourth axiom wesee that, if a tree tr is a Spell-Out position but is not a leaf, the phoneticform of tr is the phonetic form of its left daughter joined with the phoneticform of its right daughter.

De�nition 9.14

FUNC PhoneticForm: TreeS -> PhraseS

AXIOM Not SpellOutPos tr



And IsLeaf tr

And Value[Word] tr = Undef



And IsLeaf tr

And Value[Word] tr =/= Undef

==> PhoneticForm tr

= (Value[Word] tr) :: Nil


And Not IsLeaf tr

==> PhoneticForm tr

= (PhoneticForm LeftDaughter tr)

++ (PhoneticForm RightDaughter tr)

9.4 Summary

There are two reasons why the formalization of the interface levels LF andPF are less straightforward in Zwart's framework than the formalization ofthe interface levels in Chomsky's 1993 framework.

Firstly, the switch in focus from lexical to functional heads at LF resultsin some extra requirements at LF. Since LF in Zwart's framework is reached


when all functional heads in a tree checked all their features, I needed some-thing to make sure that an LF-tree always contains the required functionalprojections. Otherwise an LF-tree consisting of only a VP could be ap-proved of by the formalization. In Chomsky's 1993 framework lexical headsneeded to check all their features before LF, and to check their features theyrequire functional heads. In Zwart's approach I introduced an additionallexicon (besides the pre- and the postlexicon) which contains templates forall the types of sentences covered by the formalization. The templates con-tain the required functional heads for the given sentences, including therequired features for the case in question.

Secondly, Zwart's postlexicalism puts some extra requirements on theformalization. It is more complicated to determine the PF-position of achain because functional heads with lexical content can cause a lexical headto remain in situ although it contains one or more strong positions. AtPF, isolated formal features are assumed to be uninterpretable and if thefunctional projection the PF-position is part of does not contain any LC-features, then the LC-features of the lexical head in question need to moveto the PF-position as a Last Resort. But if the `usual' PF-position of thelexical head already contains LC-features because the functional projectionit is part of contains phonological material, then the LC-features of thelexical head remain in situ, which implies that the lexical head is spelledout in situ.

Chapter 10

Concluding remarks

The objective of this thesis is to provide a formalization of a minimalistdescription of a small fragment of Dutch. The fragment that is describedis outlined in Section 3.4. Although the Minimalist Program is still indevelopment precise de�nitions of the theory in its current stage of thedevelopment will be of use for linguists working inside and outside theMinimalist Program.

As a �rst attempt to formalization two small implementations inProlog were made. These implementations are described in Chapter 2.

The �rst implementation, which is outlined in Section 2.1, gives a surveyof the two structure-building operations Merge and Move. This implemen-tation reveals that the two structure-building operations the MinimalistProgram presupposes actually both consist of more disjunctively speci�edsub-cases. The structure-building operation Merge has three sub-cases: treeinsertion in the complement position, tree insertion in the speci�er position,and lexical insertion in the head position. The structure-building operationMove has two sub-cases: head movement and to-speci�er movement. Fur-thermore a new de�nition of the Move operation is given. This de�nitionstates that the moved element in a Move operation has to be contained inthe complement domain of the head of the target tree, not in the targettree as the original de�nition says. From this new de�nition we can derivethat movement to the complement position is impossible. An element (tree)cannot be moved to a position that contains the tree from which the movedelement must originate.

The second implementation, which is outlined in Section 2.2, is ahead-corner parser for a fragment of the Minimalist Program. I arguethat because of the nature of the structure-building operations of theMinimalist Program head-corner parsing is a suitable parsing technique

169

170 CHAPTER 10. CONCLUDING REMARKS

for the Minimalist Program. The idea of head-corners from head-cornerparsing resembles closely the idea of target trees from the MinimalistProgram, as we see in Subsection 2.2.2.

