ISO/TC37/SC4Nxxxx

Date:2020-09-18

ISOWD24617-12:2019(E)

ISOTC37/SC4/WG2

Secretariat:KATS

Languagemanagement—Semanticannotationframework(SemAF)—Part12:Quantification

Gestiondesressourceslinguistiques—Cadred'annotationsémantique—Partie12:Quantification

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Contents

Foreword.......................................................................................................................................................................5

Introduction..................................................................................................................................................................5

1Scope............................................................................................................................................................................6

2Normativereferences............................................................................................................................................6

3Termsanddefinitions............................................................................................................................................7

4Purposeandmotivation........................................................................................................................................8

5Background...............................................................................................................................................................8

6Basicconceptsintheanalysisofquantification...........................................................................................9

6.1Thenatureofquantification.............................................................................................................................................96.2Quantificationdomains:sourceandreferencedomain.....................................................................................116.3Definitenessanddeterminacy.......................................................................................................................................136.4 Distributivity.........................................................................................................................................................................146.5 SizeandCardinality...........................................................................................................................................................166.6 Scope........................................................................................................................................................................................186.7 Structuredquantificationdomains.............................................................................................................................206.8Masstermsandquantification......................................................................................................................................24

7QuantML...................................................................................................................................................................27

7.1 Overview.................................................................................................................................................................................277.2Metamodel..............................................................................................................................................................................27

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7.3Abstractsyntax.....................................................................................................................................................................287.4Concretesyntax....................................................................................................................................................................35

8 Limitations and loose ends..............................................................................................................................43

Annex A. Annotation guidelines ………………………………………………………………………. 44

Annex B. QuantML semantics …………………………………………………………………………. 47

Annex C. Example annotations and interpretations ……………………………………………….. 59

Bibliography...............................................................................................................................................................71

Harry Bunt� 11/10/2020 22:11Deleted: 44

Harry Bunt� 11/10/2020 22:11Deleted: 72

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Foreword

ISO (the International Organization for Standardization) is a worldwide federation of nationalstandards bodies (ISO member bodies). The work of preparing International Standards is normallycarriedout through ISO technical committees.Eachmemberbody interested ina subject forwhichatechnical committee has been established has the right to be represented on that committee.Internationalorganizations,governmentalandnon-governmental,inliaisonwithISO,alsotakepartinthe work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on allmattersofelectrotechnicalstandardization.

The procedures used to develop this document and those intended for its further maintenance aredescribedintheISO/IECDirectives,Part1. Inparticularthedifferentapprovalcriterianeededforthedifferenttypesof ISOdocumentsshouldbenoted.Thisdocumentwasdrafted inaccordancewiththeeditorialrulesoftheISO/IECDirectives,Part2.www.iso.org/directives

Attentionisdrawntothepossibilitythatsomeoftheelementsofthisdocumentmaybethesubjectofpatentrights. ISOshallnotbeheldresponsible for identifyinganyorallsuchpatentrights.DetailsofanypatentrightsidentifiedduringthedevelopmentofthedocumentwillbeintheIntroductionand/orontheISOlistofpatentdeclarationsreceived.www.iso.org/patents

Anytradenameusedinthisdocumentisinformationgivenfortheconvenienceofusersanddoesnotconstituteanendorsement.

For an explanation on the meaning of ISO specific terms and expressions related to conformityassessment, as well as information about ISO's adherence to the WTO principles in the TechnicalBarrierstoTrade(TBT)seethefollowingURL:Foreword-Supplementaryinformation

ThecommitteeresponsibleforthisdocumentisISO/TC37Languageandterminology/SC4Languageresourcemanagement.

Introduction

ThestandardproposedinthisdocumentisanelaborationofanapproachtoquantificationannotationthatwasoutlinedinAnnexAofISO24617-6(SemAFPrinciples).

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Languageresourcemanagement—Semanticannotationframework—Part12:Quantification

1Scope

The international standard set out in this document forms part of the ISO Semantic AnnotationFramework(SemAF).Itproposesawayofannotatingandrepresentingsemanticphenomenarelatingtoquantificationinnaturallanguage.

2Normativereferences

The following documents, inwhole or in part, are normatively referenced in this document and areindispensableforitsapplication.

ISO 12620:2009(E),Terminology and other language resources – Specification of data categories andmanagementofadatacategoryregistryforlanguageresources

ISO24612:2011(E),Languageresourcemanagement–Linguisticannotationframework(LAF)

ISO 24617-1:2012(E), Language resource management – Semantic annotation framework (SemAF) --Part1:TimeandEvents

ISO 24617-2:2012(E), Language resource management – Semantic annotation framework (SemAF) --Part2:Dialogueacts

ISO 24617-4:2014(E), Language resource management – Semantic annotation framework (SemAF) --Part4:Semanticroles(SemAF-SR)

ISO 24617-6:2016(E), Language resource management – Semantic annotation framework (SemAF) --Part6:Principlesofsemanticannotation(SemAFPrinciples)

ISO 24617-7:2014(E), Language resource management – Semantic annotation framework (SemAF) --Part7:Spatialinformation

ISO 24617-8:2016(E), Language resource management – Semantic annotation framework (SemAF) --Part8:Semanticrelationsindiscourse(DR-core)

ISO 24617-9:2019(E), Language resource management – Semantic annotation framework (SemAF) --Part9:Referenceannotationframework(RAF)

ISO/DIS24617-11:2020(E),Languageresourcemanagement–Semanticannotationframework(SemAF)--Part11:Measurablequantitativeinformation(MQI)

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3Termsanddefinitions

3.1quantificationapplicationofapredicatetooneormoresetsofarguments

3.2eventualityeventsomethingthatcanbesaidtoholdortooccur

Note1toentry:[Source:ISO24617-1].

3.3restrictorpart of a quantifying expression in natural language that specifies the reference domain (3.4) of aquantification(3.1)

3.4referencedomainsetofentitiesthataquantifiedpredicationisabout

3.5distributiondistributivityway of specifyingwhether the entities of the reference domain (3.4) of aquantification (3.1) areindividuallyinvolvedasargumentsofapredicate,orasagroup(collectively),orasamixtureofthetwo

3.6cardinalityquantifierspecificationinabsolutetermsofthesizeofthereferencedomain(3.4)ofaquantification(3.1)orofthesizeofagrouporsubsetofelementsfromthereferencedomain(3.4)involvedasargumentsinaquantifiedpredicate

3.7proportionalquantifierspecificationinrelativetermsofthesizeofthereferencedomain(3.4)ofaquantification(3.1)orofthesizeofagrouporsubsetofelementsfromthereferencedomain(3.4)involvedasargumentsinaquantifiedpredicate

3.8simpleclausenaturallanguageexpressionthatcontainsaverbanditsarguments

Note1toentry:Inlinguistics,asimpleclauseiscommonlycalledjusta‘clause’.Thatwilloccasionallyalsobedoneinthisdocument.

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3.9masstermsimplenounornounwithmodifiersthatdoesnothavebothasingularandapluralform,anddoesnotallowcombinationwithanumeral

Note 1 to entry: Typical examples of mass terms are “water”, “sand”, “dust”, “gold”, “moonlight”, “music”,“luggage”,“furniture”,“software”,“information”,“orangejuice”,“Italianmarble”.

Note2toentry:Contrastedwithmasstermsarecountterms,suchas“book”,“house”and“table”.Thecount/massdistinctionisnotreallyadistinctionbetweenwords,butbetweendifferentwaysofusingaword. Words such as “stone”and“rope”areequallyfrequentlyusedasacountnounandasamassnoun.Thedualpossibleuseofnounsisalsoillustratedbytheexamples:“There’snochickeninthepen”/”There’snochickeninthestew.”

4Purposeandmotivation

Quantification phenomena occur in almost every sentence, and their interpretation is of centralimportance for correctly extracting information from a (spoken or written) text, but no annotationschemehasyetbeenproposedthatdealswithquantificationphenomenainlanguageinageneralandsemanticallyadequateway.

Thepurposeof thisstandardis toprovidesupport fortheannotationofquantificationphenomenainnatural language in accordancewith the general principles of semantic annotation laid down in ISO24617-6and inaway that isconsistentwithexistinganddevelopingstandards for theannotationofsemanticinformationwithintheISOSemanticannotationframework(SemAF),notablyISO24617-1fortimeandevents,ISO24617-7forspatialinformation,ISO24617-4forsemanticroles,andISO24617-8for discourse relations. The annotation scheme defined in this document follows the event-basedapproach which is commonly used in contemporary semantics and generally in SemAF, viewingpredicate-argumentstructuresasexpressedinnaturallanguageintermsofparticipationinevents.

5BackgroundQuantificationphenomenahavenotbeencoveredbytheexistingpartsoftheISOSemanticannotationframework. ISO 24617-1 for time and events has some provisions for dealing with time-relatedquantification; for example, the temporal quantifier “daily” is represented as follows, where theattribute@quant is one of the attributes of temporal entities, thatmay be used to indicate that theentityisinvolvedinaquantification,andwhere“P1D”standsfor“periodofoneday”:

(1) <TIMEX3xml:id="t5"target="#token0"type="SET"value="P1D"quant="EVERY"/>

ISO 24617-7 for spatial information alsomakes use of the@quant attribute, now applied to spatialentities,andinadditionusestheattribute@scopestospecifyascoperelation.Ifthe@scopesattributeina<spatialEntity>elementidentifiedby@xml:id=”x”hasthevaluey,identifyinganotherspatialentity,thismeans that thequantifier forx has scopeover thequantifier fory.The followingexample, takenfromISO24617-7:2014,illustratesthis(where‘EC’standsfor‘externallyconnected’):

(2) Acomputerse1onss1everydeskse2. spatialEntity(id=se1, markable="computer", form=nom, countable=true, quant="1'', scopes=∅) spatialEntity(id=se2, markable="desk", form=nom, countable=true, quant="every'', scopes=se1) spatialSignal(id=ss1, markable="on", semanticType=dirTop) qsLink(id=qsl1, relType=EC, figure=se1, ground=se2, trigger=ss1) oLink(id=0l1, relType="above", figure=se1, ground=se2, trigger=ss1, frameType=intrinsic, referencePt=se2, projective=false)

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Thisisintendedtocorrespondtothefollowingformulainpredicatelogic,whichsaysthatoneverydeskthereisacomputer(ratherthanthatacertaincomputerissittingoneverydesk):

(3) ∀se2∃se1[[se2∈DESKS∧se1∈COMPUTERS]→[EC{se2,se1)∧ABOVE(se2,se1)]]

Temporalandspatialquantification,andquantificationmoregenerally,canhowevernotbeanalysedinan adequate manner by means of attributes of entities (see Bunt & Pustejovsky, 2010), sincequantification phenomena are often not properties of the entities participating in a predication, butpropertiesofrelationsbetweenthem,asdiscussedinthenextclause.

6Basicconceptsintheanalysisofquantification

6.1Thenatureofquantification

Quantification in natural language occurs whenever a predicate is applied to one or more sets ofindividualobjects,asin(4)when“gave”isviewedasa3-placepredicate:

(4) Santagavethechildrenapresent.

Asingularnounphrase like “apresent”mightseemtorefer toasingleobject,but thissentencemostlikelydoesnotmeanthatSantagaveasinglepresenttoall thechildren,butratherthateachoneofacertainsetofchildrenwasgivenadifferentpresent–sobesidesasetofchildrenalsoasetofpresentswas involved. Intechnical terms, thequantification inthenounphrase“thechildren”haswiderscopethantheonein“apresent”.Thiscanbebroughtoutbytherepresentationsinpredicatelogicshownin(5), where (5a) is the reading inwhich “the children” havewider scope, and (5b) the onewhere “apresent”haswiderscope.

(5) a.∀x[child(x)→∃y[present(y)∧give(santa,x,y)]]

b.∃ypresent(y)∧∀x[child(x)→give(santa,x,y)]

Relative scope is one of the most important and most studied aspects of quantification in naturallanguage(seee.g.Montague,1971;Cooper,1983;Kamp&Reyle,1993;Szabolcsi,1997;2008;Winter&Ruys, 2011). The annotation of scope is discussed in Clause 6.3. The semantic annotation ofquantificationinnaturallanguageismoregenerallyconcernedwithspecifyingtheprecisewayinwhichapredicateisappliedtooneormoresetsofarguments.

Quantificationhasbeen studied extensively in logic (Aristotle; Frege, 1879;Tarski, 1936;Mostowski,1957;Lindström,1966);inlinguistics(Higginbotham&May,1981:Keenan&Stavi,1986;Zwarts,1984;Partee,1988;Szabolcsi,2010;Winter&Ruys,2011),informalsemantics(Montague,1974;Barwise&Cooper,1981;vanBenthem,1984;Westerståhl,1985;Kamp&Reyle,1993;Champollion,2015),andincomputational semantics (Alshawi, 1990; Bos, 1995; Hobbs & Shieber, 1987; Pinkal, 1999; Pulman,2000;Schwertel,2005). In logic, the studyofquantificationand its role in formal reasoninghas longbeenrestrictedto theuniversal (∀, ‘forall’)andexistential (∃, ‘forsome’)quantifiers. Itwasnoted inlogicalstudies(seeMostowski,1957;Lindström,1966),thattheuniversalandtheexistentialquantifiercanbothbeviewedasexpressingapropertyofsetsofindividualobjects,involvedinapredication:theuniversal quantifier expresses the property of being a set that contains all the elements of a givendomain;theexistentialquantifierthepropertyofcontainingatleastoneoftheseelements.Moreover,thisnotionofaquantifierhasbeengeneralisedtootherpropertiesofsets,suchasthepropertiesthatinEnglishcanbeexpressedby“most”,“lessthanhalfof”,“three”,or“morethan200”.Theconceptsinthisbroaderclassofquantifiersarecalledgeneralizedquantifiers.

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Thestudyofgeneralizedquantifiers,asexpressedinnaturallanguage,hasledtogeneralizedquantifiertheory (GQT). This theory acknowledges the existence of a fundamental difference betweenquantificationinnaturallanguageandquantificationinlogic.Wordslike“all”and“some”inEnglish,aswellastheirequivalentsinotherlanguages,mayseemtobethecounterpartsoftheuniversal(∀, ‘forall’)andexistential(∃,‘forsome’)quantifiersofformallogic,andwordslike“three”,and“most”,whichhavebeencalled‘cardinalquantifiers’and‘proportionalquantifiers’(Partee,1988),mayseemtobethecounterpartsofcertaingeneralizedquantifiers,butthisisnotthecase.

Informallogic, ifpisaformulathatdenotesapropositionthentheexpressions ‘∀x.p’ and ‘∃y. p’ arequantifications,sayingthatpistrueofallindividualobjectsandthatpistrueofatleastonesuchobject,respectively. Such quantifications,which range over all individual objects in a universe of discourse,cannotbeexpressedinnaturallanguages.Itjustisnotpossibletosaythatsomethingistrue“forall”or“forsome”,where“all”and“some”wouldrefertoanyconceivableobject.TheEnglishexpressionsthatare closest to the universal and existential quantifiers of formal logic are “everything”, “everybody”,“something”and “somebody”(andsimilarly inother languages),but theseexpressionsdonotquantifyover all entities, but only over things and persons, respectively. Instead, natural languages havequantifying expressions like “all politicians”, “a present”, “some people”, and “more than five sonatas”,whichincludetheindicationofacertaindomainthatthequantificationisrestrictedto.Thishasledtothe view that quantifiers in natural language arenot determiners like “all”and ”some”, but arenounphrases (Barwise and Cooper, 1981). Determiners, instead, denotemappings from sets of entities tologicalquantifiers(propertiesofsetsofindividuals).

Notallquantifiersinnaturallanguagearenounphrases,however;temporalandspatialquantifiersmaybe expressed by adverbial expressions (“always, mostly, nowhere”,…) Not all noun phrases arequantifiers,either.Propernamesandsingulardefiniteexpressionsmayberegardedasreferringratherthanquantifyingexpressions.LeavingsuchNPsoutofconsiderationintheannotationschemespecifiedinthisdocumentwouldresultinaSwiss-cheese-likescheme,especiallyfromasemanticpointofview;theyhavethereforebeenincluded.

Some aspects of the meaning of a predication can be accounted for only if verbs are viewed asintroducingsetsofevents(inabroadsenseof‘event’,thatincludesstates,processes,…),ratherthanaspredicates.Forexample,thepasttenseoftheverbform“gave”insentence(4)indicatesthatthegive-eventsreferredtooccurinthepast.Thiscanbeexpressedinafirst-orderpredicatelogicrepresentationby introducing an additional argument in apredicate, as in (6a), orby introducing a one-place verb-derived predicatewhose argument is copied in the use of binary predicates that represent semanticroles,asin(6b).

(6) a.∀x[child(x)→∃y∃e[present(y)∧give(e,santa,x,y)]∧past(e)]

b.∀x[child(x)→∃y∃e[present(y)∧give(e)∧past(e)∧agent(e,santa)∧theme(e,y)∧ beneficiary(e,x)]]

Representation(6a)canbereadas:foreachchildxthereisapresentyandaneventesuchthatinthateventSantagavey tox, and theeventoccurred in thepast.Alternatively, representation (6b)canbereadas:foreachchildxthereisapresentyanda“give”-eventeinthepastwithSantaastheagent,xasthe beneficiary, and y as the object that was given. The latter choice, which corresponds to what isknown in the literature as the neo-Davidsonian approach, following Davidson (1967) and Parsons(1990),makesthesemanticrolesexplicitoftheparticipantsinaneventandhastheadvantagethatitallowstherepresentationofcertainquantificationaspects,suchasthecollective/individualdistinctiondiscussed below, as a property of the way in which a set of participants is involved in an event.

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Moreover, this representation is compatible with the annotation of semantic roles according to ISO24617-4,whichwouldlookasin(7):1

(7)<event xml:id=”e1” target=”#m2” pred=”give”/> <entity xml:id=”x1” target=”#m1” entityType=”santa”/> <srLink event=”#e1” participant=”#x1” semRole=”agent”/> <entity xml:id=”x2” target=”#m3” entityType=”child”/> <srLink event=”#e1” participant=”#x2” semRole=”beneficiary”/> <entity xml:id=”x3” target=”#m4” entityType=”present”/>

<srLink event=”#e1” participant=”#x3” semRole=”theme”/>

Theinterpretationofexpressionssuchas“twice”(asin“Icalledyoutwice”)and“morethanfivetimes”alsorequiretheintroductionofsetsofevents,sincetheyindicatethenumberofeventsofacertaintype.Similarlyforexpressionsoffrequency,suchas“twiceeveryday”in“Iwillcallyoutwiceeveryday”.

Thepresentannotationstandardtakesanapproachwhichcombinesgeneralizedquantifiertheorywiththe neo-Davidsonian event-based approach, including the use of semantic roles as defined in ISO24617-4.

6.2Quantificationdomains:sourceandreferencedomain

Nounphrases(NPs),expressing(generalized)quantifiers innatural language, typicallyconsistof twoparts: (1) a noun, in grammatical analysis called the ‘head’ of the NP, possibly with one or moreadjectives,prepositionalphrasesorothermodifiers,and(2)oneormoredeterminerssuchas“a”,“the”,“all”, “some”, “most”, “half of the”, and “less than 200”. The head nounwith itsmodifiers is called the‘restrictor’ of thequantifier and indicates a certaindomain that thequantifier rangesover.The termsourcedomain isused to indicate the setof entities (or, alternatively, theproperty that characterisestheseentities; seeGawron,1996) that the restrictor refers to.Thepresenceof a restrictor forms thefundamental difference between quantification in logic and quantification in natural language,mentioned above: quantification in logic ranges over the set of all entities in a given universe ofdiscourse, whereas quantification in natural language is restricted to a source domain that is madeexplicitinthequantifier’srestrictor.(Clause6.6belowdiscussesthesyntaxandsemanticsofcomplexrestrictors.)

Whilelinguisticallyrestrictedtoacertainsourcedomain,quantificationisoftenintendedtobefurtherrestricted toacertainpartof thatdomain.Forexample,a teacherwhouses thesentence (8) inclassdoes notmean to put an obligation on every person, but only on the students who participate in aparticularcourse.

(8) EverybodymusthandinhisessaybeforeThursdaynextweek

Similarly,inexample(9),“allthetwenty-sevencountries”referstoaspecificsubsetofthesourcedomaindesignated by “countries”. The use of the definite determiner forms an indication that this subset, ofcardinality27,isthecontextuallydeterminedreferencedomainofthequantification.

(9) Theproposalwasacceptedbyallthetwenty-sevencountries.

1 The XML representation specified in ISO 24617-7 uses an XML element called ‘eventuality’with an attribute`eventFrame’;insteadthenotationofISO24617-1isusedhere,withits‘event’elementand‘pred’attribute.

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Westerståhl(1985)introducedtheterm‘contextset’todesignatethecontextuallydeterminedsubsetofasourcedomainthatisrelevantinaquantifiedpredication.Parteeetal.(1990)characterizetheroleofacontextsetbysayingthat‘restrictiontoacontextsetservestorepresentwhichelementsofthelargedomainof entitieshavebeen contextually given’,where the ‘largedomainof entities’ corresponds towhatinthisdocumentiscalledthe‘referencedomain’.Moltmann(2006)relatesreferencedomainstothe definiteness of NPs: ‘Definite NPs presuppose their domain’, as illustrated in (9), where thenumerical expression “twenty-seven” expresses a presupposition about the size of the quantifier’sreferencedomain.SeealsoClause6.3belowonthedefinitenessofNPs.Aquantifier’sreferencedomainis in general determined by the familiarity, salience, recent mention, physical presence, and othercontextual considerations that make some elements of the source domain more plausible intendedreferentsparticipatingintheeventsunderconsideration.

Whereasareferencedomainiscontext-dependentbyitsverynature,asourcedomain,bycontrast, istypicallydeterminedbytherestrictorinanNP.AnNPmayhoweverhappennottocontainanyexplicitrestrictor,asin(10),inwhichcasethesourcedomainisdeterminedmainlybythecontext.

(10) a.Somelikeithot. b.Doallagree?

Thesourcedomainintheseexamplesislargelydeterminedbythepossiblecomplementsof“Some”and“all”, and partly also by the possible subjects of the verbs “like” and “agree”, but an accuratedeterminationisnotpossibleinsuchcases.Thereferencedomainin(10a)ispresumablythesameasthis source domain, and in (10b) it is the set of those persons that are present at a certainmeeting,exceptforthespeaker.

Therestrictorpartinafull-fledgedNPcontainsminimallyanounandpossiblyotherexpressionsthatmodify the noun, such as adjectives, other nouns, (as in “bread crumbs”), prepositional phrases orrelativeclauses.TheconsequencesofthepresenceofmodifiersintherestrictorpartareconsideredinClause6.6.Thedeterminerpartmaybeasequenceofdeterminersofdifferenttypes,distinguishedbysequencingandco-occurrencerestrictions.Forexample,inEnglishgrammaritiscustomarythemakeadistinction between predeterminers, central determiners, and postdeterminers (see e.g. Quirk et al.,1972;LeechandSvartvik,1975;Bennett,1987).Thisclassificationcanbeappliedinsuchawaythatthedeterminersineachclasshaveadifferentfunction(Bunt,1985):

• predeterminers express the (absolute or proportional) quantitative involvement of thereferencedomain,andmay, inaddition, saysomethingabout thedistributionofaquantifyingpredicateoverthereferencedomain–seeClause6.3;

• centraldeterminersexpressthedefinitenessoftheNP;• postdeterminersexpressapropositionaboutthecardinalityofthereferencedomain.

ThisisillustratedbytheNP“Allmyninegrandchildren”in(11),where“all”isapredeterminer,“my”acentraldeterminer,“nine”apostdeterminer,and“grandchildren”arestrictor.

(11) Allmyninegrandchildrenareboys.

Quantificationovertimeandspaceisalsoexpressedinnaturallanguagebymeansofadverbs,suchas“always”,“sometimes”,“never”,“annually”,“everywhere”,“somewhere”and“nowhere”.

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6.3Definitenessanddeterminacy

Definiteness is amorphological categorywitha language-dependentmarking; inEnglishand inmostEuropean languages it ismarkedmostclearlyby theuseofadefinitearticleand/oranominalsuffix,such as “the book” in English, and “bogen” in Danish.2 BesidesNPswith a definite determiner, otherexpressionsthatarealsoconsideredtobedefinite includeNPswithademonstrativepronoun(“thoseshoes”)ora‘universal’determiner(“everyman”,“allmen”),andsingularNPswithapossessivepronoun(“myhouse”)oragenitive(“Mary’sdog”).Propernamesandpersonalpronounssuchas“she”and“you”are also usually counted as definite.3 Determinacy, on the other hand, is the semantic property ofreferring to someparticular anddeterminate entity or collection of entities (Peters andWesterståhl,2013).Looselyspeaking,definiteexpressionsareordinarilyusedinthatway,buttherelationbetweendefinitenessanddeterminacyisnotstraightforward-see(21a)belowforanexampleofasyntacticallyindefiniteNPwhich,duetoaparticularstresspattern,isusedinadeterminateway.

Themeaningofdefiniteexpressionsisthesubjectofavastamountofliterature(seee.g.VonHeusinger,2011;Abbott,2004;2017)withalternativeapproachesandtheories.Thesemanticdifferencebetweendefinite and indefinite expressionshasbeendiscussed in termsof familiarity andnovelty (e.g.Heim,1982),salience(Lewis,1979),uniqueness,andexistencepresuppositions(seee.g.CoppockandBeaver,2015).Thefamiliarity/salienceintuitionaboutdefiniteNPscanbeaccommodatedinaGQTframeworkbyassumingthereferencedomainofaquantificationtocontainfamiliarorparticularlysaliententities.

Definiteexpressionshavebeenclaimedtodifferfromindefiniteandexplicitlyquantifiedexpressionsinhavingthefunctiontorefertocertainentities,ratherthantoquantifyoverthem(Frege,1892).Thishasbeen argued to be a false opposition (e.g. Szabolci, 2010; Abbott, 2017), for example in view of thesemanticsimilaritybetweenthe‘referential’NPin(12a)andthe‘quantificational’onein(12b).

(12) a.Thecommitteememberswentouttolunch b.Allofthecommitteememberswentouttolunch

Twomuchdebated issuesconcerningdefiniteness,whichare important foraGQT-basedapproach totheir interpretation, are whether the entity that a singular definite NP (with a count noun as head)referstoisclaimed(1)toexistand(2)tobeuniquelydetermined.Russell(1905)analysesthesentence“ThekingofFranceisbold”assayingthatthereisauniquepersonwhoisthekingofFranceandwhoisbold. Alternatively, the sentence has been analysed as saying that the king of France is bold if thereexistsexactlyonekingofFrance,andasbeingmeaninglessotherwise(Strawson,1950).CoppockandBeaver(2015)arguethatthelatterviewismostlycorrectforNPsusedasargumentsofaverb,whichcorrespondstoNPsusedasquantifiersoverparticipantsinevents,butnotnecessarilywithinthescopeofanegation(see13a)),andmoregenerallynotforpredicativeNPs,i.e.NPsusedincombinationwithacopulatoconstructapredicate,inwhichcasetheuniquenessassumptiondoesnothold(see13b,c)).

(13) a.Annadidnotgivetheonlyinvitedtalkattheconference. b.ScottisnottheonlyauthorofWaverley. c.IsScotttheonlyauthorofWaverley?

NPs with a possessive expression in central determiner position and without a pre-determiner aredefinitewhenthepossessiveexpressionisapronounorapropername,asin“myhouse”or“Tom’stwo 2Seee.g.Kramsky(1972)ontheexpressionofdefinitenessinlargenumberoflanguages.3SeeAbbott(2004)andZwarts(1994)foroverviewsofso-called‘definiteexpressions’andAbbott(2010,2017)forasurveyofissuesrelatingtodefinitenessandreferringexpressions.

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children”, but in general NPs with a possessive determiner expression are indefinite (Peters andWesterståhl, 2013), contrary to widespread belief (see e.g. Abbott, 2004). The annotation andinterpretationof anaphoricNPs is outside the scopeof thisdocument; it is the subjectmatterof ISO24617-9.

IndefiniteNPs(singularorplural),definitepluralNPs,andmassNPsdifferfromdefinitesingularNPsinnotcarryingauniquenessassumption,butwhenusedtoquantifyovereventparticipantstheyallcarryanexistencepresupposition.4Thiswillbereflectedinthesemanticsoftheproposedannotationsbytheuseofdiscoursereferentsthatdesignatenon-emptysets.

6.4 Distributivity

Thedistributivity(or‘distribution’)ofaquantificationexpresseswhetherapredicateappliestoasetofargumentsasawhole, to themembersof thatset individually,or tocertainsubsets.Theexamples in(14) illustrate thisambiguity; in the first sentence themore likely interpretation is that the twomentogethercarriedthepiano,i.e.theyactedcollectively,whereasinthesecondsentenceitismorelikelythecasethateachofthemenindividuallycarriedsomevegetables.

(14) a.Twomencarriedapianoupstairs.

b.Twomencarriedsomevegetablestothekitchen

Thedistinctionbetweencollectiveand individual readings canbebroughtoutbya representation insecond-orderpredicatelogic,asshownin(15).5

(15) a.∃X[|X|=2∧∀x[x∈X→man(x)]∧∃y∃e[piano(y)∧carry(e)∧agent(e,X)∧theme(e,y)]]

b.∃X[|X|=2∧∀x[x∈X→man(x)]∧∀y[y∈X→∃e∃z[vegetable(z)∧carry(e)∧agent(e,y) ∧theme(e,z)]]]

Representation(15a)readsasfollows:thereisacollectionXofcardinality2,whichconsistsofmen,andthereisapianoyandacarry-eventesuchthatXistheagentofthatcarry-eventeandthepianoyisthethemeofthatevent.Representation(15b)reads:thereisacollectionXofcardinality2,whichconsistsofmen,andeachofthesemenistheagentofacarry-eventwheresomevegetablesarethetheme.

Regardingtheanalysisrepresented in(15a), the ‘collection’X ismosteasilythoughtofasaset inthemathematicalsense.However,aset inthissenseisanabstractnotion,andassuchseemstobeofthewrongtypetofunctionastheagentofanevent.Intuitively,setsdonotcarryvegetables.Itispartlyforthis reason that instead of a set-theoretic approach a lattice-theoretic approach has been proposed(Link, 1983; Landman, 1991),which uses a ‘sum’ operator to form a composite individual ‘a + b’ byjoiningtwoindividuals‘a’and‘b’.Therelationbetweenacompositeindividualanditscomponentsisaformalpart-wholerelation.Whetherstipulatingthatthesumoftwoindividuals isagainanindividualhelps toresolve thecollectiveparticipant type issue isnotclear;a lattice isanabstractmathematicalconstruct, just likea set6, andsaying that thesumof two individuals is carryingvegetablesseemsno

4 There are cases of the use of a singular definite NPwithout a uniqueness assumption,which are a cause ofongoingdebate.Bodypartsareanotoriouscase:a sentence like “I squeezedLola’shand” presumablydoesnotimplythatLolahasonlyonehand.Seee.g.Coppock&Beaver(2015),Sect.2.3.5 Two-place predicates representing semantic roles are understood in this document as having as their firstargument an event and as their second argument an individual, a set of individuals, a part of an individual, aquantity,oranotherevent.6Infact,alatticeisdefinedasapartiallyorderedsetwithcertainformalproperties.

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lessstrangethansaying thatasetof two individuals iscarryingvegetables.Kamp&Reyle(1993,pp.404-405)showthataset-theoreticandalattice-theoreticapproachareformallyequivalent(atleastasfarastheinterpretationofpluralandsingularcountnounsisconcerned;quantificationinvolvingmassnounsisconsideredinClause6.8),andarereadilyconvertedintooneanother.Thisdocumentfollowsaset-theoreticapproachtotheformalsemanticsofannotationstructures,whileacknowledgingthatthecollective-individualdistinctiondoesnotprimarilyconcernthetypeofparticipant,butratherthewayin which multiple participants are involved in an event: collectively or individually. Annotationstructureswillthereforeexpresscollectivenessasapropertyofthewayinwhichasetofparticipantsisinvolved in an event; for example, in the annotation of (14a) the agent relation will be marked ascollective(seeexample(65)inClause7.4.2).

There ismore to the distribution of a quantification than just the distinction between collective andindividual (also called ‘distributive’). Consider sentence (16a), which is structurally very similar to(14a),utteredinacontextwherethepromiseexpressedin(16b)hadbeenmade:

(16) a.Theboyscarriedalltheboxesupstairs

b.IfyoucarryalltheseboxesupstairstodayI’llgiveyouanicecreamtonight.

Despitetheirstructuralsimilarity,(16a)isnotambiguousinthesamewayas(13a)forinthecontextestablishedby(16b)thespeakerdoesnotwanttosuggestthatthethreeboysdesignatedby“you”in(16b)shoulddoallthecarryingeithercollectivelyorindividually;rathertheintentionisthatthethreeboys should somehow get all the boxes upstairs, irrespective of whether they do it collectively,individually,orinotherways;thesentencecouldforinstancedescribeasetofeventsinwhichthethreeboyscollectivelycarriedtheheaviestboxes,andindividuallythelightestones(maybeevenseveralverylightonesinonego),whilepairsofboystogethercarriedtheboxesofmediumweight.Thismeansthatthedistributionofthequantificationoverthesetofthreeboysisneithercollectivenorindividual;theterm‘unspecific’hasbeenusedforthisdistribution(Bunt,1985).

FollowingLink(1983)andKamp&Reyle(1993),thenotationX*isusedinthisdocumenttodesignatethe set consisting of themembers of X and the subsets of X, and if P is a predicate applicable to themembers of X, then P* designates the generalization of P that is applicable also to subsets of X. Inparticular, if P is the characteristic function of the set X, then P* is the characteristic function of X*.Using this notation, and moreover using the notation R0 to indicate the characteristic function of areference domain that is part of a source domain with characteristic function R, the intendedinterpretationof(16a)canberepresentedinsecond-orderpredicatelogicasfollows:

(17) ∀x[box0(x)→∃y∃e[boy0*(y)∧carry-up(e)∧agent(e,y)∧∃z[box0*(z)∧[x=z∨x∈z]∧

theme(e,z)]]]

This representation says that for every box x in a given reference domain of boxes, there is a carry-eventinwhicheitheranindividualcontextuallydistinguishedboyoragroupofsuchboyscarriedthatboxxupstairsorcarriedasetofboxesupstairsthatcontainsx.

Besidesthe‘unspecificity’in(16a),wherebothindividualobjectsandsetsofindividualobjectsmaybeinvolved,thereisalsoanotherformofunspecificitywherepartsofindividualobjectsmaybeinvolved,asillustrated by (18a). This sentence could for example describe a series of eventswhere lastMondayMariohadapizza, lastWednesdayhehadoneandahalfpizzas,andonFridayhehad theremainingslicesfromWednesday.Pizzasareadomainwheretheindividualsareclearlydivisible,andwhereitiscommontoconsiderpartsofindividuals.Thesameistrueformanyotherdomainsrelatedtofoodand

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drink.Forsomeotherdomainsthisislesscommon,butinprincipleeveryphysicalobjecthasparts,andmanyabstractobjectsaswell.Whetheraquantificationshouldtakepartsofindividualsintoaccountisa context- and domain-dependent issue, but when interpreting an NP that describes domaininvolvement or size in terms of a non-integer number of individuals, this is clearly necessary. Theinterpretationofsentence(18a)asdescribingasetofeventsinwhichMariohaseatensomepiecesofpizza,addinguptoatotalofthreepizzas,canberepresentedby(18b),wherethenotation‘P⌃’isusedtodesignatethepropertyofbeingapartofanindividualthathasthepropertyP,and‘Σ⌃’designatesthejoiningtogetherofpartsofanindividual.Representation(18b)saysthatthereisaset(Y)ofpizzapartsthatwereinvolvedasthethemeinaneat-eventwithMarioastheagent,andthosepartsjoinedtogethermakeupasetofcardinality3.7

(18) a.Mariohadthreepizzaslastweek.

b.∃Y[∀y[y∈Y→[pizza⌃(y)∧∃X[|X|=3∧[x∈X→[pizza(x)]∧ΣY=X]∧

∃E[e∈E→[eat(e)∧agent(e,Mario)∧theme(e,y)]]]]

Thedistribution of a quantification is not a property of a set of participants in a set of events, but apropertyofthewayofparticipating.Thisisillustratedbyexample(19a).Presumably,eachofthemenmentionedin(19a)individuallyhadabeer,andcollectivelytheycarriedthepianoupstairs.Thiscannotbeaccountedforbytreating“themen”asreferringtoeitherasetofindividualmenortoacollectiveofmen.Thedistributionofaquantificationshouldthusbemarkedupontherelationthatdescribestheparticipationofthemeninthedrink-andcarry-events,asintheannotationfragmentshownin(19b),wheretheXMLelement‘srLink’,definedinISO24617-4,hasbeenextendedwiththeattribute‘distr’:

(19) a.Themenhadabeerbeforecarryingthepianoupstairs.

b.<entity xml:id=”x1” target=”#m1” entityType=”man”/> <event xml:id=”e1” target=”#m2” pred=”drink”/> <event xml:id=”e2” target=”#m3” pred=”carry”/> <srLink event=”#e1” participant=”#x1” semRole=”agent” distr=”individual”/>

<srLink event=”#e2” participant=”#x1” semRole=”agent” distr=”collective”/>

Collectivedistribution inaquantification innatural languagecanbeexpressedmymeansofadverbs,like“together”,“ensemble”(French),and“samen”(Dutch);individualdistributioncanalsobeexpressedby adverbial expressions, like ”one by one”, but in contrast to collective distribution, individualdistributioncanalsobeexpressedby thechoiceofdeterminer: “each” inEnglish, “chaque” inFrench,and“jeder” inGermanallexpress individualparticipation.Notethat, if insentence(19a)“Themen” isreplaced by “Each (of the)men”, then the interpretationwhere themen individually had a beer andcollectively carried the piano upstairs is no longer available; the men are now understood toindividuallycarrythepianoupstairs.Somedeterminers,suchastheEnglish“each”,“all”,and“both”canalsobeusedasadverbs,asin“Theyareallfarmers”,“Themenhadabeereach”,and“Theybothlookedhappy”;thisphenomenonisknownas‘quantifierfloating’(seee.g.Kamp&Reyle,1993).

6.5 SizeandCardinality

Cardinaldeterminersindicatethesizeofaset;in(20),thecentraldeterminer“twenty-seven”indicatesthecardinalityofthereferencedomain,whilethepredeterminer“twenty-five”indicatesthecardinality 7Expressingthesizeofacollectionofpizza-partsintermsofnumberofpizzasisspeakingasifallpizzashavethesamesize.Forexample,fourquartsoffourdifferentpizzastogetherhaveasizeof2pizzas,eventhoughitmaynotbepossibletophysicallyjointhefourpartsandformtwowell-formedpizzas.Thejoinoperator‘Σ’correspondstothemoreabstractideaofjoiningpartsofindividuals.

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ofthesubsetofthereferencedomainwhosememberswereinvolvedinvote-events.In(13a)above,thedeterminer“two”designatesthesizeofagroupofmencollectivelyinvolvedinanevent.

(20) Twenty-fiveofthetwenty-sevenstatesvotedinfavour.

So at least the following quantitative aspects of a quantificationmust be taken into account: (1) thecardinalityofthereferencedomain;(2)thenumberofelementsinvolvedinthepredication;and(3)thesizeofsets,groups,orsumsofindividualsthatareinvolvedinacollectivepredication.

The meaning of a cardinal determiner may depend on the speaker’s intention, as expressed by thestress pattern of an utterance in which it is used. Used with focal stress, “two” may give rise to apartitive interpretation; for example, in (21a) “two salesmen”means “two of the salesmen”, differentfrom(21b)wherethestressison“salesmen”.

(21) a.TWOsalesmencamein. b.TwoSALESmencamein.

The occurrence of a cardinal determiner in focus relates also to themuch debated issue whether adeterminer(oranumeral)like“two” shouldbeinterpretedas“exactlytwo”,as“twoormore”,oras“atmosttwo”.Considerthefollowingexamples:

(22) a.Twodogsaregrowling. b.DoyouhavetwoAAbatteries? c.HowmanychildrendoesMaryhave?Maryhastwochildren.

ThestandardGQTinterpretationofquantifiersoftheform“twoN” is thepropertyofbeingasetthatcontains two Ns. So for example, in DRT (Kamp and Reyle, 1993) sentence (22a) is interpreted asclaimingtheexistenceofasetof twoelementsthataredogsandgrowling.Nowsupposethereare infactthreegrowlingdogs-inthatcaseitisalsotruethattherearetwogrowlingdogs.So“two”in(22a)is infact interpretedas“twoormore”.Thisseemsreasonableforsentence(22a).Forsentence(22b),utteredinacontextwherethespeakerisexaminingaremotecontrolwithtwoapparentlyflatbatteries,thisistheonlyreasonableinterpretation.Butin(22c)theanswertothequestionlicencestheinferencethatMarydoesnothavemorethantwochildren,sointhiscase“two”means“exactlytwo”.Itiswidelyassumed(e.g.Partee,1986;KampandReyle,1993;Krifka,1999)thatthenumeral“two”indicatesthatthecardinalityoftheset(orindividualsum)denotedbytheNPthatitmodifiesisexactly2,butthatthegeneralized quantifier “two N” is interpreted in some contexts as “at least two N” and in others as“exactly two N”, due to context-specific (Gricean) pragmatic inferences - see Kadmon (2001).Quantifier readings of the type “exactly two N” are called ‘exhaustive’, and can be thought of asgeneratedbyacovertoperatorthatcouldbelexicalizedas“only”.In(22),replacing“two”by“onlytwo”incaseaandcasecenforcesorreinforcesthe“exactlytwo”reading,whereasincasebthereplacementwouldbedistinctlyoddfortheintendedmeaningofthequestion.Adetaileddiscussionofquantificationwith cardinal determiners can be found in Szabolcsi (2010). In this document it is assumed thatquantificationsarebydefaultnon-exhaustive.Similar issuesmayarise for therepetitivenessofeventquantification,asillustratedby‘Iwillcallyoutwiceeveryday”[atleast]and“Iwillsaythisonlyonce”.

Sentence (23a) illustrates the use of a cardinal determiner to indicate the cardinality of groups ofelementsfromthereferencedomainthatcollectivelyparticipateinasetofevents.Thisinterpretationcanberepresentedinpredicatelogicasshownin(23b),treatingeventsasindividualentities.Thiscan

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beannotatedasin(23c),wheretheXMLelement‘entity’hasbeenenrichedwithattributesformarkingupdefinitenessandnumberofentitiesinvolved,andthesrLinkelementwithanattribute‘size’.

(23) a.Thisassemblymachinecombines12parts.

b.∀e[[combine(e)∧agent(e,m0)]→[∃X|X|=12∧∀x.[X(x)→[part(x)∧theme(e,X)]]]

c.<entity xml:id=”x1” target=”#m1” entityType=”assembly-machine” definiteness=”det” involvement=”1”/> <event xml:id=”e1” target=”#m2” pred=”combine”/> <srLink event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” size=”12”/> <srLink event=”#e1” participant=”#x1” semRole=”theme” distr=”collective”/> For a quantification with individual distribution, the involvement of the reference domainD can beexpressed in terms of number of elements ofD, and in the case of collective distribution, the size ofcollectivelyparticipatingsetsofdomainmemberscanbemeasured in thesameway. In thecaseofaquantificationwherealsopartsD-elementsmaybeinvolved,onefindsexpressionsofinvolvementlike“twoandahalf” in “Marioate twoandahalfpizzas”. In suchacase the involvementof the referencedomain canbe computedby taking for each involvedpart the fractionof an individual that it forms,which is a rational number between 0 and 1, and adding up these numbers for all the parts thatparticipateintheevents.Thiswayofspecifyingthesizeofasetofindividualsandpartsofindividualsisageneralizationofthespecificationofthecardinalityofasetofindividualobjects.Thisisdiscussedinmore detail in Annex B. The involvement of the reference domain in amassNP quantification oftentakes the form of specifying amounts of weight, volume, or another dimension, as in “one pound ofsugar”,“twoandahalflitresofjuice”.SeeClause6.8.

6.6 Scope

6.6.1Relativeparticipantscope

Therelativescopingofquantificationsoversetsofparticipants,alreadyadumbratedinClause6.1,canbeillustratedbytheclassicalexampleofscopeambiguityin(24),whereoneinterpretationisthattheNP“Everyoneinthisroom”haswiderscopethantheNP“twolanguages”,sothatthesentencesaysthateachofthepeopleintheroommasterstwolanguages;whichtwolanguagesmaydifferfrompersontoperson,andtheotherinterpretationisthatthetwolanguagesarethesameforeveryone.

(24) Everyoneinthisroomspeakstwolanguages.

Quantifier scope ambiguities are a nightmare from a computational point of view: a sentencewith knounphrasesmayhavek!possibleinterpretationsduetoalternativescopingsalone,althoughsyntacticconstraints reduce this number. Hobbs and Shieber (1987) have shown that a sentence with thesyntacticstructureof(25),containingfiveNPs,andthushaving5!=120(=5x4x3x2)potentialscopings,has in fact ‘only’ 42 valid alternative scopings – which is still a formidable number, themore sincequantifierdistributionambiguitiesformanindependent(andevenricher)sourceofambiguity.

(25) Somerepresentativesofeverydepartmentinmostcompaniessawafewsamplesof everyproduct.

Therearecaseswherenoneofthequantificationsoveronesetofparticipantshaswiderscopethantheother. An example is so-called ‘cumulative’ quantification (Scha, 1981), as illustrated in (26) (due toReyle,1993):

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(26) Threebreweriessuppliedfifteeninns.

The intended reading here is not that each one of three breweries supplied each one of fifteen inns(wide scope of “three breweries”), nor that each one of fifteen inns was supplied by each of threebreweries(widescopeof“fiveinns”),butratherthatthereisasetAofthreebreweriesandasetBoffifteen inns, such that the members of A supplied members of B, and that the members of B weresuppliedbymembersofA.Inthiscase,thetwoquantificationscanbesaidtohaveequalscope.Thisisaninstanceofso-called‘branchingquantification’(Hintikka,1973;Barwise,1979;Sher,1997), i.e.thephenomenon thata sentencecontains twoormorequantifiersofwhich the scopesareonlypartiallyordered.Sher(1997)callsthecaseofcumulativequantification‘independentbranchingquantification’,sinceinthiscaseeachquantifierissemanticallyindependentoftheotherquantifier(s).

Thesentencein(27a)hasthesamesyntacticformastheonein(26),butheretheintendedreadingisnotcumulative;itisfromareportaboutafootballtournamentwhereteamsofboysandteamsofgirlsparticipated,andwheneverateamofboysplayedagainstateamofgirls,itssizewouldbereducedfrom11to7.Thisisexpressedinpredicatelogicin(26b)Thetwocardinaldeterminersareindicatorsnotofreferencedomaininvolvementbutofgroupsizeassociatedwiththecollectiveparticipationofboysandgirls.Thequantificationsoverboysandgirlsdonotdiffer inscopeandrequireaspecial treatmentofthecardinaldeterminers(seeAnnexB;thescoperelationinthiscaseiscalled‘equal’).

(27) a.Sevenboysplayedagainstelevengirls.

b.∀e∀X∀Y[[play(e)∧∀x[X(x)→boy(x)]∧∀y[Y(y)→girl(y)]∧agent(e,X)∧agent(e,Y]→[|X|=7∧|Y|=11]]

Insummary,acardinaldeterminerindicatesthesizeofaset–ofexactlywhichsetisdeterminedbythescopeofthequantifierexpressedbytheNPrelativetothoseofotherquantifiersinthesameclauseandbywhether theentitiesof thequantifier’s referencedomainparticipate collectivelyor individually intheclause’sevents.

6.6.2Eventscope

Studies of relative scope in quantifying expressions have been focused almost exclusively on therelativescopesofsetsofparticipants.However,whensetsofparticipantsareinvolvedinasetofeventsrather than in a single event, the relative scoping of participants and events is also an issue. This isillustrated by the two possible readings of the sentence in example (28)a. Besides the reading thatcomes down to saying that everyone is mortal, which can be represented in predicate logic as∀x[person(x)→will-die(x)],orasin(28)a,usingexplicitevents,thereisalsoareadingwhichpredictsanapocalyptic future event in which everyone will die. (Note that this interpretation requires theconsideration of events in which multiple participants occupy the same role. The ISO approach tosemanticroleannotation(ISO24617-4),doesallowthis.)