In the Chapters 4 through 9 the actual formalization of the minimal-ist description of the fragment of Dutch is given. The formalization iswritten in the formal-speci�cation language AFSL. Afterwards, the entireformalization was validated by implementing it in Prolog. The formaliza-tion is declaratively stated, not derivationally as the Minimalist Programitself: it describes which trees are correct according to the MinimalistProgram.

In Chapter 4 I give a description of trees. By considering minimalisttrees as some kind of directed graphs, we can omit indices. The functionConnectionTarget represents connections between nodes. It is used insteadof indices to indicate movements within trees.

In Chapter 5 minimalist ideas on features are formalized. I argue thatthe notion `feature structure' be introduced in order to be able to treat thefeatures of a node as a unit, although feature structures are not appliedin the Minimalist Program. Furthermore I introduce some new features,among which the features [object], [subject], [compcat] and [speccat]. The�rst two features are used to refer to the object and the subject features ofthe verb. Since a verb must agree with both its subject and its object (if it isa transitive verb), we need a way to separate the subject agreement featuresfrom the object agreement features of the verb. Furthermore, the verb as-signs case to the object. This case feature is also, as the agreement feature,a part of the value of the [object] feature. The features [compcat] and [spec-cat] are introduced to be able to implement subcategorization. The feature[compcat] indicates the category of the complement of a given head, whilethe feature [speccat] indicates the category of the speci�er of a given head.Subcategorization receives no explicit mention in the Minimalist Program,but it turns out to be vital for the formalization. It is important that thereis a way to represent what kind of complement or speci�er a given headmay select, because otherwise the formalization would for instance allowtransitive verbs to behave like intransitive verbs, by not forcing transitiveverbs to select both a subject and an object. This is especially essentialin Zwart's version (and Chomsky's 1995 version) since in this version thederivation is not guided by the features of the lexical heads in a sentence.In Chomsky's 1993 version all lexical heads need to check all their formalfeatures. Therefore the object features of the verb will require the verb toselect an object to check against. Furthermore, subcategorization provedto be essential for the word order of sentences. In Chapter 5 I also give anexact de�nition of the notion `feature checking'. I argue that the features of

171

a lexical constituent can only be checked against the features of a functionalconstituent if the feature structure belonging to the lexical constituent con-tains at least as many feature-value pairs as the feature structure belongingto the functional head.

In Chapter 6 I describe the way the lexicon is treated in the Minimal-ist Program. In Zwart's version of the Minimalist Program there are twolexicons. The �rst lexicon, which I call the prelexicon, is consulted whena lexical item enters the derivation. The second lexicon, which I call thepostlexicon, is consulted after the derivation (at PF) to obtain the phono-logical features of a lexical item. I argue that the lexicon which is consultedat the beginning of the derivation may not contain underspeci�ed featurestructures because of the nature of the feature checking operation. Checkingis only possible if a certain feature is present in a given functional head aswell as in the lexical constituent that checks its features against it. Hence,we cannot indicate that any possible value for a given feature name can bechosen by not representing it at all (under-speci�cation).

X-Theory is described in Chapter 7. In the X-rules that are speci�ed inthe formalization only bar-levels play a role, while in the original X-rules ofthe Minimalist Program category features also play a role (for instance: X! X, YP (where X and Y represent categories)). In the formalization, fea-ture percolation, including the percolation of the category feature, is takencare of separately. Feature percolation is based on the X-rules, since fea-tures percolate up from the head with bar-level zero to higher bar-levels.The positions of speci�ers, complements, heads and adjuncts are explicitlyde�ned in the X-module. This module seems to be the right location to rep-resent this type of knowledge since in the literature X-rules often implicitlyde�ne notions such as `speci�er' and `complement'. Furthermore I arguethat the two-level X-Theory as applied in Zwart's version and Chomsky's1995 version of the Minimalist Programs is problematic. X-Theory and thetheory of movement (or chains in our case) are mutually dependent. In thenew version of X-Theory heads do not always need to project, but with-out projection we cannot maintain the notions `complement domain' and`checking domain'.