There is no way to represent this second reading without explicitly introducing events; (28)a. and(28)b.showhowbothreadingscanberepresentedinfirst-orderlogicbyassigningalternativerelativescopestothequantificationsovereventsandparticipants:

(28) a.Everyonewilldie.

b.∀x[person(x)→∃e[die(e)∧future(e)∧theme(e,x)]]

c.∃e[die(e)∧future(e)∧∀x[person(x)→theme(e,x)]]

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Quantifications over events tend to have narrow scope. Champollion (2015) claims that eventquantificationalways hasnarrow scope compared to the scopeof quantified arguments, but this is acontext-dependentissue,astheexamplein(29)illustrates.Theinterpretationof(29a).asdescribingasingleeventwithmultipleparticipants,isannotatedin(29b).,wheretheXMLelement‘srLink’hasbeenenrichedwiththeattribute‘evScope’toindicatetherelativescopeoftheeventsandtheparticipants.

(29) a.Allpassengersdied[inthecrash].

b.<entity xml:id=”x1” target=”#m1” entityType=”passenger” involvement=”all”/> <event xml:id=”e1” target=”#m2” pred=”die” time=“past”/> <srLink event=”#e1” participant=”#x1” semRole=”theme” distr=”individual” evScope=”wide”/>6.6.3Negationscope

The annotation scheme defined in this document specifies away of indicating the relative scopes ofquantificationsandnegations.Theexamplesentencein(30).illustratessomeofthepossiblescopesofanegationatclauselevel.Onthereadingin(30)bthenegationscopesovertheentireclause;in(30)cthequantifier“theunions”outscopesthenegation.(30) a.Theunionsdonotaccepttheproposal. b.not(theunionsaccepttheproposal),i.e.itisnotthecasethatalltheunionsacceptthe proposal c.alltheunionsdonotaccepttheproposalThereadings(30b)and(30c)aredistinguishedinannotationsbyintroducinga@polarityattributeforparticipation link structureswith the value “widenegative” forwide-scopenegation (case (30b); see(31b)) and the value “narrow negative” for narrow-scope negation (case (30c)); see (31c)). For thesemanticsoftheseannotationsseeAnnexB.(31) a.Theunionsdonotaccepttheproposal. b.<srLink event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” polarity=”neg-wide”/> c.<srLink event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” polarity=”neg-narrow”/> Note that thiswayof annotatingnegation scopesmakes itpossible to alsohandle casesofdoubleortriplenegation,suchas“Notalltheunionsdonotaccepttheproposal”andeven“Itisnotthecasethatnotalltheunionsdonotaccepttheproposal”.

6.7 Structuredquantificationdomains

Quantificationinnaturallanguagehasbeenstudiedmostlyinrelationtothesemanticsofnounphrases(NPs)andtheircombinationwithverbphrases.Quantificationphenomenaarisealsowhenanadjectiveisappliedtoasetofarguments.Forexample,thesentencein(32a)isambiguousbetweenareadinginwhich “these books” as awhole are heavy (collective reading), and a reading inwhich each of “thesebooks”isheavy(distributivereading).Byanalogywiththepredicatelogicrepresentationofdistributiveand collective readingsof quantified verb arguments, these readings canbe analysed semantically intermsofparticipationinasetofevents(mostlyofastatickind),asshownintherepresentations(32b)and (32c)8, respectively, which opens the way for dealing with questions of the distribution of the

8Theuseof the ‘theme’ role toconnect theargumentand thestatedenotedby theadjective in thisanalysis isjustifiedbythedefinitionofthisroleinISO24617-4,whichstipulatesthataparticipantinaneventorstatehas

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participationandtherelativescopeofeventsandparticipants.Alternatively, thesimpler(butslightlyless expressive) representations in (32d,e) can be used, with a one-place predicate constantcorresponding to the adjective, rather than a set of events, since questions of scope do not arise inadjectivalmodification.Asin(16)above,thenotationwithasubscript ‘0’asin ‘book0’ isusedheretoindicatethatthereferencedomainofthephrase“thesebooks”isformednotbythesourcedomainofallbooks, but rather to some specific set of books, determined by the context and indicated by thedemonstrative“these”.

(32) a.Thesebooksareheavy.

b.∃X[∀x[x∈X↔[book0(x)∧∃e[heavy(e)∧theme(e,x)]]]]

c.∃X[∀x[x∈X↔book0(x)]∧∃e[heavy(e)∧theme(e,X)]]

d.∃X[∀x[x∈X↔[booko(x)∧heavy(x)]]]

e.∃X[∀x[x∈X↔book0(x))]∧heavy*(X)]

Example (32) illustrates the predicative use of an adjective; the attributive use is illustrated in (33),whichdisplaysthesameambiguityasthepredicativeusein(31).Predicatelogicrepresentationsofthetworeadingsareshownin(34)(ontheinterpretationwherethebookswerecarriedcollectively).

(33) Petercarriedtheheavybooksupstairs.

(34) a.∃X[∀x[x∈X↔[book0(x)∧heavy(x)∧∃e[carry(e)∧agent(e,peter)∧theme(e,X)]]]

b.∃X[∀x[x∈X↔book0(x)]∧heavy*(X)∧∃e[carry(e)∧agent(e,peter)∧theme(e,X)]]

Theindividual/collectiveambiguityof(31)and(33)isduetoanambiguityinthewaythepredicateisappliedtoitsarguments.Uponthepredicateviewofadjectivescorrespondingto(32c,d)thiscouldbeannotatedasin(36):

(35) heavybooks

(36) <entity id="x1" target="#m2" pred=”book”/> <entity id="x2" target=”#m1 pred=”heavy”/>

<adLink head="#x1" mod="#x2" distr="collective"/>

NotethatanattributiveadjectiveoccursintherestrictorpartofanNP,andassuchcontributestothedetermination of a source domain for quantified predication. Such a role can be played not only byadjectivesbutalsobynouns,prepositionalphrases(PPs),andrelativeclauses(RCs),as illustratedbytheNPsin(37),showingrestrictorsthatcontainadjectives(37a-f),nouns(37d),prepositionalphrases(37e),andrelativeclauses(37f-g).

(37) a.Thirty-twoChinesestudentsenrolled.

b.AlexshowedmetwoofhisrareChinesebooks.

c.Jimwascarryingsomeheavybooks.

d.Aliceshowedmeherbeautifularchaeologybooks.

e.AlexshowedmetworarebooksfromChina.

f.AlexshowedmetworarebooksprintedinHongKong.

thisrole if it iscentraltotheevent/state; it isessential fortheevent/statetooccur/hold;andit isnotstructurallychangedbytheevent/state.

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g.Alexshowedmetwobooksthathe’dboughtinanantiqueshopinChengdu.

Themodificationofanounbyanothernounisdifferentfrommodificationbyanadjective, inthatthemodifyingnoun can in general not verywell be regarded as a predicate.Rather, themodifyingnoundenotesaconceptorapropertydefiningasetofconceptstowhichthedenotationofthemodifiednounhassomeimplicitsemanticrelation,likeinstrument-for,purpose-of,usedfor,obtained-from,orlocation-of,asthefollowingexamplesillustrate:

(38) universitydiplomas,archaeologybooks,garbagecan,pianomusic,smokingban,diningcar, sleepingcompartments,truckdrivers,councilmembers

Hobbs et al. (1993) have proposed a treatment of noun-nounmodification in predicate logic whichintroduces a metavariable ‘NN’ that is to be instantiated by a semantically appropriate two-placepredicate through abductive reasoning, exploiting context information. For example, the nominalcompound “Boston office” in (39a) is represented as (39b). The variable NN can in this example beinstantiatedasLocated-in.

(39) a.TheBostonofficecalled.

b.office(x)∧boston(y)∧NN(x,y)

Possessive expressions have in commonwith noun-nounmodification that they introduce a relationthatisnotmadeexplicitintheexpressionorthatisexpressedinavaguewayusingthepreposition“of”inEnglishandsimilarlyvagueprepositionsinotherlanguages(e.g.“de”inRomancelanguages,“van”inDutch).Typicalexamplesareshownin(40).Whatallthese(andother)formshaveincommonisthattheyexpresssomesortofpossessionrelationbetweena(setof)possessor(s)andasetofpossessions.Possessive expressions involve quantification over possessions (and possibly also over possessors).Similarto(39),acaselike(40a1)canbeanalysedschematicallyasin(40b),introducingageneric‘Poss’relation,followingPetersandWesterståhl(2013).

(40) a.1.Tom’shouse

2.JohnandMary’stwochildren

3.twoofmybooks

4.(the)headmaster’schildren’stoys

5.(the)childrenoftheheadmaster

6.everystudent’slibrarycard

b.house(x)∧tom(y)∧Poss(x,y)

Modification by PPs, as illustrated by the examples in (41), bears some semantic similarity to noun-nounmodification in the caseof simplePPs, as the similarityof the representations (39b)and (41b)illustrate;thedifferenceisthatinthecaseofPPmodificationtheprepositiongivesanindication(albeitin a rather vague and ambiguousway) of how the entities denoted by the head noun are related tocertainotherentities.

(41) a.booksfromHongKong.

b.book(x)∧hongkong(y)∧from(x,y)

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Asinthecaseofmodificationbyanadjective,themodificationbyaPPcanbedistributiveorcollective.Thisisillustratedbythesentence“Bellpeppersforfiftypesos”,whichwasseeninapricetagofaboxofbellpeppers.This sentence is ambiguousas towhether thePP “for fiftypesos” indicates that thebellpeppersintheboxcost50pesosapiece(individualreading)orthatthewholecontentoftheboxcosts50pesos(collectivereading).NotethatthepluralNP“fiftypesos”shouldbetreatedasdenotingasingleentity,an‘amount’(ofmoney),inthesensediscussedinClause6.7.

A fundamental difference between PP modification on the one hand and adjectival and noun-nounmodification on the other, is that the embedded NP, which is linked to the modified head by apreposition,canbearbitrarilycomplex.Inparticular,iftheembeddedNPisaquantifier(ratherthanareferential expression, as in (40)), thequestionarisesofhow thisquantifier is scoped relative to thequantifiers in the main clause. Scope ambiguities may occur in PP-modification with individualdistribution because a distributive modifier expresses a quantifying predicate that is applied to theentitiesdenotedbytheNPhead,andthisquantifiermayhavewiderscopethanaquantifierinthemainclause,asillustratedin(42a).Onthemostplausiblereadingofthissentence,thequantifier“everycitythat…intheplan”takesscopeovertheexistentialquantifier“acouncilmember”.Thisphenomenonisknownas‘inverselinking’(May,1977;MayandBale,2007;RuysandWinter,2011;Barker,2014).Thepredicate logic representations in (42b, c) showthereadingwith inverse-linkingand the implausiblereadingwithoutinverselinking,respectively.

(42) a.PresidentKaymetwithacouncilmemberfromeverycitythattookaninterestintheplan.

b.∀y[city(y)→∃x[council-member(x)∧from(x,y)∧meet(kay,x)]]

c.∃x[council-member(x)∧∀y[city(y)→from(x,y)]∧meet(kay,x)]

If thesentencewiththePP-modifiedNPcontainsmorethanonequantifier, thenthequantifierof theembeddedNPmayalso takescopeovermore thanonequantifier.This is illustrated in (43),whereauniversallyquantifiedNP(“everymanfromasmalltowninIowa”)containsanexistentiallyquantifiedembeddedNP(“asmalltowninIowa”)inaPP.Theinverselylinkedreadingshownin(43b)seemsmoreprominentthanreadingswheretheembeddedquantifierhasnarrowscope.

(43) a.RecruitersapproachedeverymanfromasmalltowninIowa.

b.∃y[iowa-smalltown(y)→[∀x[man(x)∧from(x,y)]→∃z[recruiter(z)∧approach(z,x)]]]

Inverselinkingmayalsooccurinthemodificationbyarelativeclause(RC),butmuchlesssothaninPP-modificationduetothefactthatRCsareso-called`scopeislands’(Rodman,1976),whichhastheeffectthatmanyquantifierscanonlytakescopeoverotherquantifiersinsidetheRC.Thisisillustratedbythecontrastbetweenthefollowingsentences(fromBarker,2014):

(44) a.Awomanfromeveryboroughspoke.

b.Awomanwhoisfromeveryboroughspoke

The sentence with PP modification has an interpretation with inversely linked scopes (in fact thisinterpretationisstronglypreferred),whichthesentencewithRCmodificationdoesnothave.9WhenanNPheadismodifiedbyanRCtheentitiesdenotedbytheNPheadparticipateintwoevents:intheone

9 See Ruys andWinter, 2011,who discussmany other subtleties concerning scope restrictions in English, andSzabolcsi,2010whoalsoconsidersscopephenomenainotherlanguages.

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describedinthemainclauseandinanotheronedescribedintheRC.Fortheparticipationinthelatterevent,issuesofdistributionandscopearise,astheexamplein(45a)illustrates.

(45) a.Thehugetubes(thatwere)movedbythosecranes.

b.Thosecranesmovedfivehugetubes.

TheNPof(45a)isambiguousinthedistributiveaspectofthequantificationin“thehugetubes”,inthesamewayasinsentence(45b):Werethepipesmovedonebyone(individualreading)orallinonego(collectivereading);Didthecranesindividuallymovethetubesordidtheyacttogether?Althoughnotsoconspicuous, theambiguity isarealone, since thesentence in (45a)mightbe intended torefer tothosetubesthatweremovedonebyonebycertaincranesactingcollectively,ratherthantosomeothertubesthatweremovedinadifferentway.

Therestrictorofaquantifiercanhaveacomplexstructurenotonlyduetothepresenceofheadnounmodifiers,butalsoduetotheoccurrenceofconjunctionsasin(46).Conjunctionsincombinationwithadjectives and other modifiers moreover give rise to questions of scope, as illustrated by thebracketingsintheexamplesentenceswithconjunctionsandadjectivesinNPheadsin(46).

(46) a.(Morethantwothousand)(menandwomen)signedthepetition.

b.(Morethanfifty)(ancient(booksandmanuscripts))wererescued.

c.(Morethanfifty)(ancient(books)and(filmscripts))wererescued.

d.(Morethanfifty)(ancient(books,manuscriptsandpaintings))wererescued.

e.(Morethanfifty)(ancient(books),magazinesandphotoalbums)wererescued.

f.(Morethanfifty)(valuable(ancient(booksandmanuscripts)))wererescued.

g.(Morethanfifty)(valuable(ancient(books)andpaintings))wererescued.

h.Some(beautiful(old(photographs))and(valuable(ancient(books)andpaintings)) wererescued.

Similarscopeambiguitiesasforadjectivesariseforotherformsofheadmodification,suchas“Artsandcraftsmuseum”,“MenandwomenfromNigeria”,“Booksandpaintingsthatwererescued”,andsoon.

6.8Masstermsandquantification

StudiesofquantificationinnaturallanguagehaveoftenbeenrestrictedtocaseswheretheNPheadisa‘count noun’, i.e. a noun that has both a singular and a plural form, and that can be combinedwithnumbers,asin“threemen”and“twosonatas”.Incontrastwithcountnouns,massnouns,such“water”,“gold”,“music”,“poetry”,and“furniture”haveonlyoneform(usuallysingular)andcannotbequantifiedbymeans of numbers; instead, they require ‘amount expressions’ (also called ‘measure phrases’) formakingaquantifiedpredication,asillustratedin(47):

(47) Inconstructingthenewplatform,morethanfivehundredtonsofconcretewasused.

Universalquantificationwithamassnoun,asin“allthemilk”,issyntacticallyverysimilartothecountnouncase,butsemanticallydifferent;comparethetwosentencesin(48):

(48) a.Theboyspolishedalltheknivesinthedrawer.

b.Theboysdrankallthemilkinthefridge.

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In(48a)apredicateisappliedtoasetofapples,andlikewisein(48b)apredicateisappliedtoasetofquantities (or ‘portions’) of milk. A difference is that (48a) can be analysed as: “Every knife in thedrawerwastheobjectinanpolish-eventwithoneoftheboysastheagent”,butitisnotclearthattheanalogousanalysis“Everyquantityofmilkinthefridgewastheobjectinadrink-eventwithoneoftheboysastheagent”wouldmakesense,sincethesetofquantitiesofmilkinthefridgeincludesglassesofmilk,sipsofmilk,bottlesofmilkand,otherquantitiesthatwerenotassuchtheobjectofadrink-event..Auniversalmassnounquantificationoftheform“alltheM”doesnotrefertoallthequantitiesofM,butrathertoacertainsubsetofquantitiesthattogethermakeupthewholeof“theM”.(Asimilarsituationarises for countNPs in case the individuals in thequantificationdomainhavean internalpart-wholestructure,asin“Theboysateallthepizzas”.)

Count/mass is not a distinction between words, but between different ways of using words, asillustratedbythefollowingtwopairsofsentences:“There’snochickenintheyard”/”There’snochickeninthestew”and“CanIhavesomecoffee?”/”CanIhavetwocoffees?”.AdetailedanalysisofmassnounquantificationcanbefoundinBunt(1985),whichcombineselementsfromlatticetheoryandsettheoryin an integrated fashion. Quantities are analysed as having a part-whole structure, defining a sumoperationΣsuchthatthesumoftwoquantitiesofMformsanotherquantityofM(liketheoperatorin(18)).Anexpressionoftheform“alltheM”withamassnoun“M”,isinterpretedasreferringtoasetXofquantitiesofMthattogethermakeupthereferencedomainM0(i.e.thesetofallcontextuallyrelevantquantitiesofM), in thesensethat theirsumequals thesumofallquantities in thereferencedomain:Σ(X)=Σ(M0).

Quantification by means of mass NPs is, like quantification with count NPs, characterized by adistribution,scope,definiteness,domaininvolvement,andsizeofthereferencedomainorofpartsofit,buttherearesomenotabledifferencesindistributionandintheexpressionofinvolvementandsize.

Sincemass nouns do not individuate their reference, quantification bymassNPswould seemnot toallow individual distribution. Yet there is a distinction somewhat similar to the individual/collectivedistinctionofcountNPquantifiers,as(49)illustrates.

(49) a.Allthewaterinthelakeispolluted.

b.Thesandinthetruckweighstwelvetons.

c.Theboyscarriedallthesandtothebackyard.

d.Thecraneliftedallthesand.

In (49a) the predicate of being polluted applies to any sample of “the water in the lake”; thisinterpretationiscalled‘homogeneous’;thedistributionis‘parts’.In(49b)thepredicateofweighing12tons applies to the quantities of sand taken together, so this is a formof collective quantification. In(49c)theboysdidnotcarryeveryquantityofsand,butcertainquantitiesthattogethermakeup“allthesand”, similar to (48b) above; sentence (49d) can be considered to be ambiguous between such areadingandacollectivereading.

Expressions of proportional involvement, as in “all the pasta”, “most of the pasta”, “half of the pasta”cannotbeinterpretedintermsofnumbersofquantities.Astheexamplesin(48b)and(49)illustrate,completeinvolvementofamassNPreferencedomainmeansthatthemergeofthequantitiesinvolvedforms the entire domain. Non-zero involvementmeans that al least one quantity of non-zero size isinvolved,and“mostM”quantificationoverreferencedomainM0meansthatthesizeofthesumΣ(X)isgreaterthanhalfthesizeofthesumΣM0.SizemeasurementisdiscussedinAnnexB.

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Theexamplesin(48b)and(49)illustratethreedifferentwaysinwhichthequantificationdomainofamass NP can be completely involved in a predication, corresponding to three different senses ofexpressionsof the form“allM”(or “all theM”) inEnglish,andsimilarly inother languages.Completeinvolvement with parts distribution (the ‘homogeneous interpretation’), as in (49a), where “all thewater”referstothesetofallcontextuallydistinguishedquantitiesofwater,willbeannotatedwiththe‘involvement’attributehavingthevalue‘every’.Incaseslike(48b)and(49c),where“allthesand”referstoasubsetofquantitiesofsandthattogethermakeupall the(contextuallydistinguished)sand–the‘involvement’attributehasthevalue“total”.Finally,onthecollectivereadingof(49b,d),where“(all)thesand”referstothequantityofsandformedbyallcontextuallyrelevantquantitiesofsandtogether,theinvolvementwillbeannotatedas“whole”.ThisissummarizedinTable1below.

TherelativescopingofamassNPquantifierandacountNPquantifier,oroftwomassNPquantifiers,isnodifferentfromthatoftwocountNPquantifiers,asillustratedby(50):

(50) a.Everyoneshouldreadthreepapers. b.Everyoneshouldstudy500linesofpoetry.

involvement distribution interpretation example

every parts ForeveryquantityofM (49a)

total parts FortheelementsinasetofquantitiesofMthattogethermakeupthewholeofM

(48b),(49c)

whole collective ForMasawhole (49b)

Table1.InvolvementanddistributivityinmassNPquantification.

Unitscanbecomplex,like‘kilowatt-hour’(unitofelectricalenergy)or‘meter/second’(unitofvelocity).Formally, a unit is either a basic unit or a triple <〈u1, u2, Q>, where Q=× (multiplication) or Q=/(division) and u1 and u2 are (possibly complex) units. This allows for complex units such asmeter/(second×second) (meter per square second) for measuring acceleration, andeuro/(meter×meter) for measuring the price of land. ISO 24617-7 Spatial information (ISO-Space)includesamounts(called ‘measures’)ofspace formeasuringdistances; ISO24617-1Timeandevents(ISO-TimeML)includesamountsoftimeformeasuringdurations.Inbothcases,onlyelementaryunitsareconsidered,whichistoolimitedfordealingwithvelocities,accelerations,etc.

Amountexpressionscanbeusednotonlytospecifyaninvolvementorasizeinthecaseofamassnounquantification,butalsofordoingsointhecaseofacountnounquantification,asillustratedin“Fivekilosofapples.”Theabstractsyntaxofannotationsforquantitiescanbedefinedbyintroducingpairs<n,u>,where‘u’iseitheranelementaryunitoratriple,asindicatedabovein(51).AcorrespondingXML-basedconcretesyntaxusesanelement‘amount’withattribute-valuepairsforthenumericalpartandtheunitpart,asin(52)(wheremarkablem1refersto“threemiles”).

(52) a.threemiles b.<amount xml:id=”am1” target=”#m1” num=”3” unit=”mile”/>

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7QuantML

7.1 Overview

FollowingthemethodologydescribedinISOstandard24617-6(Principlesofsemanticannotation),thespecificationoftheQuantMLmarkuplanguageconsistsoffourparts:

1. Ametamodel, providing a schematic overviewof the concepts thatmayoccur in annotations,andtherelationsbetweenthem.

2. Anabstractsyntax,providingaformalspecificationoftheinventoryoftheconceptsfromwhichannotations are built up and of the possible ways of combining them, using set-theoreticaloperations,toformconceptualstructurescalled‘annotationstructures’.

3. Aconcretesyntax,definingarepresentationformatforannotationstructures.4. Asemantics,defininganinterpretationofannotationstructures(andtheirrepresentations).

Theabstractsyntaxofanannotationschemespecifies the information inannotations in termsofset-theoreticalstructuressuchaspairsandtriples.Aconcretesyntaxspecifiesarepresentationformatforsuch structures, such as the XML format used in (19), where a triple 〈e1, e2, Ri〉is represented by asequenceofXMLelements,ofwhich<srLink event=”#e1” participant=”#x1” semRole=”agent”/>representstheagentrelation,theeventstructure(e1),andtheparticipantentitystructure.

A representation format for annotation structures should ideally give an exact expression of theinformationcontainedinsuchstructures.Aconcretesyntaxthatdefinesarepresentationformatforagivenabstractsyntaxissaidtobeidealifithasthefollowingproperties:

— completeness:everystructuredefinedbytheabstractsyntaxcanberepresentedbyanexpressiondefinedbytheconcretesyntax;

— unambiguity:everyrepresentationdefinedbytheconcretesyntaxistherenderingofexactlyonestructuredefinedbytheabstractsyntax.

Therepresentationformatdefinedbyanidealconcretesyntaxiscalledanidealrepresentationformat.Anytwoidealrepresentationformatsaresemanticallyequivalent,inthesensethatrepresentationsinoneformatcanbeconvertedtotheotherinameaning-preservingway(namely,bothrepresentationshavethemeaningoftheannotationstructurethattheyrepresent).

7.2Metamodel

A metamodel gives a schematic overview of the abstract syntax of a class of annotations, typicallyslightlysimplified. It showstheconcepts thatgo intoannotationsand indicateshowtheyarerelated.Themetamodel in Fig. 1 is simplified in that it does not show the internal structure of some of theconcepts, such as the different possible ways of modifying an NP head, or the internal structure ofdomainsizeandfrequencyspecifications.

According to the analysis of quantification given in Clause 6, the set of participants in a quantifiedpredicationischaracterizedbythefollowingproperties:

1. the source domain from which the participants in a certain set of events are drawn (actualparticipantsbeingindividualelements,collectionsofelements,orpartsofthesourcedomain);

2. theeventdomaintowhichtheeventualitiesbelonginwhichtheparticipantsareinvolved;

3. thedeterminacy,ofthereferencedomainofthequantification(i.e.asubsetorpartofthesourcedomain,possiblytheentiresourcedomain);

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4. theway inwhichelementsorpartsof thereferencedomainparticipate inasetofevents: theindividuationofthereferencedomain(individualobjects,possiblyalsotheirparts,orquantitiesofmasses),thedistributionofthequantification,thesemanticrole,andtherelativescopeofthequantifiedrelationovereventsandparticipants;

5. thequantitative(absoluteorproportional)involvementofthereferencedomain;

6. the size of the reference domain, or of groups, subsets, or parts of the reference domaininvolvedinthequantifyingpredication;

7. Therepetitivenessofrecurringevents(asin“Johncalledhometwiceeveryday”).

Figure1:Metamodelfortheannotationofquantification

Themetamodelalsoshows that theeventsand theirparticipants inaquantificationare linguisticallyexpressed: theyare related toamarkable,which identifiesa regionofprimarydata.By contrast, theparticipationrelation(anditssemanticrole)andrelativescoperelationsarenotverbalized,andhencedo not relate to markables. Some of the other properties are mostly verbalized, such as size andfrequency;othersaresometimesverbalizedbutmaybeimplicit(definiteness,involvement);thisisnotshowninthemetamodel,inordernottoclutteritup.

7.3Abstractsyntax

7.3.1Overview

Thestructuresdefinedby theabstract syntaxaren-tuplesofelements thatareeitherbasicconcepts,taken froma storeof basic concepts called the ‘conceptual inventory’, orn-tuplesof such structures.Two kinds of structures are distinguished: entity structures and link structures. An entity structurecontainssemanticinformationaboutasegmentofprimarydataandisformallyapair〈m,s〉consistingof a markable, which refers to a segment of primary data, and certain semantic information. A linkstructurecontainsinformationaboutthewaytwoormoresegmentsofprimarydataaresemantically

Primarydata

Markables

Eventset

Determinacy

Distributivity

Eventdomain

Participantset

Argumentscoping

Participation

Individuation

Sourcedomain

o

Involvement

Semanticrole

Eventscope

Repetitiveness Repetitiveness

Polarity Exhaustive-ness

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related; for example, in semantic role annotation a link structure is a triple 〈e1,e2,Ri〉wheree1 is anentity structure that contains information about an event, e2 is an entity structure that containsinformationaboutaparticipantintheevent,andRiisasemanticrole.

Accordingtotheanalysisofquantification,reflectedinthemetamodel,ofcentralimportancearesetsofevents,setsofentitiesparticipatinginevents,andthesemanticrelationbetweenthem.Thefirsttwoofthesecorrespondtoentitystructures,whilethelattercorrespondstoalinkstructure.

7.3.2Entitystructuresforeventsandparticipants

Ofthepropertiesthatcharacterizeasetofparticipantsinvolvedinaquantification,thesourcedomain,the involvement of the reference domain, and the definiteness of the reference domain must bespecified in order for the quantification to be semantically interpretable; these elements are thusobligatoryintheannotationofaquantification.Theentitystructure〈m,s〉forasetofparticipantsthuscontainsminimallyatriple:

(53) εp=〈m,〈S,q,d〉〉

with S = source domain specification, q = reference domain involvement, and d = definiteness. SuchtriplescorrespondtoNPsthatdonotcontaincardinaldeterminersoramountqualifiers.

Cardinal determiners, as already adumbrated in Clause 6.2, can indicate the involvement of thereference domain, the size of the reference domain, or the size of groups, subsets or parts of thereferencedomain.ThesameistrueforamountexpressionsasdeterminersinmassNPs.

Thefunctionofacardinaldetermineroramountqualifierdependsonitssyntacticposition.Ofthethreepositions in a determiner sequence (pre-determiner, central determiner, post-determiner), cardinaldeterminers canoccuronly inpost-determinerpositionand inpre-determinerposition inapartitiveconstruction,suchas“Twoofmysons”and“Fivehundredgrammesofthispasta”inEnglish,and“Undemesamis”inFrench.Inpre-determinerposition,acardinaldeterminerexpressesdomaininvolvement(asin “Fifteenofthesestudentsreadtwopapers),orgroupsize(asin“Twoofmysonscarriedapianoupstairs”, in a situationwhere one pair of sons carried one piano, another pair another piano, and athird pair a third piano), or the size of reference domain subsets whose members participateindividuallywithinthescopeofanotherquantifier,asin“Everystudenthastoreadthreepapers”,onthereading with individual distribution over papers and wide scope of “Every student” (so that eachstudent is associatedwithapossiblydifferent subsetof threepapers). Inpost-determinerposition, acardinaldetermineralwaysindicatesthesizeofthereferencedomain(asin“twoofmythreesons”).

Inadditiontothethreeelementsmentionedin(53),aparticipantentitystructuremaythuscontainafourth component that specifies a reference domain size or the size of subsets of participants,dependingonthedistributionandtherelativescopingofparticipants.Insum,thesemanticinformationin participant entity structures may be a triple 〈source domain, involvement, definiteness〉, or aquadruple〈sourcedomain,involvement,definiteness,size〉.

Aparticipantentitystructureisthusoneofthestructuresin(54):(54) εp=〈m,〈S,q,d〉〉or=〈m,〈S,q,d,N〉〉.

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Of these threeor four components, the sourcedomain specification (S), the involvement (q), and thesize specification (N)may have a complex internal structure,which is considered in Clause 7.3.4. Inexceptionalcases,suchastheexamples in(10), therestrictorpartoftheNPisempty,andthesourcedomainisimplicit.ThecomponentsqandNareanumericalpredicate,suchasλz.|z|>5,orameasurepredicatesuchasλz.Weight(z)>(5,kilo).Theinvolvementspecificationqmayalsobeaproportionalpredicate,suchas ‘mostof’.SincethecomponentsqandNaredifferentforamassNPquantifierthanwhentheNPconcernsacountabledomain,thereforethecomponentSin(54)isapairS=〈D,v〉wherevindicates the individuation of the domain (v = ‘count’, or v = ‘mass’, or v = ‘count/parts’ if parts ofindividualsareconsidered).Thecomponentd(definiteness)isanunstructuredvalue,viz.‘determinate’or‘indeterminate’.Propernameslike“Santa”or“DonaldDuck”aretreatednotasquantifiersbutasexpressionsthatrefertoasingleindividual.Thisappliesalsotoaverycommonpropername,like“JohnSmith”,althoughthereare many people with that name: whenever a proper name is used, the speaker has a particularindividualinmind,whoisnotnecessarilyuniqueinanabsolutesense,butwhoisuniquelydeterminedforthespeakerandhisinterlocutorsinthegivencontextbyhissalience,familiarity,orrecentmention.Entitystructures〈m,εEV〉forsetsofeventsaresimplerthanthoseforsetsofparticipants;theycontain,besides a markable, just a predicate that characterizes an event domain, which is a class of events,analogoustothesourcedomainofasetofparticipants..

(55) εEV=〈m,eventdomain〉AdditionalentitystructuresaredefinedinClause7.3.4fortheexpressionofNPheadnounmodification.

7.3.3Linkstructures

Theabstractsyntaxdefineslinkstructuresforparticipationinaneventandfortherelativescopingofparticipants. Participation structures (56a) connect participants to events specifying their semanticrole,thedistributivity,whetherthequantificationovereventshaswideornarrowscope,thepolarity,theexhaustiveness, andoptionally the repetitivenessof theparticipation.Scope linkstructures (56b)indicateascoperelationbetweentwoparticipantentitystructures.(56) a.LP=〈εEV,εp,semanticrole,distributivity,eventscope,polarity,exhaustiveness,repetitiveness〉 b.LSC=〈εp1,εp2,scoperelation〉

7.3.4Structuredquantificationdomains

Ofthecomponentsofaparticipantentitystructure,thesourcedomainassociatedwithaquantifiedNPrequires a structured specification when the restrictor contains one or more head noun modifiersand/ormultiple,conjoinedheads,asillustratedbytheexamplesin(46).Theabstractsyntaxsupportsarticulateannotationofstructuredquantificationdomainsbyallowingthesourcedomaintobeeitherasingleunmodifieddomainor apair 〈〈D1,D2,…Dk〉,modifiers〉 consistingof anon-empty sequenceofsubdomains,correspondingtothemembersofaconjunctionofheads,anda(possiblyempty)sequenceofmodifiersthatapplyto(all) themembersof thisconjunction. Inviewof thepossiblecomplexityofconjunctivemodifiedNPheads,asubdomainDimayagainbeaconjunctionandmayagainbemodified,as illustratedby“valuable(ancient(books)andpaintings)” in(46h).ThespecificationoftherestrictorpartofanNPthereforemakesuseofrecursiveandnon-recursive‘domainspecificationstructures’,the

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latter for thesimplecaseofa (sub-)domain formedby thedenotationofa singleheadnounpossiblywithoneormorerestrictivemodifiers.

TheanalysisofdistributionandscopeofNPheadnounmodifiers inClause6 leads to theconclusionthatfourtypesofmodificationcanbedistinguished,assummarizedinTable2:

1) withindividual(count)orparts(mass)distributionandnon-inverselinking;2) withindividual(count)orparts(mass)distributionandinverselinking;3) withcollectivedistribution(countormass)andwithoutinverselinking;4) withunspecificdistribution(countormass)andwithoutinverselinking.

NPheadnoun Distribution Linkinversion Modifiercategory

countmass

individualparts

No ADJ,NN,GP,PP,RC

countmass

individualparts

Yes GP,PP,RC

count,mass collective No ADJ,GP,PP,RC

count,mass unspecific No GP,RC,PP

Table2.TypesofNPheadmodification.GP=Genitivepossessivestructure.

ForannotatingNPheadmodifications,adjectivesandmodifiernounsdonotneedtospecifythelinkingtype,sincethisisneverinverse,whereasPPsandrelativeclausesdoneedthis.ThemodificationofanNPheadnounisannotatedwithlinkstructuresthatareembeddedwithinNPannotationstructures(i.e.,participant structures), and therefore do not need to specify the entity that they link the modifierinformationto.Noun-noun(NN)modificationofacountnounalwayshas individualdistribution,andofamassnounalwayshaspartsdistribution,sothedistributioninaNN-modificationdoesnotneedtobeannotated.Ifthe modifier is a bare noun, the linguistic information in the modification is a property thatcharacterizesacertainconcept.However,themodifyingnounmayitselfbymodifiedbyanadjective,asin“chemicalwastedump”(tobecontrastedwith“oldwastedump”),orbyanothernoun,as in“coronavirusinfections”.SoinNN-modificationthemodifyinginformationconsistsofthepropertyexpressedbythe modifying noun, combined with the information in any restrictions that may modify that noun.Inverse linking does not arise in this case, therefore the link structure for NN-modification is a pairconsistingofaunarypredicate,possiblywith(adjectivalorNN)restrictions:(57) LNN=〈predicate,restrictions〉Adjectives can be used distributively or collectively (as in “Kenwas carrying some heavy books”). Anadjectivethatmodifiesanounthatmodifiesanothernounistreatedinthisdocumentasintroducingacomplexconcept, suchas ‘toxicwaste’or ‘natural language’.Adverbialmodificationofadjectives (e.g.“very beautiful”, “too expensive”, “more expensive than expected”,…} } is considered to be outside thescopeofthestandardspecifiedinthisdocument.Alinkstructureforadjectivalmodificationisthereforeapairconsistingofaunarypredicateandadistributivity:

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(58) LAD=〈predicate,distributivity〉

In PP modification, the semantic information in the PP consists of the relation expressed by thepreposition and the information of the embedded NP, described by a participant structure. Formodification by a PP both the distributivity is relevant and the scoping (inverse linking or not – thelattercasewillbecalled‘linear’).HencealinkstructureforPPmodificationisaquadruple:(59) LPP=〈relation,participantstructure,distributivity,linking〉Inmodificationbyarelativeclause,thesemanticinformationtobecapturedinannotationsconsistsofthe specification of the events with their participants as described in the (relative) clause, theannotation of which is through a QuantML annotation structure, plus the semantic role that theparticipantsindicatedbytheheadplayintheRC’ssetofevents,thedistributivityofthemodification,andwhetherinverselinkingoccurs.Thelinkstructureforarelativeclauseisthus:(60) LRC=〈semanticrole,annotationstructure,distributivity,linking〉For example, the participant entity structures, containing modifier link structures and recursivelyembeddedentity structures, for thequantifications corresponding to theunderlinedNPs in (37a,b,c),repeated here as (61a-c), and in (61d-g) are as follows (for the collective reading of (61c)) - squarebracketsareusedheretomarkdomainspecificationstructuresforbetterreadability:

(61) a.Thirty-twoChinesestudentsenrolled. m1=Thirty-twoChinesestudents,m2=Chinese,m3=students

〈m1,〈[〈〈m3,〈student,count〉〉,〈m2,〈chinese,individual〉〉〉],32,indet〉〉

b.Aliceshowedmetwofascinatingmarinehistorybooks. m1=twofascinatingmarinehistorybooks,m2=fascinating,m3=marine, m4=marinehistory,m5=history,m6=books

〈m1,〈[〈〈m6,〈book,count〉〉,〈〈m2,〈fascinating,individual〉〉,〈m4,〈〈m5,〈history,count〉〉, 〈m3,marine〉〉〉〉〉],2,indet〉〉

c.Jimwascarryingfiveheavybooks. m1=fiveheavybooks,m2=heavy,m3=books

〈m1,〈[〈〈m3,〈book,count〉〉,〈m2,〈heavy,collective〉〉〉],5,indet〉〉

d.WemetsomestudentsfromaDutchuniversitym1=somestudentsfromaDutchuniversity,m2=students,m3=fromaDutchuniversity, m4=aDutchuniversity,m5=Dutch,m6=university

〈m1,〈[〈〈m2,〈student,count〉〉,〈m3,〈from,〈m4,〈[〈〈m6,〈university,count〉〉,〈m5, 〈Dutch,individual〉〉〉],some,indet〉〉,individual,linear〉〉〉],some,indet〉〉

e.Thecommitteememberstalkedtoastudentfromeveryuniversitym1=astudentfromeveryuniversity,m2=student,m3=fromeveryuniversity,m4=every university,m5=university

〈m1,〈[〈〈m2,〈student,count〉〉,〈m3,〈from,〈m4,〈[〈m5,〈university,count〉〉],all,det〉〉,individual, inverse〉〉],some,indet〉〉

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7.3.5Formalspecification

Asmentionedabove,theabstractsyntaxofQuantMLconsistsofa‘conceptualinventory',specifyingtheconcepts fromwhich annotations are built up, and a specification of the possibleways of combiningtheseelementstoform‘annotationstructures’.

ConceptualinventoryTheconceptualinventoryspecifiestheingredientsofannotationsaccordingtothemetamodel inFigure1.These ingredientsare theentities thatpopulateentitystructuresand linkstructures.TheQuantMLconceptualinventoryisspecifiedbelow.

Annotation structures for quantification are associated with the units that in linguistics are called‘clauses’, i.e.afiniteverbanditsarguments.Itisatthislevelofsyntacticstructurethatissuesariseofthe relative scopes of participants in different roles, as well as relative scopes of events andparticipants. Such annotation structures are quadruples, consisting of an event structure, a set ofparticipant structures, a set of link structures that relate participants to events, and a set of linkstructures that specify scope relations between sets of participants; see (62), where εEV is an eventstructure;εP1,…,εPnareparticipantstructures;LP1,…,LPnareparticipationlinkstructures,andsc1,…,sckarescopelinkstructures.

(62) 〈εEV,{εP1,…,εPn},{LP1,…,LPn},{sc1,…,sck}〉

Entitystructures:

Entity structures are pairs 〈m,s〉 consisting of a markable m and certain semantic information,designated here by ‘s’. For convenience, some auxiliary structures are used in the definition of theQuantMLentitystructures.Thefollowingtypesofentitystructurearedefined:

1. Participant structures: s = 〈DS, q, d〉 or s = 〈DS, q, d, N〉, where DS is a domain specificationstructure(seeauxiliarystructuresbelow),qisaspecificationofreferencedomaininvolvement,disadefiniteness,andNisanumericalsizespecification(seeauxiliarystructuresbelow).Ifthereferencedomainconsistsofasingle individualconcept,as in thecaseofapropername(e.g.“Santa”) or a singular definite description (“the Christmas man”, “the president”), then thedomaininvolvementissetto“single”andthedefinitenessto“determinate”. Aspecificationofreferencedomaininvolvementiseither(1)aproportionalpredicate(‘most’,‘all’,‘total’,‘single’,a percentage or a fraction), or (2) a non-numerical quantitative predicate (like ‘many’, seebelow),or(3)anumericalsizespecification(seeauxiliarystructuresbelow).

2. Eventstructures:sisapredicatedenotinganeventdomain.3. Modifierstructures: a.Adjectivalstructure:s=〈property〉; b.Modifyingnominalstructure:s=〈property〉or〈property,sequenceofadjectivalmodifiers〉; c.PPstructure:s=〈relation,participantstructure〉; d.Relativeclausestructure:s=〈semanticrole,annotationstructure〉; e.Possessivestructure:s=〈Poss,participantstructure〉.

Linkstructures:Thefollowingtypesoflinkstructurearedefined:

1. Participationlinks:Asextet〈eventstructure,participantstructure,semanticrole,distributivity,exhaustiveness, [repetitiveness], event scope, polarity〉. To simplify the description of

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participation links, the following values will often be suppressed: exhaustiveness = ‘non-exhaustive’,eventscope=‘narrow’,polarity=‘positive’.

2. Scoperelationlinks:〈participantentitystructure,participantentitystructure,scoperelation〉.

Auxiliarystructures:1. Adomain specification structure is a nested pairDS = 〈m,S〉,wherem is amarkable and S is

eitherapair〈P,v〉,consistingofapredicatePandanindividuationspecificationv,orasequence〈DS1, ... DSk〉, of domain specification structures, or a pair 〈DS, M〉, where DS is a domainspecificationstructureandMisamodificationorasequenceofmodifications(seenextitem).

2. A modification is a link structure for noun-noun modification, adjectival modification, ormodificationbyaPPorarelativeclause,i.e.,apair〈predicate,restrictions〉,orapair〈adjectivalstructure,distribution〉,oratriple〈PPstructure,distribution,linking〉,oratriple〈relativeclausestructure,distribution,linking〉,oratriple〈possessivestructure,distribution,linking〉.

3. Anumericalsizespecification,whichcanbeusedto indicateareferencedomain involvement,the size of a reference domain, the size of groups of reference domain elements, or therepetitivenessofasetofevents,iseither(a)apair〈r,n〉,where‘n’isapositive(real)number,apercentage(like’5%’),orafraction(like’‘2/3’),and‘r’isoneofthenumericalrelations‘equal’,‘greaterthan’, ‘greaterthanorequal’, ‘lessthan’, ‘lessthanorequal’,or(b)anestedpair〈r,〈n,u〉〉with‘r’and‘n’asbefore,and‘u’eitherabasicunitofmeasurementoraunitstructure.Aunitstructureisatriple〈u1,op,u2〉,where‘u1‘and‘u2‘areeitherabasicunitoraunitstructure,and‘op’iseithertheoperationofmultiplicationorthatofdivision.

The types of entities to be provided by the conceptual inventory follow from these entity and linkstructures:

1. predicates denoting source domains in domain specification structures; these conceptscorrespondtothemeaningsoflexicalitems(inparticularNPheadnouns)ofthelanguageoftheprimarydata,suchas‘book’,‘student’,and‘water’;seeAnnexB,SectionB2fordetails;

2. predicatesthatcharacterizeaneventdomain,correspondingtothemeaningsofverbsandotherlexical items of the language of the annotated primary data, such as ‘lift’, ‘carry’, ‘read’, ‘see’,‘meet’;

3. predicates corresponding to the meanings of adjectives in adjectival restriction links (insidedomainspecificationstructures),suchas‘Chinese’,‘heavy’,and‘rare’;

4. relationscorrespondingtomeaningsofprepositionsinPPs,suchas‘from’and‘in’;5. semanticroles(inparticipationlinksandinrelativeclauselinks);forthispurpose,thesemantic

rolesdefinedinISO245617-4(Semanticroles)areused;6. predicates forspecifyingproportionalreferencedomain involvement: ‘most’, ‘all’; formassNP

quantifiers: ‘total’, and ‘most-m’; for proper names and definite descriptions the specialpredicate‘single’;

7. non-numericalquantitativepredicates forspecifyingreferencedomain involvement, referencedomainsize,orthesizeofcertainpartsofareferencedomain,correspondingtothemeaningsoflexicalitemslike“many”,“much”,“several”,“few”,and“little”(andthespecialvalue“single”forpropernamesanddefinitedescriptions);

8. parameters for specifying definiteness (in participant structures): ‘determinate’ and‘indeterminate’(inthisdocumentsometimesabbreviated‘det’and‘indet’);

9. basic units of measurement, such as ‘meter’, ‘kilo’, ‘litre’, and ‘hour’ – see ISO 24617-6(Principles of semantic annotation), Hao et al. (2017), and ISO DIS 24617-11; formeasuringtemporallengththeunitslistedinISO24617-1(ISO-TimeML)areused;

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10. theoperators’division’and‘multiplication’forformingcomplexunits;11. thevalues‘positive’,‘widenegative’,and‘narrownegative’forspecifyingapolarity;12. parametersforspecifyingdistribution:‘collective’,‘individual’,‘single’,‘parts’,‘unspecific’;13. parametersforspecifyingindividuation:‘count’,‘mass’,and‘count’/parts’;14. theparameters‘exhaustive’,‘non-exhaustive’;15. parametersforspecifyingeventscope:‘wide’,‘narrow’,and‘free’;16. ordering relations for specifying relative scopes of sets of participants (in participant scope

links):‘wider’,‘dual’,‘equal’,and‘unscoped’;17. parameters for specifying whether scope inversion occurs (in PP modification): ‘inverse’ or

‘linear’(defaultvalue).

7.4Concretesyntax

7.4.1XMLSpecification

AconcretesyntaxisspecifiedhereintheformofanXMLrepresentationofannotationstructures.Foreachtypeofentitystructure,definedbytheabstractsyntax,acorrespondingXMLelementisdefined;each of these elements has an attribute @xml:id whose value is a unique identification of (anoccurrence of) the information in the element, and an attribute @target, whose value anchors theannotationintheprimarydata,havingamarkableasvalue(orasequenceofmarkables).Inaddition,theseelementshavethefollowingattributes:

1. theXMLelement<entity>,forrepresentingparticipantstructures,hastheattributes@domain,@involvement,@definitenessandoptionally@size;

2. the XML element <event>, for representing event structures, has the attributes @pred forspecifyinganeventtypeand(optionally)@repforspecifyingrepetitiveness;

3. the XML element <qDomain>, for representing domain specification structures: has theattributes @source (with multiple values in the case of a conjunctive specification) and@restrictions;

4. theXMLelement<sourceDomain>,forrepresentingquantificationsourcedomainspecificationswithoutmodifiers:hastheattributes@predand@individuation;

5. the XML element <adjMod>, for representing adjectivalmodifiers, with the attributes@predand@distr,andoptionallytheattribute@restrictions;

6. theXMLelement<nnMod>,forrepresentingnounsasmodifiers,withtheattributes@predand@distr,andoptionally@restrictions;

7. theXMLelement<ppMod>,forrepresentingPPmodifiers,withtheattributes@pRel,@pEntity,@distrand@linking;

8. theXMLelement<relClause>, forrepresentingrelativeclauses,withtheattributes@semRole,@clause,@distrand@linking;

9. the XML element <possRestr>, for representing possessive restrictions, with the attributes@possessor,@distr,and@linking;

10. theXMLelement<numericalPred>hastheattributes@numRel(withvalueslike‘greaterthan’,and@num(whichhasnonnegativenumbers,percentages,andfractionsasitspossiblevalues);

11. theXMLelement<measure>hastheattributes@numand@unit;12. theXMLelement<complexUnit>,hastheattributes@unti1,@operation,and@unit2.