In Chapter 8 I show that it is not problematic to treat head movementin a representational way by considering traces to be copies (contra Rizzi[Riz90] and Brody [Bro95]). Furthermore I argue that a [determiner] featureis needed to distinguish the treatment of pronouns and interrogative wordson the one hand from nouns on the other hand with respect to the selectionof determiners. The former group requires an `empty' D (i.e. a D with nophonological content), while nouns, except for the plural forms, require a Dwith lexical content.

In Chapter 9 the interfaces (LF and PF) of the Minimalist Program are

172 CHAPTER 10. CONCLUDING REMARKS

described. The main result of the formalization of the interfaces is the dis-covery that an additional lexicon, which contains templates for all types ofsentences covered by the formalization, is needed for Zwart's version of theMinimalist Program. Since LF in Zwart's framework is reached when allfunctional heads in a tree checked all their features, I needed something tomake sure that an LF-tree always contains the required functional projec-tions. Otherwise an LF-tree consisting of only a VP could be approved ofby the formalization. In Chomsky's 1993 framework, lexical heads neededto check all their features before LF, and to check their features they requirefunctional heads.

Suggestions for future research The formalization described in thiswork shows that a more formal approach to minimalist ideas leads to clearerde�nitions and sometimes to the discovery of inconsistencies and incom-pleteness. Therefore I think it can be interesting and useful to develop toolswith which linguists, for instance, can compare several solutions to the sameproblem or can test the result of a change in a de�nition. The formalizationdescribed here could be used as a basis for a parser that could serve as sucha tool.

Furthermore, research on the comparison of aspects of the MinimalistProgram with other linguistic theories might be of interest. The formaliza-tion presented here could help with such a comparison. For example, theformalization lead to the conclusion that under-speci�cation in the lexiconis not allowed in the Minimalist Program because of the nature of featurechecking, although under-speci�cation is common in feature-based theoriessuch as HPSG.

174 APPENDIX

the value Plural for the feature name Number, while fstruct2 contains thevalue Singular for the feature name Number, fstruct3 will not be speci-�ed for the feature name Number (see fourth axiom of WeakUnify: Value

(fstruct1 WeakUnify fstruct2, aname = Undef).The �rst axiom of WeakUnify expresses that the value of the feature

name name in fstruct3 (= fstruct1 WeakUnify fstruct2) is equal to thevalue of name in fstruct1 if the values of name in fstruct1 and fstruct2

are equal.The second axiom of WeakUnify expresses that the value of the feature

name name in fstruct3 is equal to the value of name in fstruct1 if thevalue of name in fstruct2 is unde�ned.

The third axiom of WeakUnify expresses that the value of the featurename name in fstruct3 is equal to the value of name in fstruct2 if thevalue of name in fstruct1 is unde�ned.

The fourth axiom of WeakUnify expresses that the value of the atomicfeature name aname in fstruct3 is unde�ned if fstruct1 and fstruct2

contain values for aname that are not equal.The �fth axiom of WeakUnify expresses that the value of the complex

feature name sname in fstruct3 equals the weak uni�cation of the valueof sname in fstruct1 with the value of sname in fstruct2 if this value isde�ned for both fstruct1 and fstruct2.

The function Unifiable �lters out con icting occurrences of the samefeature value. The function requires that the atomic feature values atom1 infstruct1 and atom2 in fstruct2 are equal if they are values connected withthe same feature name aname. Furthermore the function requires that thecomplex feature values fstruct3 in fstruct1 and fstruct4 in fstruct2

are uni�able if they are connected with the same feature name sname.As Unify combines the properties of WeakUnify and Unifiable, two

feature structure fstruct1 and fstruct2 only unify if they do not containany con icting feature values.

De�nition 10.1

DECL name : FeatureNameS

DECL aname : AtomNameS

DECL sname : StructNameS

DECL val : FeatureValueS

DECL atom : AtomS


FUNC WeakUnify : FeatureStructS, FeatureStructS ->

FeatureStructS

AXIOM Value (fstruct1 WeakUnify fstruct2, name)

APPENDIX 175

= Value (fstruct1, name)

<== Value (fstruct1, name) = Value (fstruct2, name)



<== Value (fstruct2, name) = Undef



<== Value (fstruct1, name) = Undef

AXIOM Value (fstruct1 WeakUnify fstruct2, aname)

= Undef

<== Value (fstruct1, aname) =/= Undef

And Value (fstruct2, aname) =/= Undef

And Value (fstruct1, aname)

=/= Value (fstruct2,aname)

AXIOM Value (fstruct1 WeakUnify fstruct2, sname)

= Value(fstruct1,sname)

WeakUnify Value(fstruct2,sname)

<== Value (fstruct1, sname) =/= Undef

And Value (fstruct2, sname) =/= Undef

FUNC Unifiable : FeatureStructS, FeatureStructS -> BoolS

AXIOM fstruct1 Unifiable fstruct2

<=> FORALL aname, atom1, atom2

( Value(fstruct1,aname) = atom1

And Value(fstruct2,aname) = atom2

==> atom1 = atom2

)

And FORALL sname, fstruct3, fstruct4

( Value (fstruct1, sname) = fstruct3

And Value (fstruct2, sname) = fstruct4

==> fstruct3 Unifiable fstruct4

)

FUNC Unify : FeatureStructS, FeatureStructS

-> PARTIAL~FeatureStructS

AXIOM (fstruct1 Unify fstruct2) = fstruct3

<=> fstruct1 Unifiable fstruct2

And fstruct3 = (fstruct1 WeakUnify fstruct2)

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Samenvatting

In dit proefschrift wordt een formalisatie besproken van een deel van eentaalkundige theorie. Deze theorie, het Minimalistische Programma, be-schrijft de laatste resultaten op het gebied van de generatieve taalkunde.

De aanzet tot de generatieve taalkunde werd ongeveer 40 jaar geledengegeven door Noam Chomsky. Een van de doelen van de generatieve taal-kunde is het formuleren van de onderliggende principes die de grammatica'svan alle menselijke talen bepalen. Deze principes worden ook wel aangeduidals de universele grammatica.

Chomsky baseerde het idee van de universele grammatica op het feit datkinderen zich een complex systeem als de grammatica van een taal in be-trekkelijk korte tijd eigen maken. Dit maakt het aannemelijk dat kinderenal bij de geboorte uitgerust zijn met een zekere kennis van taal. Chomskyveronderstelde dat taalverwerving een proces is waarbij kinderen, naast hetverwerven van het lexicon van de taal, een beperkt aantal syntactische keu-zes moeten maken uit de mogelijkheden die de aangeboren universele gram-matica biedt.

Een voorbeeld van een keuze (ook wel parameter) binnen de universelegrammatica is, of het al dan niet noodzakelijk is binnen een taal dat eenzin een `uitgesproken' subject bevat. In een taal als het Italiaans is hetbijvoorbeeld mogelijk persoonlijke voornaamwoorden weg te laten als zijhet subject van een zin vormen. De keuze of hun taal een `leeg' subject magbevatten, baseren kinderen op de zinnen die zij horen in hun omgeving.

Met de introductie van het Minimalistische Programma begin jaren 90,wordt het aantal parameters binnen de universele grammatica gereduceerdtot �e�en: de woordvolgordeparameter. Alle andere parameters, dus ook debovengenoemde `lege subject parameter', verdwijnen uit de theorie of wor-den opgeslagen als lexicale informatie. De eigenschappen van het lexiconworden in het Minimalistische Programma door de universele grammaticabe��nvloed.