Involvement specificationswhere@rel has the value “equal”will be abbreviated by the value of the@numattribute;seeexample(63).

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For the two types of link structure defined by the abstract syntax, a corresponding XML element isdefined:

1. <participation> has the attributes@event,@participant, @semRole, @distr, and@evScope(default value: “narrow”), and optionally @exhaustiveness (default value: “non-exhaustive”,abbreviated “nex”),@repetitiveness (defaultvalue:greater thanorequal to1),and@polarity(defaultvalue:“positive”);

2. <scoping>hastheattributes@arg1,@arg2,@scopeRel.

Theattributesdefined in this concrete syntaxhaveoptionally that come in threevarieties: (1) entitystructures or link structures, such as@domain,@event, and@restrictions; (2) concepts denoted bynatural language content words, such as @pred and @pRel (in PP restrictions); (3) values thatcorrespond to linguistic concepts and parameters for making certain semantic distinctions, such as@definiteness, @distr, and @scopeRel. For attributes of the second kind, notably for the @predattribute, the values are derived from the nouns, verbs, adjectives and prepositions identified bymarkables in the annotated data. These values can be obtained bymeans of lexical lookup (possiblysupportedbyworddisambiguation)ofthecontentofthemarkables.Inthisdocument,thesevaluesarerepresentedby canonical formsof the lexical itemsof the languageof theprimarydata suchasverbstems,singular(masculine)formsofnouns,andsingular(masculine)formsofadjectives–theprecisechoiceoftheseformsdependsontheobjectlanguageunderconsideration.Forexample,using‘Lx(m)’to designate the lexical content of a markable ‘m’ and ‘CFL1’ to designate a function that deliverscanonical forms of (disambiguated) lexical items for the language ‘L1’, the values of the threeoccurrencesofthe@predattributeinexample(63)belowareCFEN(Lx(m5))=“enroll”,CFEN(Lx(m3))=“student”,CFFR(Lx(m3))=“étudiant”,andCFEN(m2)=“chinese”;forbetterreadabilityofQuantML/XMLannotationssuchvaluesareshownratherthan“CFL1(Lx(m5))”etc.(Forconvenience,thesamevaluesarealsousedintheabstractsyntax.)

For attributes of the third kind the values are largely but not entirely language-independent; thisdocument only considers attribute values of general linguistic significance,which is not restricted toEnglishoranyotherparticularlanguage.

7.4.2Exampleannotations

(63) Thirty-twoChinesestudentsenrolled.

Markables:m1=Thirty-twoChinesestudents,m2=Chinese,m3=Chinesestudents,m4=students,m5=enrolled

QuantML/XMLannotationrepresentation: <entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”32” definiteness=”indet’”/>

<event xml:id=”e1” target=”#m5” pred=”enroll”/> <qDomain xml:id=”x2” target=”#m3” source=”#x3” restrictions=”#r1”/> <sourceDomain xml:id=”x3” target=”#m4” individuation=”’count’” pred=”student”/>

<adjMod xml:id=”r1” target=”#m2” distr=”individual” pred=”chinese”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow”/>

(64) Alexownssome(valuable(ancient(Chinesebooks)andJapanesepaintings)).

Markables:m1=Alex,m2=owns,m3=somevaluableancientChinesebooksandJapanese

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paintings,m4=valuable,m5=valuableancientChinesebooksandpaintings,m6=ancient,m7-ancientChinesebooks,m8=Chinese,m9=books,m10=Japanese,m11=paintings

QuantML/XMLannotationrepresentation:<entity xml:id=”x1” target=”#m1” domain=”#x1” involvement=”single” definiteness=“det”/>

<sourceDomain xml:id=”x1” target=”#m1” individuation=”count” pred=”alex”/> <event xml:id=”e1” target=”#m2” pred=”own”/>

<entity xml:id=”x2” target=”#m3” domain=”#x3” involvement=”some” definiteness=”indet’”/> <qDomain xml:id=”x3” target=”#m5” source=”#x4 #x6” restrictions=”#r1”/>

<qDomain xml:id=”x4” target=”#m7” source=”x5” restrictions=”#r2 #r3”/> <sourceDomain xml:id=”x5” target=”#m9” individuation=”count” pred=”book”/> <qDomain xml:id=”x6” target=”#m12” source=”x7” restrictions=”#r4”/> <sourceDomain xml:id=”x7” target=”#m11” individuation=”count” pred=”painting”/>

<adjMod xml:id=”r1” target=”#m4” distr=”individual” pred=”valuable”/> <adjMod xml:id=”r2” target=”#m6” distr=”individual” pred=”ancient”/> <adjMod xml:id=”r3” target=”#m8” distr=”individual” pred=”chinese”/>

<adjMod xml:id=”r4” target=”#m10” distr=”individual” pred=”japanese”/> <participation event=”#e1” participant=”#x1” semRole=”theme” distr=”single” evScope=”free”/>

(65) Thethreemenmovedtwopianos Markables:m1=Thethreemen,m2=men,m3=moved,m4=twopianos,m5=pianos

QuantML/XML:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”3” definiteness=”det’”/>

<sourceDomain xml:id=”x2” target=”#m2” individuation=”count” pred=”man”/> <event xml:id=”e1” target=”#m3” pred=”move”/> <entity xml:id=”x3” target=”#m4” domain=”#x4” involvement=”2” definiteness=”indet” pred=”piano”/> <sourceDomain xml:id=”x4” target=”#m5” individuation=”count”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”collective”/> <participation event=”#e1” participant=”#x2” semRole=”theme” distr=”individual”/>

(66) Allthewaterintheselakesispolluted.

Markables:m1=allthewaterintheselakes,m2=waterintheselakes,m3=water,m4=inthese lakes,m5=theselakes,m5=ispolluted QuantML/XML: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”every” definiteness=“det”/>

<qDomain xml:id=”x2” #target=”#m2” domain=”#x3” restrictions=”#r1”/> <sourceDomain xml:id=”x3” target=”#m3” pred=”water” indiv=”mass”/> <ppMod xml:id=”r1” target=”#m4” pRel=”in” pEntity=”#x4” distr=parts linking=”inverse”/> <entity xml:id=”x4” #target=”#m5” domain=”#x5” involvement=”all” definiteness=“det”/> <sourceDomain xml:id=”x5” target=”#m6” pred=”lake” indiv=”count”/> <event xml:id=”e1” target=”#m7” pred=”polluted”/> <participation event=”#e1” participant=”#x1” semRole=”theme” distr=”every” evScope=”narrow”/>

(67) Theboysdrankallthebeer.

Markables:m1=theboys,m2=boys,m3=drank,m4=allthebeer,m5=thebeer

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”all” definiteness=“det”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”boy” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”drink”/> <entity xml:id=”x3” #target=”#m4” domain=”#x4” involvement=”total” definiteness=“det”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”beer” indiv=”mass”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow”/>

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<participation event=”#e1” participant=”#x3” semRole=”patient” distr=”individual” “unspecific”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”dual”/>

(68) Thecraneliftedallthesand.

Markables:m1=Thecrane,m2=crane,m3=lifted,m4=allthesand,m5=thesand,m6=sand

QuantML-XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”single” definiteness=“det” size=”1”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”crane” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”lift”/> <entity xml:id=”x3” #target=”#m4” domain=”#x4” involvement=”total” definiteness=“det”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”sand” indiv=”mass”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”collective” evScope=”narrow”/>

<scoping arg1=”#x1” arg2=”#x3” scopeRel=”dual”/>

(69) Threebreweriessuppliedfifteeninns

Markables:m1=Threebreweries,m2=breweries,m3=supplied,m4=fifteeninns,m5=inns

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”3” definiteness=”indet”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”brewery” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”supply”/> <entity xml:id=”x3” #target=”#m4” domain=”#x4” involvement=”15” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”inn” indiv=”count”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow”/> <participation event=”#e1” participant=”#x3” semRole=”beneficiary” distr=”individual” evScope=”narrow”/>

<scoping arg1=”#x1” arg2=”#x3” scopeRel=”dual”/>

(70)Thepresidentdidnotaccepttheproposals

Markables:m1=Thepresident,m2=president,m3=didnotaccept,m4=theproposals, m5=proposals

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”single” definiteness=“det/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”president” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”accept”/> <entity xml:id=”x3” #target=”#m4” domain=”#x4” involvement=”all” definiteness=“det”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”proposal” indiv=”count”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”

polarity=”neg-narrow”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”individual” evScope=”narrow”/>

<scoping arg1=”#x1” arg2=”#x3” scopeRel=”wider”/>

7.5Semantics

Theannotationsdefinedinthisstandardhaveacompositionalsemanticinterpretation,inthesensethatthe interpretation of an annotation structure is computed by combining the interpretations of itscomponent entity structures and participation link structures, in amanner that is determined by itsscope link structures. The specification of this semantics takes the form of translating annotationstructures to (possibly underspecified) DRSs, whose interpretation is defined by DiscourseRepresentation Theory (DRT, Kamp & Reyle, 1993). Combining GQT with neo-Davidsonian eventsemantics,naturallanguagequantifiersareinterpretedaspropertiesofsetsofparticipantsinvolvedin

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sets of events. Champollion (2015) has shown the viability of this type of combination. Casting thesemanticsinthisformisparticularlyconvenientforcombiningannotationsofquantificationwithothertypesof semantic information,usingannotationschemesof the ISOSemanticAnnotationFramework(SemAF,ISO24617).Thepresentsub-clausegivesabriefoverviewofthesemantics;moredetails,areprovidedinAnnexB.

FollowingtheprinciplesofsemanticannotationlaiddowninISO24617-6,themeaningofaQuantMLannotationisspecifiedfortheannotationstructuresdefinedbytheabstractsyntax,andisinheritedbythe representations specified by the concrete syntax. More specifically, an interpretation function isdefined that computes a DRS for each well-formed annotation structure. Conceptually, the unit forquantification annotation is what in linguistic terminology is a ‘(simple) clause‘, i.e., a verb with itsargumentNPs,describinganevent(orasetofevents)with itsparticipants.Theannotationofsuchaunithasthestructureshownin(62)andconsistof(1)aneventstructure,(2)anumberofparticipantstructures, (3) participation link structures that relate the participants to the events, and (4) scoperelations among the participants. The first three components provide the building blocks of thesemanticcontentoftheannotation,whilethescoperelationsdeterminethewaythesebuildingblockscombinetoprovideaninterpretationoftheclauseasawhole.

Thesemanticentities thatcorrespond toparticipantentitystructuresmaybeofanykind: real-worldobjects, abstract entities, individual concepts, intentional and intensional entities, hypothetical andfictionalentities.Theannotationschemedefined in thisdocumentaims tobeneutralwith respect toontological and linguistic views on the existence of objects of various kinds and the necessity todistinguishtheminsemanticaccountsofnaturallanguage.10

A participation link structure has the form shown in (71), where the first two components are thelinked event and participant structure, and the other components indicate properties of the way inwhich the participants are involved in the events, specifying a semantic role (R), a distribution (d),whether the event structure has wider or narrower scope than the participant structure (σ), anexhaustiveness(ξ),therepetitiveness(ifany)([ρ])(anoptionalcomponent),andapolarity(p).

(71) LP1=〈εE,εP,R,d,σ,p〉

Notethataparticipation linkstructureembedsthe linkedeventstructureandparticipantstructure–annotations as defined by the abstract syntax are nested structures (as opposed to their ‘flat’ XML-representations).Theinterpretationofawell-formedannotationstructure,inwhichalltheparticipantsare linked tocertainevents (orare linked tootherparticipants inpossessive structures) is thereforedeterminedbytheinterpretationoftheparticipationlinkstructures.

The semantics of a participation link structure is compositionally defined as a combination of thesemanticsofitscomponentsbymeansoftheinterpretationfunctionIQasspecifiedin(72),where‘∪’istheoperationofmergingtwoDRSs,asdefinedinDRT,and‘∪*’isthe‘scopedmerge’operation,definedbelowin(78).

(72) a.IQ(〈εE,εP,R,d,narrow,p〉)=(IQ(εP)∪*IQ(εE))∪IQ(R,d,narrow,p) b.IQ(〈εE,εP,R,d,wide,p〉)=(IQ(εE)∪*IQ(εP))∪IQ(R,d,wide,p) c.IQ(〈εE,εP,R,d,free,p〉)=IQ(εE)∪IQ(εP)∪IQ(R,d,free,p) 10Moltmann (2015): “Whethernatural languagepermits quantificationover ‘nonexistent’ intentional objects issubjectofamajorcontroversy,asisthenatureofsuchentitiesthemselves”.Szabolcsi(2012)notesthat“manybutnotallimportantissuesinnounphrasequantificationcanbeaddressedinapurelyextensionalsemantics”.

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Forexample,considersentence(73),containingaverbwithasingleargument,sothattheannotationstructureisjustasinglelinkstructure.

(73) “Morethantwothousandstudentsparticipated”

Aquantifierof the form“More than two thousandD” is interpretedasaDRSof the form(74),wherecapital lettersareused fordiscoursereferents thatcorrespondtonon-emptysetsof individuals.ThisDRS says that there is a subset of the quantification domain D containing more than two thousandelements. This subset consists of those elements of the reference domain that participate in a set ofevents (called the ‘participant set’ in the QuantMLmetamodel, see Fig. 1). The condition |X| > 2000specifiestheinvolvementofthereferencedomain.

(74)

IfR=Agent,thedistribution(d)isindividual,andtheeventscope(σ)isnarrow,thentheinterpretationofthethirdcomponentin(72)istheDRSin(75),whichsaysthatthereisanon-emptyparticipantsetofwhicheverymemberisanagentinanon-emptysetofevents:

(75)IQ(Agent,individual,narrow)=

Applying(72)andmergingtheDRSin(75)withtheDRSsinterpretingtheparticipantstructureandtheeventstructureresultsin(76)fortheinterpretationoftheannotationofsentence(73).

(76)

Foraverbwithmultipleargumentsindifferentsemanticroles,theinterpretationsofthelinkstructuresarecombined inawaythatreflects therelativescopingof thearguments. If thequantification inoneargument outscopes the quantification in another, then the combination is performed not by simpleDRS-merge,butbyamorecomplexoperationcalled‘scopedmerge’.Thisisillustratedbytheanalysisof sentence (77) for the wide-scope reading of “Fifteen students”.The annotation structure in (77a)contains two participant structures, two link structures and one scoping relation. The semantics isconstructedby(77c),where∪*isthescopedmergeoperation,definedin(78).

(77) Fifteenstudentsreadthreepapers.

Markables:m1=Fifteenstudents,m3=students,m4=read,m5=three, m6=threepapers,m7=papers.

X|X|>2000x∈X→D(x)

X

Ee∈E→agent(e,x)

x∈X→

X⊆student|X|>2000

E⊆participate

agent(e,x)

e∈E→

x∈X→

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a.QuantMLannotationstructure:A=〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉= 〈〈m3,read〉,{〈m1,〈〈m2,〈student,count〉〉,15,indet〉〉,〈m4,〈〈m5,〈paper,count〉〉,3,indet〉〉},

{〈〈m3,read〉,〈m1,〈〈m2,〈student,count〉〉〉,15,indet〉〉,agent,individual,narrow〉,〈〈m3,read〉,〈m4,〈〈m5,〈paper,count〉〉,3,indet〉〉,theme,individual,narrow〉},{〈〈m1,〈〈m2,〈student,count〉〉,15,indet〉〉,〈m4,〈〈m5,〈paper,count〉〉,3,indet〉〉,wider〉}〉

b.QuantML/XMLannotationrepresentation: <entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”15” definiteness=”indet’”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”student”/> <event xml:id=”e1” target=”#m3” pred=”read”/> <entity xml:id=”x3” target=”#m4” domain=”#x4” involvement=”3” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”paper”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”individual” evScope=”narrow”/> <scoping arg1=”#x1” arg2=”#x2” scopeRel=”wider”/> c.Semantics: IQ(A)=IQ(〈εE,{εP1,εP2},{LE,P1,LE,P2},〈εP1,εP2,wide〉}〉)=IQ(LE,P1)∪*IQ(LE,P2).

Thescopedmergeoperationisdesignedtocombinetheinformationaboutquantifiedparticipationintwoparticipationlinkstructures,andisdefinedasfollows:(78)ThescopedmergeoperationcombinestheinformationinitsargumentDRSsintoaDRSthatreflectstherelativescopingofthequantificationsinvolved,aswellastherelativescopingsofparticipantsandevents,whileunifyingtheeventdiscoursereferentsinthetwoarguments.(Ifthisunificationisnotpossible,thentheoperationfails.)TheDRSs representing the semanticsof such structures canhavea limitedvarietyof forms, listed inAnnex B, Section B.4.1. Two of the most common forms are shown in (79a) and (80a), and moreschematicallyin(79b)and(80b);theycorrespondtotheinterpretationofaparticipationlinkstructurewithnarroweventscopeandwithindividualandcollectivedistributivity,respectively.Cijdesignatesasetofconditions,Riasemanticrole,andKiasub-DRS.MassNPquantificationwithpartsdistributionhasthesamesemanticrepresentationas(79).Foraquantificationwithwideeventscope,everythingelsebeingthesame,thesemanticsislike(79)butwiththerolesoftheparticipantset(X)andtheeventset(E)interchanged.(79) a.Ai=

b.A=

Xi⊆DiCi1

Ei⊆DEiCi2e∈E→Ri(e,x)

x∈Xi→

Xi⊆DiCi1x∈Xi→Ki

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(80) a.Ai=

b.Ai=

The scoped merge of two arguments A1 and A2 of the form (79) brings the quantification over theparticipantsetinthesecondargumentwithinthescopeoftheoneovertheparticipantsetinthefirstargument, as shown schematically in (81a) and in more details in (81b), where ‘E’ designates theunificationofE1andE2-whichispossible(only)becauseA1andA2areaboutthesameevents.

(81) a.A1∪*A2=

b.A1∪*A2=

Appliedtothetwolinkstructuresof(77),theright-handsideof(81b)isinstantiatedas(82).

(82)

NotethatthescopedmergeoftwoDRSsoftheform(79)hasagainthatsameform;thereforescopedmerge application may be repeated to deal with more than two arguments, leading to recursivelynested quantifier interpretations. For example, in a clause with three pairwise scoped argumentscorrespondingtothreeNPsexpressingthequantifiedargumentsofaditransitiveverb(suchas“give”),

Xi⊆Di,Ei⊆DEiCiei∈Ei→Ri(e,Xi)

Xi⊆Di,Ei⊆DEiCi1Ki

X1⊆D1C11

X2⊆D2C2x2∈X2→K1∪K2

x1∈X1→

X1⊆D1C11

X2⊆D2C21

E⊆DEie∈E→[R1(e.x),R2(e.y)]

y∈Y→

x∈X→

X⊆student|X|=15

Y⊆paper|Y|=3

E⊆reade∈→[agent(e.x),theme(e.y)]

y∈Y→

x∈X→

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when the first argument outscopes the second and the second outscopes the third, this leads to aninterpretationstructurelike(83).

(83)

The interpretation of participation link structures for non-quantifying NPs that refer to a singleparticipant(propernames,definitedescriptions,singularpronominalNPs)hastheform(84),whichisformallysimilarto(80),butwherethediscoursereferent‘z’rangesoverindividuals.

(84) B=

Becauseof this formalsimilarity,suchinterpretationscanbecombinedwiththoseofquantifyingNPsusing the scopedmerge operation. The combination of participation link structure interpretations isdiscussedinmoredetailinAnnexB.

For annotation structures that do not fully specify the relative scopes of all the sets of participantsinvolved in the same events, the semantic interpretation takes the form of a set of (sub-)DRSs thatexpressthesemanticsoftheparticipationlinkstructures,plusthescoperestrictionsfortheirpossiblecombination.SuchaninterpretationisknowninDRTasan‘underspecifiedDRS’(UDRS,Reyle,1994).

AnnexBspecifiesthesemanticsofQuantMLannotationstructuresinmoredetail,includingannotationof quantifications with negative polarity, with parts of individuals and parts of mass objects, ofcumulativequantification,andquantificationswithcomplexstructureddomains,andvariouskindsofmodifiers,includingmodifierswithinverselinking.

8 Limitations and loose ends

Someof thephenomena relating toquantification innatural language that arenot considered in thisdocumentarenon-restrictiveandnon-intersectivemodifiers,generics,andhabituals, reciprocals,andreflexives.Thisisduepartlytothefactthattheirtheoreticalstatushasnotbeenfullyresolved,asisforexamplethecaseforgenericsandhabituals;seeKamp&Reyle,1993,Section3.7.4.Krifkaetal.(1995)analyse generics in terms of a special default quantifier; others introduce a notion of ‘normal’ or‘prototypical’intotheinterpretationframework(e.g.Eckhardt,2000).

Quantifications that involve personal or possessive pronouns can only be handled adequately incombinationwiththeannotationof(co-)referencerelations,whichisthesubjectdomainofISO24617-9.Inthefuture,anannotation‘plug-in’(Bunt,2019)maybedefinedforintegratingquantificationandcoreferenceannotationsatthelevelsofabstractandconcretesyntaxandsemantics.

X⊆D1C1

Y⊆D2C2

Z⊆D3C3z∈Z→K1∪K2∪K3

y∈Y→

x∈X→

z,E⊆DEiC1e∈E→K3

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AnnexA.AnnotationGuidelines(informative)

A.1Overview

Quantification in natural language occurs when a predicate is combined with one or more sets ofarguments.Thishappenswhenasimpleclauseisformedfromaverbanditsarguments,andalsowhenanounphraseisformedinwhichaheadnouniscombinedwithadjectivesorothermodifiers,suchasprepositionalphrasesorrelativeclauses.Theannotationofquantificationisthusrelevantatthelevelofclausesandattheclause-internallevelofnounphrases.

QuantML is a triple-layered annotation scheme, with a concrete syntax, an abstract syntax, and asemantics.Intheformaldefinitionofthescheme,theselayersareconnectedbythreefunctions:(1)anencoding functionFAC that assigns toeverywell-formedstructureof theabstract syntaxoneormorerepresentationoftheconcretesyntax;(2)adecodingfunctionFCAthatassignstoeverystructureoftheconcretesyntaxauniquestructureoftheabstractsyntax;(3)aninterpretationfunctionIQthatassignstoeverywell-formedstructureoftheabstractsyntaxasemanticinterpretation.Annotatorsonlyworkwith theconcretesyntax; theycanrelyon theexistenceof the functionsFCA and IQ forcomputing thesemanticsoftheirannotations.TheguidelinesinthisannexapplytotheQuantML/XMLrepresentationformat.

A.2Nounphrases

FollowingtheTheoryofGeneralizedQuantifiers,nounphrases(NPs)areviewedasdenotingpropertiesor families of sets of entities. This is true not only of plural NPs but also true singular NPs, like “apresent” in example (4) in this document: “Santa gave the children a present”. NPs are annotated inQuantML with the <entity> tag, with values for its attributes chosen according to the followingguidelines.

@domain:IftheNPheadisabarecommonnoun,thenassigntothisattributeasvaluetheidentifierofa <sourceDomain> element; the latter has the attribute@individuation,which specifieswhether thenounisusedasamassnounorasacountnoun,andinthelattercasewhetherpartsoftheindividualsin this domain are considered (if so, @individuation should be given the value “cParts”), and theattribute@pred,whosevalueisthecharacteristicpredicateofthedomain:11

<entityxml:id=”x1”target=”#m1”domain=”#x2”involvement=…definiteness=…/> <sourceDomainxml:id=”x2”target=”m2”individuation=…pred=”[noun]”/>

IftheNPisa(singular)propername,thenthesameconstructionshouldbeused,asfollows:

<entityxml:id=…target=…domain=”#x2”involvement=”single”definiteness=“det”/> <sourceDomainxml:id=”x2”target=…pred=”[name]”/>

IftheNPheadhasmodifiers,thenassigntothe@domainattributeasvalueavariablethatidentifiesa<qDomain>element,whichhasanattribute@restrictionswhosevaluesindicatemodifiers(seebelow,sectionA3),anda@domainattributewhosevaluereferstoa<sourceDomain>element,ortoanother<qDomain>elementiftheheadcontainsnestedmodifiers:

<entityxml:id=…target=…domain=”#x2”involvement=…definiteness=…size=…/>

11 Formally, pred=”LxL1(m2) “, i.e. the value of “pred” is computed from themarkable that is the value of the@targetattributebythelexicallookupfunctionLxL1,ifL1isthelanguageofthesourcetext(see7.4.1).

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<qDomainxml:id=”x2”target=…source=…restrictions=…/>

@involvement:IftheNPcontainsa(pre-)determiner,suchas“all’,“each”,“every”,“a”,“no”,“some”,or“most”, then a corresponding QuantML string should be used as the value of this attribute. FordeterminerlesspluralNPs,thevalue“a”maybeusedforcountheadnouns,thevalue“some”forpluralheadnouns,andthevalue“some-m”formassnouns,e.g.“DoesAnnehavechildren?”=“DoesAnnehaveachild?”and“Doyouhavefreshpasta?”=“Doyouhavesomefreshpasta?”

ForquantificationbyamassNP,thethreecasesdistinguishedinTable1inClause6.8shouldbemarkedupashavingtheinvolvement“every”,“total”,or“whole”.

For a singulardefinitedescription (“theChristmasman”, “thepresident”), orpossessive (“mymother”,“John’sbirthday”)theinvolvementshouldbespecifiedas“single”.

@definiteness:Thisattributeshouldbeassignedthevalue“indet”unlessthereisevidencethattheNPquantifiesoveraparticular,contextuallydeterminedpartofthesourcedomaindefinedbytheNPheadplus its modifiers. Such evidence may be the occurrence of a definite article, a possessive, or ademonstrative.Propernamesarealsounderstoodasdefinite:theuseofanamesuchas“John”carriestheassumptionthatthereisonecontextuallydistinguishedpersonnamed“John”.(SeealsoClause6.3inthemaindocument.)

@size:ThisattributeshouldbeassignedavalueonlyiftheNPcontainsanumericaldeterminerthatisnotinterpretedasexpressinginvolvement.

A.3NPheadmodifiers

Adjectivesareannotatedwith<adjMod>elements,inwhichthe@distrattributeshouldbeassignedthevalue “individual” if the adjective applies to the individual members of the reference domain, and“collective”ifitappliestothesememberstogether;the@predattributegetsisvalueinthesamewayasNPheadnouns.

Nounsasmodifiersareannotatedwith<nnMod>elements,inwhichthe@predattributegetsisvalueinthesamewayasNPheadnouns.

NP headmodification by a prepositional phrases is annotatedwith <ppMod> elements, inwhich the@distrattributeshouldbeassignedthevalue“individual”ifthePPappliestotheindividualmembersofthe referencedomain, and “collective” if it applies to thesemembers together; the@linkingattributeshould be assigned the value “inverse” if the quantification of the NP in the PP outscopes thequantificationoftheNPhead,elseitshouldgetthevalue“linear”.

The@predattributegetsisvalueinthesamewayasNPheadnouns.

Possessive modifications are annotated with <possRestr> elements, in which the @distr attributeshouldbeassignedthevalue“individual”ifthepossessiverestrictionappliestotheindividualmembersofthereferencedomain,and“collective”ifitappliestothesememberstogether;the@linkingattributeshould be assigned the value “inverse” if the quantification of the NP that refers to the possessoroutscopesthequantificationoftheNPhead,elseitshouldgetthevalue“linear”.

Relative clauses are annotated with <relClause> elements, in which the @distr attribute should beassigned the value “individual” if the adjective applies to the individual members of the reference

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domain,and“collective”ifitappliestothesememberstogether;the@predattributegetsisvalueinthesame way as NP head nouns; the @linking attribute should be assigned the value “inverse” if therelativeclausecontainsaquantificationthatoutscopesthequantificationoftheNPhead,elseitshouldgetthevalue“linear”.

A.4Verbs

Verbs are annotated in QuantML using the entity tag <event>, with attributes @pred, whose valuespecifiesaneventtype,suchas“kiss”,“love”,and“cook”,andoptionally@rep,whosevaluespecifiesanatural number or a rangeof natural numbers (for dealingwith expressions like “twice”, “more thanthreetimes”).The@predvaluesareobtainedinthesamewayasforNPheadnouns.

A.5Participationlinks

Fortheattributesin<participation>links,thefollowingguidelinesapply:

@semRole:assignoneofthesemanticrolesdefinedinISO24617-4.

@distr:Doeseachofthemembersoftheparticipantsetparticipateintheeventsbyhim/her/itself?Ifyes, assign thevalue “individual”.Do theyact together,orare theyactedupon together? In that caseassignthevalue“collective”.Ifsomeofthemact(orareactedupon)together,andothersbythemselves,assign the value “unspecific”. For apropernameordefinitedescription, use the value “single”. For amass NP, use the value “parts” if some or all the parts of a mass noun denotation participate, and“collective”ifthepartsact(orareactedupon)together.

@evScope: A quantifying NP nearly always outscopes the quantification over events, therefore“narrow”isthedefaulteventscope-thisvalueisassumedifnoothervalueisspecified.Assignthevalue“wide”onlymultipleparticipantsparticipatedinthesameeventsinthesamesemanticrole.Iftheentitystructureannotatesapropernameoradefinitedescription,assignthevalue“free”.

A.6Scopelinks

Usethescoperelation“wider”ifoneoftherelatedquantificationsoutscopestheother,taking@arg1fortheonewithwiderscope.Use“dual”onlyinthecaseofcumulativequantification(mutualoutscoping).Use“equal”onlyforthecaseofgroupquantification;seeexample(C2).Ifoneoftherelatedentitystructures(orboth)annotatesapropernameoradefinitedescription,use“unscoped”.

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AnnexB.QuantMLSemantics(informative)

B1Overview

The interpretation function IQ, introduced inSection7.5, specifiesa recursive translationofQuantMLannotationstructures intoDRSs.Therecursionendsat theminimalbuildingblocksof theannotationstructures,which are elements of theQuantML conceptual inventory.These elements canbedividedintotwotypes:(i)‘structural’ones,thatfunctionasparametersinthespecificationofIQanddeterminestructuralpropertiesofDRSs;and(ii)‘lexical’ones,thatcorrespondtopredicatesorargumenttermsinDRSconditions.Elementsoftype(i)areforexampledefinitenessvalues(‘determinate’,‘indeterminate’)and event scope values (‘wide’, ‘narrow’); their role as parameters in IQ is described in Section B3.Elementsoftype(ii)areforexamplethepredicatesthatexpressthesemanticsofnounsandverbs;theirtranslationtoDRSelementsisspecifiedbytheassignmentfunctionFQ,describedinSectionB2.

B2‘Lexical’conceptualinventoryitems

TheassignmentFQfunctionfor‘lexical’conceptualinventoryitemsisdefinedasfollows:

o Predicates that characterize quantification source domains or event domains (typicallycorrespondingtonounsandverbs),andwhichinannotationrepresentationsaredesignatedbycanonicalformsoflexicalitemsofthelanguageoftheprimarydata,aresemanticallyidenticaltopredicates in DRS conditions. For such predicates FQ(P) = P. Similarly for predicates thatcorrespondtoadjectives,expressingrestrictionsonquantificationdomains,orprepositionsthatexpress relations in PP modifications. The same is also true for predicates that designatesemanticroles,whichdonothaveanexplicitbasisinnaturallanguagewords.

o Non-numericalquantitativespecificationsofdomaininvolvementbymeansofexpressionssuch“a few”, “a little”, “several”, “many” in English, and for example by “beaucoup”, “quelques”,“plusieurs”,inFrenchandby“eenpaar”,“eenboel”,“ettelijke”inDutch,areone-placepredicates.The interpretationof suchpredicates is context-dependentand language-specific. InQuantMLannotations, predicates corresponding to words in the primary data are used for suchspecifications, aswell as in their DRS-translations, leaving their precise interpretation to theinterpretationoftheDRS.Forsuchpredicates,again,FQ(P)=P.

o Theinterpretationofaproportionalspecificationofdomaininvolvement,e.g.by‘most’,dependsonthereferencedomain,forexample,“most(ofthe)booksareold”isinterpretedassayingthatmore than half of the books in the reference domain are old. The assignment function FQthereforeassignstotheinvolvementspecification ‘most’thefunctionFQ(most)= λZ.λX.|X|*>(|Z0|*/2),which canbe applied to adomain specification like ‘book’ toproduce thepredicateλX.|X|>(|book0|/2),i.e.thepredicateofhavingmoreelementsthanhalfthenumberofbooksinthereferencedomain(similarlyfordomainsthatincludepartsofindividuals,asin“mostofthepizza”).Fractionalspecifications, like“twothirdsof”andpercentualspecifications, like“twentypercent of” are treated similarly, as are “all” and “total” formass NP quantification: FQ(all) =λZ.λX. X=Z0, and FQ(total) = λZ λX. ΣX=ΣZ0. The involvement “most-m” of a mass NPquantification,asin“Mostofthemilkwasspilled”,presupposessomewayofmeasuringthesizeofquantitiesofamassdomainM.Suchsizesarecustomarilymeasuredusingacertaindomain-dependent dimension, for example, quantities of milk are typically measured in terms ofvolume,quantitiesofsugarinweight,andquantitiesofropeinlength.Theinvolvement“most-m” is therefore interpreted asFQ(most-m)=λM.λX.|ΣX|M > (|ΣM0|M/2),where |z|M designatesthesizeofzusingthedimensionthatisnormallyusedtomeasurequantitiesofM.

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o Numericalpredicatesthatareusedtospecifyabsolutedomaininvolvement,referencedomainsize, or the size of certain parts of a reference domain, such as λn. n=2 (abbreviated “2” inQuantML/XML)andλn.n>1(abbreviated“>1”),aswellas(λn.n>500,kilo)arealsousedinDRSconditions. The interpretation of such complex predicates is defined not by FQ but by therecursivefunctionIQ,see(B1)below.

o Thebasicunitsofmeasurement, suchas ‘meter’, ‘kilo’, ‘litre’, and ‘hour’, areusedas terms inDRSconditions.FortheseelementsFQ(u)=u.

InsteadoftheusualboxnotationofDRTalsoamorecompactstringnotationwillbeused,withopeningand closing square brackets corresponding to DRS boxes, and a bar to separate the list of discoursereferentsfromconditions.Someconvenientshorthandnotationswillalsobeused,suchas[X⊆P|C1]for[X|C1,x∈X→P(x)],[X=P|C1]for[X|C1,x∈X↔P(x)],and[x∈P|C1]for[x|C1,P(x)].

B3Entitystructures

B3.1Participantstructures

Thegeneralformofaparticipantstructureisatripleorquadruple〈DS,q,d,(N)〉,dependingonwhetherareferencedomainsizeNisspecified.ThecomponentDSisinthesimplestcaseasingleunstructureddomainspecification, i.e.apairS= 〈m,〈D,v〉〉 consistingofamarkablem,adomainpredicateD,andaspecificationof the individuationofD(countormassorcountwith internalpart-wholestructure). Ingeneral,DSmaycontainasequenceofdomainspecificationsandasequenceofmodifiers:

〈〈〈S1,S2,…Sk〉,〈M1,M2,,…Mn〉〉,q,d,N〉

Domainspecificationsmayinturnincludeasubsequenceofdomainspecificationsandlocalmodifiers.FortheannotationofthegeneralizedquantifierexpressedbyanindeterminateNP,andmoregenerallyif the annotatedmaterial gives no reason to introduce a reference domain different from the sourcedomain, thesemantic interpretationof theparticipantstructure isasshown in(B3).Thepredicateq’occurring in (B3)-(B8) isdefined in (B1), viz.by composing IQ(q)with the interpretationFQ(v)of theindividuationspecification.Ifthequantificationinvolvesindividualsand/orpartsofindividuals,thenitsinvolvementismeasuredintermsofnumberofindividualsbyaddingupthesizesofparticipatingpartsexpressed as fractions of individuals. This size, designated by |..|*, differs from the cardinality of theparticipantset,unlesstheparticipantsethappenstocontainonlyentireindividuals(inwhichcase|X|*= |X|). Ifq isaquantitativepredicate in the formofanamountexpression 〈N,u〉, thentheunit(‘u’) insuchastructurebelongstoacertaindimension:alitreisaunitofvolume,akiloisaunitofweight,ameteraunitoflength,andsoon.Thesemanticsofaunittermisthereforeapair〈Du,u’〉,consistingofadimensionDandaunitu’asdefinedinthatdimension(seeBunt,1985),Forexample,thesemanticsoftheunitinanexpressionlike“twolitresofmilk”referstothedimension‘volume’andaunitasaformalobjectinthatdimension.In(B1),thesubscripts‘1’,‘2’indicatethefirstandsecondmemberofapair.

(B1) q’=λz.IQ(q)(((FQ(v))(z)),whereFQ(v)isdefinedas: FQ(count)=λX.|X|;FQ(count/parts)=λX.|X|*;FQ(mass)=λX.ΣX; IQ(q)isdefinedas:IQ(q)=FQ(q)ifqisanumericalpredicate; IQ(q)=(FQ(N(FQ(u)1(FQ(v))(z)),FQ(u)2)ifqisanamountexpression〈N,u〉,withnumerical predicateN.ThedomainpredicatesD’,D’0,D1’,etc.,occurring in ((B3) - (B9),aredefined in (B2), seealso (18) forthenotationP^.

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(B2) D’=IQ(D,v),with:IQ(D,count)=IQ(D,mass)=FQ(D);IQ(D,count/parts)=(FQ(D))^

B3.2.1Participantstructuresforunstructureddomains

For participant structureswith an unstructured domain, the interpretation is defined by the clauses(B3)-(B5). If the reference domain is a contextually determined part of the source domain, then theparticipantstructure is interpretedas in(B4),whereD0designatesthecharacteristicpredicateof thereferencedomainrelatedwiththesourcedomainD.Inboth(B3)and(B4)caseaappliesifthedomaininvolvementspecification(qa)isabsolute;casebifitisproportional(qp).(B3)a.IQ(〈D,v〉,qa,indet)=[X|qa’(X),x∈X→D’(x)] b.IQ(〈D,v〉,qp,indet)=[X|(qp’(D0))(X),x∈X→D’(x)]

(B4) a.IQ(〈D,v〉,qa,det)=[X|qa’(X),x∈X↔D0‘(x)] b.IQ(〈D,v〉,qp,det)=[X|(qp’(D0))(X),x∈X↔D0‘(x)]

IftheannotatedNPcontainsasizespecification(‘N’)ofthereferencedomain,thentheinterpretationoftheparticipantstructureisasspecifiedin(B5),againwithcaseaforabsoluteinvolvementspecificationandcasebforproportionalspecification:

(B5)a.IQ(〈D,v〉,qa,det,N)=[X|N’(|D0|),qa’(X),x∈X→D0‘(x)] b.IQ(〈D,v〉,qp,det,N)=[X|N’(|D0|),(qp’(D0))(X),x∈X↔D0‘(x)]If v = count/parts then the domain predicatesD andD0, in (B3) - (B5) are replaced byD^x andD0x,respectively.

B3.2.2Participantstructureswithcomplexdomains

The domain component of a participant structure can be complex in two ways: by the head of thecorrespondingNP being a conjunction, and by the head (or one of its conjuncts) being restricted bymodifiers.AquantifiedconjunctiveNPintroducesasequenceofcomponentdomainsintheannotationstructure,whichcorresponds toadisjunctivecondition in the interpretation.As in thecaseofsimpledomains,theinterpretationoftheentitystructuresdependsonwhethertheinvolvementspecificationisabsoluteorproportional:

(B6) a.IQ(〈〈,D2,…Dk〉,qa,indet〉)=[X|qa’(X),x∈X→[|D1‘(x)∨D2‘(x)…∨Dk‘)x)]] b.IQ(〈〈,D2,…Dk〉,qp,indet〉)=[X|qp’(D10‘∪D20‘∪…∪Dk0’)(X),x∈X→[|D1‘(x)∨D2‘(x)…∨ Dk‘(x)]]

(B7) a.IQ(〈〈D1,D2,…Dk〉,qa,det〉)=[X|qa’(X),x∈X↔[|D10‘(x)∨D20‘(x)…∨Dk0‘(x)]] b.IQ(〈〈D1,D2,..Dk〉,qp,det〉)=[X|qp’(D10‘∪D20‘∪...∪Dk0’)(X), x∈X↔[|D10‘(x)∨D20‘(x)...∨Dk0‘(x)]]

(B8) a.IQ(〈D1,D2,…Dk〉,qa,det,N〉)= [X|qa’(X),N’(|D10‘∪D20‘∪…∪Dk0’|),x∈X↔[|D10‘(x)∨D20‘(x)…∨Dk0‘(x)]]

b.IQ(〈D1,D2,…Dk〉,qp,det,N〉)=[X|qp’(D10‘∪D20‘∪…∪Dk0’)(X),N’(|D10‘∪D20‘∪…∪Dk0’|), x∈X↔[|D10‘(x)∨D20‘(x)…∨Dk0‘(x)]]

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If the nominal head of a quantifyingNP (or one of its conjuncts, if it is conjunctive) ismodified (byadjectives,nouns,possessives,PPs,orrelativeclauses)thenthedomainspecificationinitsannotationcontains additional restrictions. Table 2 in Clause 7.3.4 lists the 6 possible combinations ofdistributivityandlinkinversionforthemodificationofheadnounswithdifferentvariousindividuation.Toshowthesemanticsof thevarious typesofmodification, the followingspecifications firstdescribethe effect of a single restriction for a non-conjunctive NP head. This is subsequently generalized formultiplerestrictionsandconjunctiveNPheads.

Amodificationspecificationconsistsofarestrictingpredicate‘r’,possiblywithadditionalspecificationsofdistributivityandlinking(seeClause7.3.5),andintroducesanadditionalconditionintheembeddedDRS(comparedtoB3)asshownin(B9a),wherer’=IQ(r):

(B9a) IQ(〈〈〈D,count〉,〈r〉〉,q,indet〉)= IQ(〈〈〈D,count〉,〈r,individual〉〉,q,indet〉)= IQ(〈〈〈D,count〉,〈r,individual,linear〉〉,q,indet〉)= IQ(〈〈〈D,count/parts〉,〈r,individual,linear〉〉,q,indet〉)= IQ(〈〈〈D,mass〉,〈r,parts,linear〉〉,q,indet〉)=[X|q’(X),x∈X→([|D(x)]∪r’(x))] =[X|q’(X),x∈X→[|D(x),r’(x)]]

Similarly for a modifier with unspecific distribution and linear linking, except that the modifier isgeneralizedfrombeingdefinedonlyforindividuals(ormassquantities)toalsobeingapplicabletosetsofindividualsinthereferencedomain-see(17)inClause6.4.Thisisexpressedin(B9b),(NotethatX*containsalltheelementsofXaswellasallthesubsets.)

(B9b) IQ(〈〈〈D,count〉,〈r,unspec,linear〉〉,q,indet〉)=[X|q’(X),x∈X*→([|D*(x)]∪r’*(x))]

For the unspecific modification of a mass noun, a specification of the involvement of the referencedomainisappliedtothetotalityformedbythequantitiesinvolved.Thisisexpressedin(B9c).

(B9c) IQ(〈〈〈D,mass〉,〈r,unspec,linear〉〉,q,indet〉)=[X|q’(Σ(X)),x∈X→([|D(x)]∪r’(x))]

For the unspecific modification of a head with a count/parts individuation, the entities that themodificationappliestoareeitherindividualsorpartsofindividuals.Thisisexpressedin(B9d).

(B9d) IQ(〈〈〈D,count/parts〉,〈r,unspec,linear〉〉,q,indet〉)=[X|q’(Σ⌃(X)),x∈X⌃→([|D⌃(x)]∪r’⌃(x))]

Amodificationwithcollectivedistributionintroduces,regardlessoftheindividuationofthedomain,anadditionalconditionattheDRStoplevel,asshownin(B9e),where‘v’canbeanyvalue:

(B9e) IQ(〈〈〈D,v〉,〈r,collective,linear〉〉,q,indet〉)=[X|q’(X),r’(X),x∈X→D*(x)]

Theinterpretationspecificationin(B9)forindeterminateNPshasacounterpartforthecorrespondingdeterminatecases, justlike(B3)hasthedefinitecounterpart(B4),aswellasforthedeterminatecasewithsizespecification,like(B5).

For interpreting a modification with inverse linking it is most convenient to first construct theinterpretationofthelinearlylinkedcase,andsubsequentlyswitchthescopesofthequantifiersinvolvedintheinversionaround.Forexample,fortheNP“ThreestudentsfromeveryDutchuniversity” in(B10)thetop-levelquantificationinthecaseoftheinterpretationwithlinearlinkingisshownin(B11).

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(B10) ThreestudentsfromeveryDutchuniversityparticipated.

(B11)

Toobtainthemoreplausibleinverselylinkedreading,thetwoquantificationsinthisDRSareswitchedaround,usingthescope-switchingoperationdefinedin(B12)afterfirstlinkingthetop-levelquantifiedparticipantstotheevent(s)underconsideration,togettheresult(B13).

(B12) InvScope([X|C1,x∈X→[Y|C2,y∈Y→N]])=[Y|C2,y∈Y→[X|C1,x∈X→N]]

(B13)

As noted in Clause 7.3.4, modifications with inverse linking can be expressed by PPs, by possessiverestrictions, and (marginally) by relative clauses. The semantic interpretation of PP modifierstructures,relativeclausestructures,andpossessivestructuresisdescribedbelowinClauseB3.3.

B3.2.3Participantstructuresforpropernamesanddefinitedescriptions

While proper names and (singular) definite descriptions are referring expressions rather thanquantifiers,andcouldthusbeconsideredtobeoutsidethescopeofquantificationannotation,itwouldseemratherawkwardtoforexampleincludethetreatmentofpluralexpressionslike“thechildren”butnot of their singular counterpart “the child”. The annotation scheme presented in this documentthereforedoes includea treatmentofpropernamesanddefinitesingularNPs,withoutgoing into thedetails of the presuppositions that may be associated with their use concerning uniqueness andexistence(seee.g.CoppockandBeaver,2015).

Entitystructuresfornounphrasesconsistingofapropernameareinterpretedasintroducingasingleparticipant.Forexample,theDRSin(67a)interpretsthepropername“JohnSmith”asthecontextuallydistinguishedindividualwhosatisfiestheconditionjohnsmith0(x),withthepresuppositionthatthereisonlyonesuchindividual.

(B14a)

Singulardefiniteexpressionslike“thepresident”areinterpretedinthesameway:

X|X|=3 U

student(x)u∈U←[|dutch(u),university(u)]u∈U→[|dutch(u),university(u),from(x,u)]

x∈X→

Uu∈U←[|dutch(u),university(u)] X

|X|=3,dutch(u),university(u),x∈X→[student(x),[E|e∈E→[participate(e),agent(e,x),from(x,u)]

u∈U→

xjohnsmith0(x)|johnsmith0|=1

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(B14b

B3.3Eventstructures

IfPEisthecharacteristicpredicateofacertaineventdomain,astypicallynamedbyaverbbutpossiblybyanoun,thenthesemanticsofanevententitystructurewiththateventdomainisspecifiedby(B15):

(B15) IQ(PE)=[E|e∈E→PE(e)]

B3.4Modifierstructuresandpossessiverestrictions

B3.4.1Adjectives

Adjectives are one-place predicates, represented by names that correspond to lexical items of thelanguageof theprimarydata(seeClause7.4 in themainpartof thedocument). Inorder touse theirsemantics in composing themeanings of annotation structures in the sameway as other adnominalmodifiers (relative clauses, PPs, and nominalmodifiers), the interpretation of an adjectivalmodifierstructureisdefinedasfunctionwhich,appliedtoanargument,yieldsaDRS(cf.(B9a)).

(B18) a.IQ(〈A,individual〉)=λz.[|A(z)]

B3.4.2Nouns

Theentitystructureforanounmodifyinganothernounisapair〈m,N〉consistingofamarkableandaproperty,ora structure 〈m, 〈N, r1,.., rn〉〉,n≥1where theproperty (N)hasoneormoremodifiers.Thespecification in (B19) of the semantics of a noun modifying another noun follows Hobbs (1993) inintroducing the ‘anonymous’ relation “NN” to indicate the implicit semantic relation between themodifyingnounandthenounitmodifies(compareexample(39)inClause6.7).

(B19) a.IQ(N)=λz.[y|N’(y),NN(z,y)] b.IQ(〈N,r1,..,rn>)=λz.[y|N’(y),NN(z,y),r1‘(y),…,rn‘(y)]

Forexample, theexpression “a toxicwastedump” canbe interpretedasbeingaboutadump thathassome unknown relation to toxic waste. Note that there is an ambiguity here, as illustrated by theexample“anoldwastedump”,whichismoreplausiblyinterpretedasanolddumpforwaste;thismeansthat“old”shouldratherbeannotatedasamodifierof“dump”.