De woordvolgordeparameter bepaalt welke woordvolgorde mogelijk is ineen bepaalde taal. Verschillende woordvolgordes tre�en we onder andere

185

186 SAMENVATTING

aan bij Nederlandse en Engelse bijzinnen. In het Nederlands verschijnenobjecten in bijzinnen v�o�or het werkwoord:

. . . dat zij de prins kust

In het Engels daarentegen, verschijnen objecten in bijzinnen n�a hetwerkwoord:

. . . that she kisses the prince

( . . . dat zij kust de prins)

Het Minimalistische Programma is dus minimalistisch in die zin dat hetaantal parameters is gereduceerd tot �e�en. Verder is het MinimalistischeProgramma restrictiever dan eerdere generatieve theorie�en omdat hetboomdiagramwaarmee de syntactische structuur van een zin wordt weerge-geven hetzelfde is voor alle talen. In eerdere generatieve theorie�en kwamenwoordvolgordeverschillen tot stand door verschillen in boomdiagrammen(zie bijvoorbeeld de onderstaande twee boomdiagrammen).

S

COMP S

dat

NP VP

zij

NP V

de prins kust

S

COMP S

that

NP VP

she

V NP

kisses the prince

Omdat de boomdiagrammen in het Minimalistische Programma gelijk zijnvoor alle talen, zorgen verplaatsingen nu voor woordvolgordeverschillen.Ook de verplaatsingen die de verschillende constituenten (bijvoorbeeld hetsubject en het werkwoord) van de zin ondergaan binnen het boomdiagramzijn gelijk voor alle talen. De woordvolgordeparameter zorgt er echter voor,dat de constituenten in verschillende talen op verschillende plaatsen bin-nen een reeks verplaatsingen kunnen worden uitgesproken. Zo wordt hetwerkwoord in een bijzin in het Nederlands uitgesproken onderin het boom-diagram, op het punt waar het werkwoord het boomdiagram binnenkomt(vanuit het lexicon) voordat het zich verplaatst. In het Engels daarentegen,wordt het werkwoord in bijzinnen uitgesproken op een positie waar het te-rechtgekomen is na enkele verplaatsingen. Op deze manier is het mogelijkdat het werkwoord in Nederlandse bijzinnen later wordt uitgesproken dan inEngelse bijzinnen, alhoewel het boomdiagram hetzelfde is voor beide talen.

SAMENVATTING 187

Het doel van dit proefschrift is een formalisatie te bieden van een minima-listische beschrijving van een klein fragment van het Nederlands. Alleen bij-zinnen, declaratieve hoofdzinnen, vraagwoordvragen en ja/nee-vragen vanhet eenvoudigste type (namelijk alleen een subject, een object en een werk-woord bevattend) worden behandeld. Alhoewel het Minimalistische Pro-gramma nog steeds in ontwikkeling is, zijn precieze de�nities van de theoriein haar huidige staat van belang voor zowel lingu��sten die werkzaam zijnbinnen het Minimalistische Programma als voor lingu��sten die werken aanandere taalkundige theorie�en.

Voor lingu��sten die binnen het Minimalistische Programma werkzaamzijn, schept een formalisatie duidelijkheid in discussies, bijvoorbeeld wan-neer er meerdere de�nities van een begrip in omloop zijn. Bovendien kunnendoor formalisatie fouten opgespoord worden die anders moeilijk te ontdek-ken zijn. Een formalisatie vergemakkelijkt bijvoorbeeld de opsporing vaninconsistenties die ontstaan door het herde�ni�eren van fundamentele begrip-pen.

Voor lingu��sten die werken binnen andere taalkundige raamwerken, kaneen formalisatie het Minimalistische Programma toegankelijker maken. Deinformele beschrijvingen van het Minimalistische Programma zijn namelijkvaak moeilijk te volgen voor niet-ingewijden.