B3.4.3Relativeclauses

Likeadjectivesandnominalnounmodifiers,arelativeclauseisinterpretedsemanticallyasaone-placepredicatethatcanbeusedinDRS-conditions,expressingrestrictionsonaquantificationdomain.Initslinguistic form, a relative clause (RC) is verymuch like amain clause, except that one of the verb’sargumentsismissing;itssemanticroleisplayedbythemodifiedNPhead.

xpresident0(x)|president0|=1

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As specified in Clause 7.3.5, the linguistic information in a relative clausemodifier structure has theform (B20), in which Ra is the ‘missing’ semantic role and αRC is the annotation structure of thecombinationofeventsandparticipantsintheRC.

(B20) sRC=〈Ra,αRC〉

ThecomponentαRChasthesamestructureastheannotationstructureofamainclause,asspecifiedin(62),repeatedhereas(B21):

(B21) αRC=〈εEV,{εP1,…,εPn},{LP1,…,LPn},{sc1,…,sck}〉

The interpretationofsuchanannotationstructure, if it is fullyscoped,hasamostdeeplynestedsub-DRSembeddedwithinthescopeofallthequantifiersintheannotatedclause,inwhichtheparticipantsare linked to events in their respective semantic roles, the nucleus of the structure (see Clause 7.5,(74)).ToconstructtheinterpretationoftheRCasaone-placepredicate,theconditionRa(e,z)thatlinksthe‘missing’participant(z)totheevent(e)inthe‘missing’semanticroleRaisinsertedinthenucleus,and this participant variable is abstracted over. This is expressed schematically in (B22), where‘IN(K,C)’designatestheoperationof insertingconditionCinthenucleusofK, ‘evv(K)’designatestheeventvariableofK,andα’abbreviatesIQ(αRC).12

(B22) IQ(Ra,αRC)=λz.IN(α’,Ra(evv(α’),z))

Predicates as defined in (B22) can be substituted for r1’ in (B9) to provide theDRS interpreting thedomain specification with a linearly linked RC-restriction, and via scope inversion formodificationswithinverselinking.

B3.4.4Prepositionalphrases

TheinterpretationofaPP-restrictioncanbedescribedinasimilarwayasthatofarelativeclause. Inthecaseoflinearlinking,theinterpretationisbuiltupfromtheinterpretationsoftheprepositionandtheNPthatformthePP.Aprepositionisassumedhere(forsimplicity)todenoteabinaryrelationRP,and an NP to denote a generalized quantifier whose QuantML annotation is a participant entitystructure. The semantic interpretation of a quantifyingNP has the schematic form shown in (B23a),whereC1andC2aresetsofconditions;iftheNPinthePPisnotaquantifier,butapropername(asin“fromTokyo”)ora(singular)definitedescription,thenitsinterpretationhastheformshownin(B23b).

(B23) a.[X|C1,x∈X→[|C2]]

b.[x|C1]

ToconstructtheinterpretationofthePPasaone-placepredicate,theconditionRP‘(x,z)thatrelatesthemodifiedNPheadtotheNPinthePPthroughthePP’srelationRPisaddedtotheembeddedDRSinthequantifiercaseandtothemainDRSinthenon-quantifiercase:

(B24) a.λz.[X|C1,x∈X→[|C2,RP‘(x,z)]]

b.λz.[x|C1,RP‘(x,z)]

12 A relative clause that contains quantifierswith equal scope hasmore than one nucleus, see example (B58).Thesenucleiallhavethesameeventvariable,sothevalueof‘evv’isstilluniquelydefined;theinsertionoperation‘IN’isinthatcaserepeatedforeachnucleus.

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Thepredicatesin(B24)areconstructedasspecifiedin(B25).Theoperations‘INA0’and‘INA1’,definedin(B26),takeasinputaDRSthatinterpretsaquantifiedparticipantentitystructure(caseB24a))oranon-quantified one (case (B24b)), corresponding to the NP in a PP, and a binary relation RP‘,correspondingtoaPP’spreposition.ThisrelationisusedtoformaDRS-conditionbyapplyingitto(1)the quantified discourse referent in εP‘ (case (B24a), the variable ‘x’) or to the top-level discoursereferentinεP‘(case(B24b),thevariable‘x’),and(2)toavariablethatisabstractedover.ThisconditionisinsertedintheembeddedDRSinthequantifiedcaseandinthemainDRSinthenon-quantifiedcase.(B25) a.IQ(RP,εP)=INA1(εP’,RP‘)

b.IQ(RP,εP)=INA0(εP’,RP‘)

(B26) a.INA1([X|C1(X),x∈X→C2],λu.λvR(u,v))=λz.[X|C1(X),x∈X→C2,λu.λvR(v,u)(x)(z)] =λz.[X|C1(X),x∈X→C2,R(x,z)]

b.INA0([x|C1(x)],λu.λvR(u,v))=λz.[x|C1(x),λu.λvR(v,u)(x)(z)]=λz.[x|C1(x),R(x,z)]

A one-place predicate as built in this way can be substituted for r1’ in (B9) to form the DRS thatinterprets a linearly linked PP-modification, and via scope inversion (after merging with theparticipationlinkstructureinterpretation)totheinterpretationofaninverselylinkedPP-modification.

B3.4.5Possessives

Prenominal possessive structures can be formed with possessive pronouns, as in (B27a), and withgenitives,whichinsomelanguagesmaybequitecomplexandincludequantifiers,asin(B27b,c),givingrise to issues of distributivity and inverse/linear linking. Semantically, possessive structures can beanalysed in termsofapossessor,apossessee,andabinaryrelation ‘Poss’between them(PetersandWesterståhl, 2013). In QuantML they are treated like prepositional phrases, except that the relationbetweenthediscoursereferentsofthemodifiedNPandthepossessor(s)isinvariablythePossrelation.

(B27) a.Tomcataloguedmostofhisbooks. b.Twoofeverystudent’sessayswerelost. c.Theheadmaster’schildrens’toysdisappeared.

The examples b and c show a quantifying possessive construction, inversely linked to its NP head,assumingthatthesesentencesshouldbeinterpretedas“Foreverystudent,twoofhis/heressayswerelost”and“Ofeveryoneoftheheadmaster’schildrenthetoysdisappeared”,respectively.

Apostnominalpossessiverestriction,asin”ThedeskoftheUNSecretary-General”istreatedinthesamewayasotherPPmodifications,exceptthatthepreposition“of“isinterpretedastherelation‘Poss’.

B4Linkstructures

B4.1Participationlinks

B4.1.1LinkswithpositivepolarityAs specified in (72) in Clause 7.5, the interpretation of a participation link structure with positivepolarityisformedbytheDRS-mergeoftheinterpretationsof(1)theeventstructure,(2)theparticipantstructure, and (3) thequintet 〈R,d, s,ξ, [ρ],pos〉 that contains the linking information (R= semanticrole,d=distributivity,s=eventscope,ξ=exhaustiveness,ρ=repetitiveness).Forthemostcommon

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link structure (positive, non-exhaustive, non-repetitive), the interpretation of the link structure isspecifiedby(B28):

(72) a.IQ(〈εE,εP,R,d,narrow,p〉)=(IQ(εP)∪*IQ(εE))∪IQ(R,d,narrow,p) b.IQ(〈εE,εP,R,d,wide,p〉)=(IQ(εE)∪*IQ(εP))∪IQ(R,d,wide,p) b.IQ(〈εE,εP,R,d,free,p〉)=IQ(εE)∪IQ(εP)∪IQ(R,d,free,p)

(B28) a.IQ(R,individual,narrow,nex,pos)=IQ(R,parts,narrow,nex,pos)=

[X|x∈X→[E|e∈E→R(e,x)]]

b.IQ(R,individual,wide,nex,pos)=IQ(R,parts,wide,nex,pos)=

[E|e∈E→[X|x∈X→R(e,x)]]

c.IQ(R,collective,narrow,ξ,pos)=[E,X|e∈E→R(e,X)]

d.IQ(R,collective,wide,ξ,pos)=[E|e∈E→[X|R(e,X)]]

e.IQ(R,unspecific,narrow,nex,pos)=[X|x∈X→[E|e∈E→[y∈X*|x=y∨x∈y,R(e,y)]]]

f.IQ(R,unspecific,wide,nex,pos)=[E|e∈E→[X|x∈X→[y∈X*|x=y∨x∈y,R(e,y)]]]

g.IQ(R,single,s,ξ,pos)=[x,E|e∈E→R(e,x)]

B4.1.2Linkswithnegativepolarity

Participation link structures with negative polarity come in two varieties: for wide-scope negation,when the negation outscopes all quantifications over participants and events, and for narrow-scopenegation,asinthereadingsbandc,respectively,ofthesentencein(B29a).

(B29) a.Theunionsdonotaccepttheproposal. b.Itisnotthecasethatalltheunionsaccepttheproposal. c.Alltheunionsdonotaccepttheproposal(noneofthemacceptsit).

Themeaningofaclausewithwide-scopenegationisthenegationofthesameclausewithoutnegation.This is expressed in (B30), using the negation operator at DRS top-level that was introduced byKrahmer&Muskens(1995),symbolizedas‘∼’.(StandardDRTonlyallowsnegationofsub-DRSs,whichcausessomeproblems indealingwithnegatedanddisjunctivesentences;seee.g.Krahmer,1995andQian, 2015). If the polarity of the link has narrow scope then (B31) applies, which makes use of acombinator thatbrings theevent informationofaparticipation linkwithin thescopeof thenegation.Thiscombinatory,symbolizedas⊕n,isdefinedin(B32).

(B30) IQ(〈εE,εP,R,d,s,ξ,neg-wide〉)=∼IQ(〈εE,εP,R,d,s,ξ,pos〉)

(B31) IQ(〈εE,εP,R,d,s,ξ,neg-narrow〉)=IQ(εP)∪(IQ(R,d,s,ξ,neg-narrow)⊕nIQ(εE))

(B32) [X|C1,x∈X→¬K1]⊕nK2=D[X|C1,x∈X→¬(K1∪K2)]

B4.1.3Exhaustivelinking

Exhaustive linkingoccurswhenthesetof individuals involvedinaquantifiedpredicationcontainsalltheparticipantsofwhichthepredicationissaidtohold,asin“(Only)Twopeopleattendedthewedding”.and in “(Only) Two colleagues did not attend the wedding”. The exhaustiveness can be expressed bystipulatingthatthediscoursereferent(set)inthelinkinterpretation(forwhichmostly‘X’isused)doescontain all these individuals; see e.g. the bidirectional in (B33a,b). If the distributivity of the link is

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collectiveor single, then thenotionofexhaustivenessby itsverynaturedoesnotapply, and in somecases the event scope does not either. This is expressed in (B33c-e), where ‘s’ stands for any eventscope,‘ξ’foranyexhaustiveness,and‘neg’foreither‘neg-wide’or‘neg-narrow’.

Theinterpretationofquintuples〈R,d,s,ξ,p〉withξ= ‘exhaustive’isdefinedbythefollowingclauses(seealso(B28)):

(B33)a.IQ(R,individual,narrow,exhaustive,pos)=IQ(R,parts,narrow,exhaustive,pos)= [X|x∈X↔[E|e∈E→R(e,x)]]

b.IQ(R,individual,wide,exhaustive,pos)=IQ(R,parts,wide,exhaustive,pos)= [E|e∈E→[X|x∈X↔R(e,x)]]

c.IQ(R,unspecific,narrow,exhaustive,pos)=[X|x∈X↔[E|e∈E→[y∈X*|x=y∨x∈y, R(e,y)]]]

d.IQ(R,unspecific,wide,exhaustive,pos)=[E|e∈E→[X|x∈X↔[E,y∈X*|x=y∨x∈y, e∈E→R(e,y)]]]

Thecorrespondingclausesfornegative-polaritylinksareasfollows;

(B34) a.IQ(R,individual,narrow,exhaustive,neg-narrow)=IQ(R,parts,narrow,exhaustive, neg-narrow)=[X|x∈X→¬[E|e∈E→R(e,x)]]

IQ(R,individual,narrow,exhaustive,neg-wide)=IQ(R,parts,narrow,exhaustive, neg-wide)=∼[X|x∈X↔[E|e∈E→R(e,x)]]

b.IQ(R,individual,wide,exhaustive,neg-narrow)=IQ(R,parts,wide,neg-narrow)=

[E|e∈E→¬[X|x∈X↔R(e,x)]]

IQ(R,individual,wide,exhaustive,neg-wide)=IQ(R,parts,wide,neg-wide)=

=∼[E|e∈E↔¬[X|x∈X↔R(e,x)]]]

c.IQ(R,collective,narrow,ξ,neg)=[E,X|¬[e∈E→R(e,X)]]

d.IQ(R,collective,wide,ξ,neg)=[E|¬[e∈E→[X|R(e,X)]]]

e.IQ(R,unspecific,narrow,exhaustive,neg-narrow)=[X|x∈X*↔¬[E|e∈E→R(e,x)]]

IQ(R,unspecific,narrow,exhaustive,neg-wide)=∼[X|x∈X*↔[E|e∈E→R(e,x)]]

f.IQ(R,unspecific,wide,exhaustive,neg-narrow)=[E|e∈E→¬[X|x∈X*↔R(e,x)]]

IQ(R,unspecific,wide,exhaustive,neg-wide)=∼[E|e∈E→[X|x∈X*↔R(e,x)]]

g.IQ(R,single,s,ξ,neg)=[E,x|¬[e∈E→R(e,x)]]

B4.1.3Repetitivelinking

Participationinak-timesrecurringeventcanbeannotatedbymeansofaparticipationlinkstructurewith repetitiveness k, the semantics of which is given by (B35) for the case of individual, non-exhaustiveparticipationwithnarroweventscope:

(B35) IQ(R,individual,narrow,nex,k,pos))=[X|x∈X→[E]k(E),e∈E→R(e,x)]]

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The addition of a repetitiveness specification to participation link structures leads to variants of theclauses (B28) - (B34) of the definition of IQ, like (B35) is a variant of (B28a). A repetitivenessspecificationisapair〈r,n〉,where‘n’isapositiveintegerand‘r’isoneofthenumericalrelations‘equal’,‘greaterthan’,‘greaterthanorequal’,‘lessthan’,‘lessthanorequal’;annotationsoftheform〈equal,n〉willbeabbreviatedby‘n’.

Temporal (and spatial) quantification by means of NPs where the head has a temporal (or spatial)character, as in (B37), naturally fall within the scope of the QuantML annotation scheme. Thecombining of such a temporal quantification with an adverbial quantifier, as in (B37b), allows atreatmentoffrequency,asillustratedin(B38).

(B37) Someparentscalleveryday.

(B38) a.Someparentscalltwiceeveryday.

b.Markables:m1=Someparents,m2=parents,m3=call,m4=everyhour,m5=hour

c.AnnotationRepresentation: <entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”some” definiteness=”indet’”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”parent”/> <event xml:id=”e1” target=”#m3” pred=”call”/> <entity xml:id=”x3” target=”#m4” domain=”#x4” involvement=”all” definiteness=”det”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”day”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow” repetition=”2”/> <participation event=”#e1” participant=”#x3” semRole=”inTime” distr=”individual” evScope=”narrow”/> <scoping arg1=”#x1” arg2=”#x2” scopeRel=”wider”/> (B39) [X⊆parent|x∈X→[D⊆day0|d∈D→[E⊆call||E|=2,e∈E→[agent(e,x),intime(e,d)]] B4.2Scopelinks

Scope linksdeterminehow the interpretationsof participation link structures are tobe combined toformDRSsthatcorrectlyrepresentthescoperelationsamongthequantifiersinaclause.

FortwoquantifyingNPs,thescoperelationbetweenthecorrespondingparticipantentitystructuresεP1and εP1 is either that one outscopes the other (‘wider’), or that theymutually outscope one another(‘dual’), or that they have equal scope. The corresponding participation structures are combined bymeansoftheirscopedmerge(∪*),theirdualmerge(∪D),ortheirDRS-merge(∪)respectively.

Atreatmentofnon-quantifyingNPs(propername,definitedescription,personalpronoun),whichdoesnothaveanoutscopingrelationtoaquantifyingNP,isincludedintheannotationschemedefinedinthisdocument for convenience.Anon-quantifyingNPandaquantifyingNP (or twonon-quantifyingNPs)are treatedas related througha scope linkstructurewithscoping relation ‘unscoped’,which triggerstheirinterpretationstobemergedbythe‘unscopedmerge’operator(∪’).Thisoperatorcombinestheparticipant-related information in its arguments like theDRS-merge; theevent-related information ismergedinthescope-determinedpositioninthequantifyingNPannotationinterpretation.(Theevent-relatedinformationinthenon-quantifyingNPcanmovearoundfreely,asithastheeventscope“free”.)

(B41)specifiesthesemanticsofthescoperelations;(B42)showsthesemanticsofscopelinkstructures.

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(B41) IQ(wider)=λx.λy.x∪*y;IQ(equal)=λx.λy.x∪’y;IQ(dual)=λx.λy.x∪2y

(B42) a.IQ(〈LP1,LP2,wider〉)=IQ(wider)(IQ(LP1),IQ(LP2))=IQ(LP1)∪*IQ(LP2)

b.IQ(〈LP1,LP2,equal〉)=IQ(equal)(IQ(LP1),IQ(LP2))=IQ(LP1)∪IQ(LP2)

c.IQ(〈LP1,LP2,dual〉)=IQ(dual)(IQ(LP1),IQ(LP2))=IQ(LP1)∪DIQ(LP2)

d.IQ(〈LP1,LP2,unscoped〉)=IQ(unscoped)(IQ(LP1),IQ(LP2))=IQ(LP1)∪’IQ(LP2)

B5Clause-levelannotationstructures

The annotation of a simple sentence (or ‘clause’), consisting of a verb and its arguments, being thenaturalunit forquantificationannotation,has the structure shownabove in (66),viz.:A= 〈εEV, {εP1,…,εPn}, {LP1,…, LPn}, {sc1,…, sck}〉. The interpretations of the link structures LP1,…, LPn combine theinterpretationofeachparticipantstructurewiththeeventstructure.IfAisafully-scopedannotationstructurethenIQ(A)isthecombinationofIQ(LP1),…,IQ(LPn},wherethepairwise combination of link structure interpretations is defined in (B42). As A is fully scoped, thenthereisasequenceL1,..LnofparticipationlinkstructuressuchthatLi∈{LP1,…,LPn}andthateachpairofneighboursLi,Li+1islinkedthroughoneofthethreepossiblescoperelations.LetsidesignatethescoperelationbetweenLiandLi+1.Theinterpretationoftheannotationstructureisthencomputedasfollows(usingshortnotationsi’=IQ(s1)andLi’=IQ(L1i):(B43) IQ(A)=s1’(L1’,s2’(L2’,s3(L3’,…,sn-1’(Ln-1’,Ln’)))…)

Ifthescoperelationsinanannotationstructuredonotspecify(explicitlyorbyimplication)therelativescopesofeverypairofparticipantstructures,thenitssemanticinterpretationisnotasingleDRSbutasetof(sub-)DRSsplusaspecificationofscopeconstraints,togetherforminganunderspecifiedDRS.

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AnnexC.Exampleannotationsandinterpretations(informative)

C1Collectivequantification

(C1) “Threemenmovedfivepianos”

Uponthecollectivereading for“Threemen”, the individualreading for“fivepianos”,and“Threemen”,outscoping“fivepianos”,thesentenceisannotatedasfollows.

Markables:m1=Threemen,m2=men,m3=moved,m4=fivepianos,m5=pianos

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”3” definiteness=“indet”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”man” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”move”/> <entity xml:id=”x3” #target=”#m4” domain=”#x2” involvement=”2” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”piano” indiv=”count”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”collective”/> <participation event=”#e1” participant=”#x3” semRole=”patient” distr=”individual” evScope=”narrow”/>

<scoping arg1=”#x1” arg2=”#x3” scopeRel=”wider”/>

Abstractsyntax:annotationstructure13:A=〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉,with εE=〈m3,move〉 εP1=〈m1,〈〈m2,man〉,3,indeterminate〉〉,εP2=〈m4,〈〈m5,pianos〉,5,indeterminate〉〉 LP1=〈εE,εP1,Agent,collective,narrow〉,LP2=〈εE,εP2,Theme,,narrow〉 sc1=〈LP1,LP2,wider〉

Semantics(widescopereadingfor“Threemen”): IQ(εP1)=[X⊆man||X|=3] IQ(εP2)=[Y⊆piano||Y|=5] IQ(LP1)=[X⊆man,E⊆move||X|=3,e∈E→ [agent(e,X)]] IQ(LP2)=[Y⊆piano||Y|=5,y∈Y→[E⊆move|e∈E→ theme(e,y)]]

IQ(A)=IQ(〈εE,{εP1,εP2},{LP1,LP2},{〈εP1,εP2,wider〉}〉)=IQ(LP1)∪*IQ(LP2)= [X⊆man,Y⊆piano||X|=3,|Y|=5,y∈Y→[E⊆move|e∈E→[agent(e,X),theme(e,y)]]]Onthereadingwhere“Threemen”isoutscopedby“fivepianos”,theinterpretationoftheannotationstructureisobtainedbyapplyingthescopedmergetothesametwoargumentsinreverseorder:

IQ(A)=IQ(〈εE,{εP1,εP2},{LP1,LP2},{〈εP2,εP1,wider〉}〉)=IQ(LP2)∪*IQ(LP1)= [Y⊆piano||Y|=5,y∈Y→[X⊆man,E⊆move|[X|=3,e∈E→[agent(e,X),theme(e,y)]]]

C2Groupquantification

Collectivequantificationwithwideeventscopeallowsinterestingreadingsofsentenceswithmorethanonecollectivequantifier, as illustratedbyexample (C2)on thereadingwheregroupsofboysplayedwithgroupsofgirls(seeexample(27)inthemaindocument),i.e.whereineachoneofacertainsetofplay-eventsagroupofsevenboysandagroupofelevengirlsparticipated.

13Forimprovedreadability,henceforthsharpbracketsenclosingsingleitemswillbesuppressed,leadingtoe.g.εE=〈m3,move〉insteadofεE=〈m3,〈move〉〉.

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(C2) Sevenboysplayedagainstelevengirls.

Markables:m1=“Sevenboys”,m2=“boys”,m3=“played”,m4=“elevengirls”,m5=“girls”

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”7” definiteness=”indet”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”boy” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”play”/> <entity xml:id=”x3” #target=”#m4” domain=”#x2” involvement=”11” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”girl” indiv=”count”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”group” evScope=”wide”/> <participation event=”#e1” participant=”#x3” semRole=”agent” distr=”group” evScope=”wide”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”equal”/>

Abstractsyntax: A=〈{εP1,εP2},{LP1,LP2},{sc1}〉 εP1=〈m1,〈〈boy,count〉,7,indet〉〉,εP2=〈m3,〈〈girl,count〉,11,indet〉〉 εE=〈m2,play〉 LP1=〈εE,εP1,agent,collective,wide〉,LP2=〈εE,εP2,agent,collective,wide〉 sc1=〈LP1,LP2,equal〉

The intended interpretation is obtained by interpreting each of the two participation link structuresaccording to the specifications in (72) and (B28d), and in view of the scoping relation being ‘equal’,combiningtheresultsbyDRS-merge.

IQ(A) = IQ(〈εE, {εP1, εP2}, {LP1, LP2}, {sc1}〉) = IQ(LP1) ∪ IQ(LP2)

IQ(LP1) = IQ(〈εE, εP1, Agent, collective, wide〉) = [ E ⊆play|e∈E→[X⊆boy||X|=7,agent(e,X)] IQ(LP2) = IQ(〈εE, εP2, Agent, collective, wide〉) = [ E ⊆play|e∈E→[Y⊆girl||Y|=11,agent(e,Y)]

IQ(LP1) ∪ IQ(LP2) = [E⊆play|e∈E→[X⊆boy,Y⊆girl||X|=7,|Y|=11,agent(e,X),agent(e,Y)]]

C3Cumulativequantification:

(C4) Threebreweriessuppliedfifteeninns

Markables:m1=“Threebreweries”,m2=“supplied”,m3=“fifteeninns”

QuantML/XMLannotation:see(69).