In Hoofdstuk 1 van dit proefschrift wordt een korte beschrijving gege-ven van de belangrijkste begrippen van het Minimalistische Programma. InHoofdstuk 2 worden twee kleine implementaties in de programmeertaal Pro-log behandeld. Deze implementaties zijn gebouwd om de mogelijkheden totformalisatie van het Minimalistische Programma te onderzoeken. Op ba-sis van de twee implementaties is besloten door te gaan met de formalisatievan het Minimalistische Programma, zij het in een formele-speci�catietaal inplaats van in Prolog. Deze keuze is gemaakt omdat formele-speci�catietalengeschikter zijn voor het formuleren van expliciete de�nities dan een logischeprogrammeertaal als Prolog. De voordelen van formalisatie met behulp vaneen formele-speci�catietaal komen aan de orde in Hoofdstuk 3. Verder bevatdit hoofdstuk een beschrijving van de gebruikte formele-speci�catietaal, eenminimalistische beschrijving van het fragment van het Nederlands dat wordtbehandeld in de formalisatie, en een korte beschrijving van de formalisatie.

De uiteindelijke formalisatie wordt besproken in Hoofdstuk 4 tot en met9. Ieder hoofdstuk bevat de beschrijving van een module van de formalisatie.De verschillende modules zijn achtereenvolgens: boomdiagrammen, featurestructuren, het lexicon, X-Theorie, ketens, en interfaces. De formalisatiegeeft een declaratieve (of representationele) beschrijving van taal vanuit hetperspectief van het Minimalistische Programma, terwijl het MinimalistischeProgramma beschouwd kan worden als een procedurele theorie. Dit houdtin dat de formalisatie geen beschrijving biedt van de manier waarop boomdi-

188 SAMENVATTING

agrammen gebouwd worden, hetgeen het Minimalistische Programma doet,maar dat alleen restricties beschreven worden die het Minimalistische Pro-gramma aan bomen oplegt.

In Hoofdstuk 4 worden boomdiagrammen behandeld. De formalisatiebehandelt boomdiagrammen als een soort directed graphs. Het resultaathiervan is dat (procedurele) verplaatsingen kunnen worden weergegeven als(representationele) ketens.

In Hoofdstuk 5 komen de minimalistische idee�en over features aan deorde. Een voorbeeld van een feature is `persoon' voor werkwoorden. Devervoeging loop staat bijvoorbeeld in de eerste persoon, terwijl loopt in detweede of derde persoon staat. Ik laat zien dat het wenselijk is het begrip`feature structuur' te introduceren om de mogelijkheid te hebben de featuresvan een constituent als eenheid te beschouwen. Verder introduceer ik eenaantal nieuwe features waarvan ik aantoon dat ze noodzakelijk zijn voorde formalisatie. Bovendien geef ik een precieze de�nitie van het begrip`feature checking'. Feature checking is verbonden met verplaatsingen in hetMinimalistische Programma. Een constituent in een boomdiagrammag zichalleen verplaatsen, indien hij redenen heeft zijn features te vergelijken metdie van een knoop elders in de boom. Ik de�nieer het begrip feature checkingzodanig dat de features van een constituent alleen `gecheckt' kunnen wordenals de verplaatste constituent minstens evenveel features bevat als de positiewaarheen verplaatst wordt.

In Hoofdstuk 6 bespreek ik de manier waarop het lexicon wordt behan-deld in het Minimalistische Programma. Verder toon ik aan dat het on-mogelijk is om in het lexicon aan te geven dat een feature iedere mogelijkewaarde aan kan nemen door het feature onder te speci�ceren (weg te laten),zoals in veel andere taalkundige theorie�en gebeurt. Feature checking is na-melijk alleen mogelijk wanneer ieder feature dat aanwezig is in de positiewaarheen verplaatst wordt, ook daadwerkelijk aanwezig is in de verplaatsteconstituent.

X-Theorie beschrijft boomdiagrammen op een beknopte manier. In hetMinimalistische Programma wordt een poging gedaan boomdiagrammen zocompact mogelijk te houden. In Hoofdstuk 7 wordt aangetoond dat de com-pacte boomdiagrammen problemen opleveren door de onderlinge afhanke-lijkheid van X-Theorie en de theorie van verplaatsing van constituenten. Inde minimalistische boomdiagrammen ontbreekt de informatie die nodig isom aan te geven waarvandaan en waarheen constituenten zich mogen ver-plaatsen, waardoor er verwarring kan ontstaan. Daarom stel ik voor eenoudere versie van X-Theorie toe te passen, namelijk een versie die mindercompacte bomen oplevert.

In Hoofdstuk 8 laat ik zien hoe een serie verplaatsingen in de declaratieveformalisatie kan worden beschouwd als een keten van knopen. Verder wordt

SAMENVATTING 189

aangetoond dat geen enkele vorm van verplaatsing problemen oplevert in eendeclaratieve benadering van het procedurele Minimalistische Programma.

In Hoofdstuk 9 worden de fonetische en semantische interfaces van hetMinimalistische Programma beschreven. Het belangrijkste resultaat van ditdeel van de formalisatie is het bewijs dat geleverd wordt voor de noodzaakvan een extra `lexicon' dat sjablonen bevat voor verschillende zinstypenzoals hoofd- en bijzinnen.

Met behulp van de formalisatie die in dit proefschrift wordt beschreven,is aangetoond dat een formelere benadering van minimalistische idee�en leidttot eenduidige de�nities en soms tot het ontdekken van tekortkomingen.

Groningen Dissertations in Linguistics(GRODIL)

1. Henri�ette de Swart (1991). Adverbs of Quanti�cation: A GeneralizedQuanti�er Approach.

2. Eric Hoekstra (1991). Licencing Conditions on Phrase Structure.3. Dicky Gilbers (1992). Phonological Networks: A Theory of Segment

Representation.4. Helen de Hoop (1992). Case Con�guration and Noun Phrase Inter-

pretation.5. Gosse Bouma (1993). Nonmonotonicity and Categorial Uni�cation

Grammar.6. Peter I. Blok (1993). The Interpretation of Focus.7. Roelien Bastiaanse (1993). Studies in Aphasia.8. Bert Bos (1993). Rapid User Interface Development with the Script

Language Gist.9. Wim Kosmeijer (1993). Barriers and Licencing.10. Jan-Wouter Zwart (1993). Dutch Syntax: A Minimalist Approach.11. Mark Kas (1993). Essays on Boolean Functions and Negative Polarity.12. Ton van der Wouden (1994). Negative Contexts.13. Joop Houtman (1994). Coordination and Constituency: A Study in

Categorial Grammar.14. Petra Hendriks (1995). Comparatives and Categorial Grammar.15. Maarten de Wind (1995). Inversion in French.16. Jelly Julia de Jong (1996). The Case of Bound Pronouns in Peripheral

Romance.17. Sjoukje van der Wal (1996). Negative Polarity Items and Negation:

Tandem Acquisition.18. Anastasia Giannakidou (1997). The Landscape of Polarity Items.19. Karen Lattewitz (1997). Adjacency in Dutch and German.20. Edith Kaan (1997). Processing Subject-Object Ambiguities in Dutch.21. Henny Klein (1997). Adverbs of Degree in Dutch.22. Leonie Bosveld-de Smet (1998). On Mass and Plural Quanti�cation:

The Case of French `des'/`du'-NPs.23. Rita Landeweerd (1998). Discourse Semantics of Perspective and

Temporal Structure.24. Mettina Veenstra (1998). Formalizing the Minimalist Program.

GrodilSecretary of General LinguisticsP.O. Box 7169700 AS GroningenThe Netherlands

university of groningen formalizing the minimalist program ...the minimalist program pro efsc hrift...

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