Abstractsyntax: A=〈εE,{εP1,εP2},{LP1),LP2),{sc1}〉,with εP1=〈m1,〈〈brewery,count〉,3,indet〉〉,εP2=〈m3,〈〈inn,count〉,15,indet〉〉,εE=〈m2,〈supply〉〉 LP1=〈εE,εP1,Agent,individual,narrow〉,LP2=〈εE,εP2,Beneficiary,individual,narrow〉 sc1=〈LP1,LP2,dual〉A ‘dual scope’ relation between two participant structures is interpreted as mutual outscoping. Itsinterpretationinvolvestheuseofamergeoperationsomewhatsimilartothe‘scopedmerge’operation,called‘dual-scopemerge’andsymbolisedby∪2.Theoperationisdefinedfortwoargumentsthathavetheformshownin(79),repeatedhereinstringnotationas(C5):

(C5) Ai=[Xi⊆Di|Ci,xi∈Xi→Ki]

The‘dual-scopemerge’∪Doftwosuchargumentsisdefinedby(C6).

(C6) A1∪DA2=[Xi⊆Di|Ci∪C2,xi∈Xi→[X2⊆D2|x2∈X2→(Ki∪K2)], x2∈X2→[X1⊆D1|x1∈X1→(Ki∪K2)]]

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Theuseofthisoperationinspecifyingthesemanticsofcumulativequantificationsisillustratedbytheinterpretationoftheannotationstructureby(C7).

(C7) IQ(A)=IQ(〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉)=IQ(LP1)∪DIQ(LP2)=

=[X⊆brewery,Y⊆inn||X|=3,|Y|=15,x∈X→[Z⊆Y|y∈Z→[E⊆supply|e∈E→agent(e,x),beneficiary(e,y)]],y∈Y→[U⊆X|x∈U→[E⊆supply|e∈E→agent(e,x),beneficiary(e,y)]]]

C4Massnounquantification

(C11) Thegirlshaveeatenallthechocolate.

Themostplausible readingof this sentence is theonewhereeachof “thegirls” participated in somechocolateeating,andallthechocolatewasconsumedbythem.Thisisthecumulativereading,forwhichtheQuantMLannotationisafollows:

Markables:m1=Thegirls,m2=girls,m3=haveeaten,m4=allthechocolate,m5=chocolate

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”all” definiteness=“det”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”girl” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”eat”/> <entity xml:id=”x3” #target=”#m4” domain=”#x2” involvement=”total” definiteness=“det”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”chocolate” indiv=”mass”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”parts” evScope=”narrow”/>

<scoping arg1=”#x1” arg2=”#x3” scopeRel=”dual”/>

Abstractsyntax:A=〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉εE=〈m3,drink〉εP1=〈m1,〈〈m2,〈girl,count〉〉,all,determinate〉〉εP2=〈m4,〈〈m5,〈chocolate,mass〉〉,total,determinate〉〉

LP1=〈εE,εP1,Agent,individual,narrow〉 LP2=〈εE,εP2,Theme,parts,narrow〉 sc1=〈LP1,LP2,dual〉

Semanticinterpretationoftheentitystructurefor“allthechocolate”:

(C12) IQ(εP2)=IQ(〈〈chocolate,mass〉,total,det〉)=[Y⊆chocolate0|Σ(Y)=Σ(chocolate0)]

The interpretations of the other components are as before. The interpretation of the annotationstructureasawholeisthus:

(C13) IQ(〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉)=IQ(LP1)∪DIQ(LP2)= [X=boy0,Y⊆chocolate0,|Σ(Y)=Σ(chocolate0), x∈X→[E⊆deat,y∈Y|e∈E→[agent(e,x),theme(e,y)]], y∈Y→[E⊆eat,x∈X|e∈E→[agent(e,x),theme(e,y)]]]

Inwords, thisDRS says that there is a set Y of quantities of chocolate that togethermake up all thecontextually relevant chocolate, and a set E of eat-events such that each of the girls in the set X ofcontextuallydistinguishedgirls(formingthereferencedomainofthequantifier“thegirls”)haveeatensomeofthequantitiesofchocolate,andeachofthequantitiesofchocolatewaseatenbyoneofthegirls.

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HomogeneousquantificationbyamassNPisillustratedbyexample(66),“Allthewaterintheselakesispolluted”,simplifiedhereto(C10):

(C14) Allthewaterispolluted.

Markables:m1=allthewater,m2=water,m3=ispolluted

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”every” definiteness=“det”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”water” indiv=”mass”/> <event xml:id=”e1” target=”#m3” pred=”polluted”/> <participation event=”#e1” participant=”#x1” semRole=”theme” distr=”parts” evScope=”narrow”/> Abstractsyntax:A=〈εE,{εP1},{LP1{}〉εE=〈m3,polluted〉εP2=〈m1,〈〈m2,〈water,mass〉〉,every,determinate〉〉

LP1=〈LE,LP1,Theme,parts,narrow〉

Theintendedinterpretation,whichsaysthateverysampleofwaterispolluted,isobtainedbytakingthesemanticsofthesingleparticipationstructure:

IQ(A)=IQ(〈εE,{εP1},{LP1},{}〉)=IQ(LP1)=[X=water|x∈X→[E⊆pollute|e∈E→theme(e,y)]]

QuantificationbyamassNPwithameasurephraseisillustratedbyexample(C15):

(C14) Thistruckhasdeliveredmorethanfiftythousandlitersofwater.

Markables:m1=Thistruck,m2=truck,m3=delivered,m4=morethanfiftythousand,m5=more thanfiftythousandliters,m6=morethanfiftythousandlitersofwater,m7=water

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”single” definiteness=“det”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”truck” indiv=”count”/> <event xml:id=”e1” target=”#m3” pred=”deliver”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”/>

<entity xml:id=”x3” #target=”#m6” domain=”#x4” involvement=”#a1” definiteness=“indet”/> <sourceDomain xml:id=”x4” target=”#m7” pred=”water” indiv=”mass”/> <measure xml:id=”a1” target=”#m5” num=”#n1” unit=”liter”/> <numericalPred xml:id=”n1” target=”#m4” numRel=”greater” num=”50.000”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”parts” evScope=”narrow”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”unscoped”/>

Abstractsyntax:A=〈εE,{εP1,εP2},{LεP1,LP2},{sc1}〉εE=〈m3,deliver〉εP1=〈m1,〈〈m2,〈truck,count〉〉,single,determinate〉〉,εP2=〈m6,〈〈m7,〈water,mass〉〉,total,determinate〉〉

LP1=〈LE,LP1,Agent,single,narrow〉,LP2=〈LE,LP2,Theme,parts,narrow〉

Annotationinterpretation: IQ(εP1)=[x∈truck0||truck0|=1],IQ(εP2)=[Y⊆water|Vol(Σ(Y))>(50.000,liter)] IQ(LP1)=[x∈truck0,E⊆deliver||truck0|=1,e∈E→agent(e,x)] IQ(LP2)=[Y⊆water|Vol(Σ(Y))>(50.000,liter),y∈Y→[E⊆deliver|e∈E→theme(e,y)]] IQ(A)=IQ(LP1)∪’IQ(LP2)=[x∈truck0,Y⊆water||truck0|=1],Vol(Σ(Y))>(50.000,liter), y∈Y→[E⊆deliver|e∈E→[agent(e,x),theme(e,y)]]

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C5Propernames

Propernamesaretreatedasreferringtoasingleentity,ratherthanasaquantifier.Byannotatingthemwith participant entity structures and participation link structures, they can take part in thecompositionalinterpretationofclauseannotations.Participantentitystructuresforpropernameshavethe involvement ‘single’, and participation link structures have the distributivity ‘single’. Theinterpretationofsuchanentitystructure, illustratedherebytheDRS[x|santa0(x), |santa0|=1]forthepropername“Santa”,reflectsthepresuppositionthatthereisonecontextuallydistinguishedreferentinthereferencedomain,identifiedas“Santa”.

(C21)Santagavethechildrenapresent

Markables:m1=Santa,m2=gave,m3=thechildren,m4=children,m5=apresent,m6=present

QuantML/XMLannotation: <entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”single” definiteness=“det”/> <sourceDomain xml:id=”x2” target=”#m1” indiv=”count” pred=”santa”/>

<event xml:id=”e1” target=”#m2” pred=”give”/> <entity xml:id=”x3” #target=”#m3” domain=”#x4” involvement=”all” definiteness=“det”/> <sourceDomain xml:id=”x4” target=”#m4” indiv=”count” pred=”child” />

<entity xml:id=”x5” target=”#m5” domain=”#x6” involvement=”a” definiteness=”indef”/> <sourceDomain xml:id=”x6” target=”#m6” indiv=”count” pred=”present”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single evScope=”free”/> <participation event=”#e1” participant=”#x3” semRole=”beneficiary” distr=”individual” evScope=”narrow”/>

<participation event=”#e1” participant=”#x5” semRole=”theme” distr=”individual” evScope=”narrow”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”unscoped”/> <scoping arg1=”#x3” arg2=”#x5” scopeRel=”wider”/> Abstractsyntax: εE=〈m2,give〉 εP1=〈m1,〈〈〈m1,santa,count〉,single,det〉〉,εP2=〈m3,〈〈m4,〈child,count〉,all,det〉〉 εP3=〈m5,〈〈〈m6,〈present,count〉,a,indet〉〉 LP1=〈εE,εP1,Agent,single,narrow,free〉,LP2=〈εE,εP2,Beneficiary,individual,narrow〉 LP3=〈εE,εP3,Theme,individual,narrow〉 sc1=〈LP1,LP2,unscoped〉,sc2=〈LP2,LP3,wider〉

Annotationinterpretation: IQ(εP1)=[x|santa0(x),|santa0|=1],IQ(εP2)=[Y|y∈Y↔child0(y)],IQ(εP3)=[Z|z∈Z→present(z)] IQ(εE)=[E|e∈E→give(e)] IQ(LP1)=[x,E⊆give|santa0(x),|santa0|=1,e∈E→agent(e,x)] IQ(LP2)=[Y=child0|y∈Y→[E⊆give|e∈E→beneficiary(e,y)]] IQ(LP3)=[Z⊆present|z∈Z→[E⊆give|e∈E→theme(e,z)]] IQ(A)=IQ(LP1)∪’(IQ(LP2)∪*IQ(LP3))=[x,Y=child0|santa0(x),|santa0|=1, y∈Y→[Z⊆present|z∈Z→[E⊆give|e∈E→[agent(e,x),beneficiary(e,y),theme(e,z)]]]]

Example(C22)illustratesthehandlingofclauseswithmorethanonepropername.

(C22) SantabroughtthepresentstoXandra.

Markables:m1=Santa,m2=brought,m3=thepresents,m4=presents,m5=Xandra

QuantML/XMLannotation: <entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”single” definiteness=“det”/> <sourceDomain xml:id=”x2” target=”#m1” indiv=”single” pred=”santa”/>

<event xml:id=”e1” target=”#m2” pred=”bring”/> <entity xml:id=”x3” #target=”#m3” domain=”#x4” involvement=”all” definiteness=“det”/>

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<sourceDomain xml:id=”x4” target=”#m4” indiv=”count” pred=”present” /> <entity xml:id=”x5” target=”#m5” domain=”#x6” involvement=”single” definiteness=“det”/> <sourceDomain xml:id=”x6” target=”#m6” indiv=”single” pred=”xandra”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”individual” evScope=”narrow” />

<participation event=”#e1” participant=”#x5” semRole=”goal” distr=”single” evScope=”free”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”unscoped”/> <scoping arg1=”#x3” arg2=”#x5” scopeRel=”unscoped”/> <scoping arg1=”#x3” arg2=”#x5” scopeRel=”unscoped”/>

Abstractsyntax:A=〈εE,{εP1,εP2,εP3},{LεP1,LP2,LP3},{sc1,sc2}〉 εE=〈m2,〈bring〉〉 εP1=〈m1,〈〈m1,〈santa,count〉〉single,det〉〉,εP2=〈m3,〈〈m4,〈present,count〉〉,all,def〉〉 εP3=〈m5,〈〈m6,〈xandra,count〉〉,single,det〉〉 LP1=〈εE,εP1,Agent,single,free〉,LP2=〈εE,εP2,Theme,unspecific,narrow〉 LP3=〈εE,εP3,Goal,single,free〉 sc1=〈LP1,LP2,unscoped〉,sc2=〈LP1,LP3,unscoped〉,sc1=〈LP3,LP2,unscoped〉

IQ(A)=IQ(LP1)∪’IQ(LP2)∪’IQ(LP3)= [x,z,Y=present0|santa0(x),|santa0|=1, y∈Y→[E⊆bring|e∈E→[agent(e,x),theme(e,y),goal(e,z)]]]

C6Definitedescriptions

(C23) Thepresidentatetwopizzas.

Markables:m1=Thepresident,m2=ate,m3=twopizzas,m4=pizzas

QuantML/XMLannotation: <entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”single” definiteness=“det”/>

<sourceDomain xml:id=”x2” target=”#m1” pred=”president” indiv=”count”/> <event xml:id=”e1” target=”#m2” pred=”eat”/> <entity xml:id=”x3” #target=”#m3” domain=”#x4” involvement=”2” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”pizza” indiv=”count”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”infividual” evScope=”narrow”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”unscoped”/>

Annotationstructure:A=〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉 εE=〈m2,eat〉 εP1=〈m1,〈〈president,count〉,single,determinate〉〉,εP2=〈m3,〈〈pizza,count〉,2,indeterminate〉〉 LP1=〈εE,εP1,Agent,single,narrow〉,LP2=〈εE,εP2,Theme,individual,narrow〉 sc1=〈LP1,LP2,unscoped〉

Semantics: IQ(A)=IQ(LP1)∪IQ(LP2)=[x,Y⊆pizza|president0(x),|presidant0|=1, y∈Y→[E⊆eat|e∈E→[agent(e,x),theme(e,y)]]]

C7Quantificationinvolvingpartsofindividuals

Example(C31)illustratesthequantificationoverparticipantsetsthatcontainbothindividualobjectsandtheirparts(seeClause6.4),andthemeasurementofthesizeofsuchsets,discussedinB.3.1.

(C31) Marioatetwoandahalfpizzas.

Markables:m1=Mario,m2=ate,m3=twoandahalfpizzas,m4=pizzas

QuantML/XMLannotation:

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<entity xml:id=”x1” #target=”#m1” domain=”#x2” involvement=”single” definiteness=“det”/> <sourceDomain xml:id=”x2” target=”#m1” pred=”mario” indiv=”count”/> <event xml:id=”e1” target=”#m2” pred=”eat”/> <entity xml:id=”x3” #target=”#m3” domain=”#x4” involvement=”2.5” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”pizza” indiv=”cParts”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”countParts” evScope=”narrow”/> <scoping arg1=”#x1” arg2=”#x3” scopeRel=”unscoped”/>

Abstractsyntax:A=〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉 εE=〈m2,eat〉 εP1=〈m1,〈〈Mario,count〉,single,determinate〉〉,εP2=〈m3,〈〈pizza,count/parts〉,2.5,indeterminate〉〉 LP1=〈εE,εP1,Agent,single,narrow,free〉 ,LP2=〈εE,εP2,Theme,unspecific,narrow〉 sc1=〈LP1,LP2,unscoped〉

Semantics: IQ(〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉)=IQ(LP1)∪’IQ(LP2}= [x,Y⊆pizza^|mario0(x),|mario0|=1,x∈X→[Y||Y|*=2.5, y∈Y→[E⊆eat|e∈E→[agent(e,x),theme(e,y)]]]

C8Quantificationwithunspecificdistribution

Example(C41)illustratestheuseofquantificationswithunspecificdistributionforbothquantificationsoverparticipantsoccurring in the sentence: “theboys”maydo someof the carrying individuallyandsomecollectively,and“theboxes”maybecarriedindividuallyorasmembersofasetofboxes.(Nopartsof boys or parts of boxes are considered.) The most plausible interpretation of this sentence is acumulativeone,hencetherelativescopingofthetwoparticipantquantifiersis“dual”.

(C41)Theboyscarriedalltheboxesupstairs”.

Markables:m1=Theboys,m2=carried,m3=alltheboxes,m4=boxes Abstractsyntax:A=〈εE,{εP1,εP2,},{LP1,LP2},〈sc1}〉 εE=〈m3,carry〉 εP1=〈m1,〈〈m2,boy〉,all,det〉〉,εP2=〈m4,〈〈m5,box〉,all,det〉〉 εE=〈m3,read〉

εP1=〈m1,〈〈m2,student〉,all,det〉〉,εP2=〈m4,〈〈m5,paper〉,3,indet〉〉LP1=〈εE,εP1,Agent,individual,narrow〉,LP2=〈εE,εP2,Theme,unspecific,narrow〉sc1=〈LP1,LP2,dual〉

Participationlinkstructureinterpretations:

IQ(LP1)=[X=boy0|x∈X→[E⊆carry-up,y∈X*|x=y∨x∈y,e∈E→agent(e,y)]] IQ(LP2)=[Y=box0|y∈Y→[E⊆carry-up,z∈Y*|y=z∨y∈z,e∈E→theme(e,z)]]

The semantic interpretation of the annotation structure is represented by the DRS below, which.isobtainedinthesamewayasinexample(C6).

[X=boy0,Y=box0|x∈X*→[E⊆carry-up,y∈Y*|e∈E→agent(e,x),theme(e,y)], y∈Y*→[E⊆carry-up,x∈X*|e∈E→agent(e,x),theme(e,y)]]

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C9Quantificationwithunderspecifiedscoping

Inexample(C51)theQuantMLannotationisincomplete:thescopingofthequantificationexpressedby“a lecturer” relative to the other participant quantifications is not specified The semantics of theannotationinsuchacasecapturesthesemanticsofeachofthequantificationsseparatelyplusthescopeinformationavailable,andtakestheformofanunderspecifiedDRS.

(C51) Fifteenstudentssenttwoessaystoalecturer.

Markables:m1=Fifteenstudents,m2=students,m3=read,m4=twoessays,m5=essays,

QuantML/XMLannotation:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”15” definiteness=”indet’”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”student”/> <event xml:id=”e1” target=”#m3” pred=”send”/> <entity xml:id=”x3” target=”#m4” domain=”#x4” involvement=”2” definiteness=”indet”/> <sourceDomain xml:id=”x4” target=”#m5” pred=”essay”/> <entity xml:id=”x5” target=”#m6” domain=”#x4” involvement=”a” definiteness=”indet”/> <sourceDomain xml:id=”x6” target=”#m7” pred=”lecturer”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual”/> <participation event=”#e1” participant=”#x3” semRole=”theme” distr=”individual”/> <scoping arg1=”#x1” arg2=”#x2” scopeRel=”wider”/>

QuantMLannotationstructure:A=〈εE,{εP1,εP2,εP3},{LP1,LP2,LP3},{sc1}〉 εE=〈m3,send〉

εP1=〈m1,〈〈m2,〈student,count〉〉,15,indet〉〉,εP2=〈m4,〈〈m5,〈essay,count〉〉,2,indet〉〉εP3=〈m6,〈〈m7,〈lecturer,individual〉〉,a,indet〉〉LP1=〈εE,εP1,Agent,individual,narrow〉,LP2=〈εE,εP2,Theme,unspecific,narrow〉LP3=〈εE,εP2,Goal,individual,narrow〉sc1=〈LP1,LP2,wider〉

The annotation structure is interpreted as the collection of labelled participation structures plus thescopinginformation.

Semantics: IQ(A)=IQ(〈εE,{εP1,εP2,εP3},{LP1,LP2,LP3},{〈LP1,LP2,wider〉}〉)=〈{LP1’,LP2’,LP3’},{LP1’>LP2’}〉),where LP1’=IQ(LP1)=[X⊆student||X|=15,x∈X→[E⊆read|e∈E→agent(e,x)]]

LP2’=IQ(LP2)=[Y⊆essay||Y|=3,y∈Y→[E⊆read|e∈E→theme(e,y)]]

LP3’=IQ(LP3)=[Z⊆lecturer|z∈Z→[E⊆read|e∈E→goal(e,z)]]

C10Quantificationandnegation

(C61) Nobodycalled,interpretedas“Itisnotthecasethatsomebodycalled”.

Markables:m1=Nobody,m2=called

QuantML/XMLannotation: <entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”some” definiteness=”indet”/> <sourceDomain xml:id=”x2” target=”#m1” indiv=”count” pred=”person”/>

<event xml:id=”e1” target=”#m2” pred=”call”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” polarity=”neg-wide”/>

Abstractsyntax:A=〈εE,{εP1},{LεP1},{}〉 εE=〈m2,call〉

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εP1=〈m1,〈m1,〈person,count〉,some,indet〉〉 LP1=〈εE,εP1,Agent,individual,narrow,nex,neg-wide〉

Annotationinterpretation: IQ(εP1)=[X|x∈X→person(x)]

IQ(εE)=[E|e∈E→call(e)]

Using(B30)and(B34):

IQ(A)=∼IQ(〈εE,εP1,Agent,individual,narrow,nex,pos〉)= ∼[X,⊆person,E⊆call|x∈X→[e∈E|agent(e,x)]] (C62) Thegirlsdidnotsmile,interpretedas“Noneofthegirlssmiled”(narrow-scopenegation).

Markables:m1=Thegirls,m2=girls,m3=smile

QuantML/XMLannotation:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”all” definiteness=”def’”/>

<sourceDomain xml:id=”x2” target=”#m2” pred=”girl”/> <event xml:id=”e1” target=”#m3” pred=”smile”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” eventScope=”narrow” polarity=”neg-narrow”/>

Abstractsyntax:A=〈εE,{εP1},{LP1},{}〉εP1=〈m1,〈〈m2,〈girl,count〉〉,all,det〉〉,εE=〈m3,smile〉,LP1=〈εE,εP1,Agent,individual,narrow,neg-narrow〉

Semantics: IQ(A)=IQ(〈εE,{εP1},{LP1},{}〉)=IQ(LP1)=IQ(〈εE,εP1,Agent,individual,narrow,neg-narrow〉)= =IQ(〈smile〉,〈〈girl,count〉,all,det〉,Agent,individual,narrow,neg-narrow〉)= =[X|x∈X↔girl0(x)]∪([X|x∈X→¬[E|e∈E→agent(e,x)]]⊕n[E|e∈E→ smile(e)])= =[X=girl0|x∈X→¬[E⊆smile|e∈E→agent(e,x)]]

C11Complexdomains

(C71) Alexsoldthetwoancientbooks.

Markables: m1=Alex, m2=sold, m3=the two ancient books, m4=ancient books, m5=ancient, m6=books

QuantML/XMLannotation:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”single” definiteness=”det”/>

<sourceDomain xml:id=”x2” target=”#m1” pred=”alex”/> <event xml:id=”e1” target=”#m2” pred=”sell”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”single” evScope=”free”/>

<entity xml:id=”x3” target=”#m3” domain=”#x4” involvement=”all” definiteness=”det’” size=”2”/> <qDomain xml:id=”x4” target=”#m4” source=”#x5” restrictions=”#r1”/>

<sourceDomain xml:id=”x5” target=”#m6” individuation=”count” pred=”book”/> <adjMod xml:id=”r1” target=”#m5” distr=”individual” pred=”ancient”/>

<scoping arg1=”#x1” arg2=”#x3” scopeRel=”unscoped”/>

Abstractsyntax:A=〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉 εE=〈m2,sell〉

εP1=〈m1,〈〈m1,〈Alex,count〉〉,single,det〉〉εP2=〈m3,〈〈〈m6,〈book,count〉〉,〈m5,〈ancient,individual〉〉〉,all,det,2〉〉

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LP1=〈εE,εP1,Agent,individual,narrow〉,LP2=〈εE,εP2,Theme,individual,narrow〉sc1=〈LP1,,LP2,unscoped〉

Semantics: IQ(〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉=IQ(LP1)∪’IQ(LP2) =IQ(〈εE,εP1,Agent,individual,free,positive〉)∪’ IQ(〈εE,εP2,Theme,individual,narrow,positive〉) =IQ(〈sell〉,〈〈〈Alex,count〉,single,det〉,Agent,individual,free,positive〉)∪ IQ(〈sell〉,〈〈〈〈m6,〈book,count〉〉,〈m5,〈ancient,individual〉〉〉,count〉,all,det,2〉, Theme,individual,narrow,positive〉) =[x,E⊆sell|alex0(x),|alex0|=1,e∈E→agent(e,x)]∪’ [Y⊆book0|Y|=2,y∈Y→[ancient(y),E⊆sell|e∈E→theme(e,y)]] =[x,Y⊆book0|alex0(x),|alex0|=1,|Y|=2, y∈Y→[E⊆sell|ancient(y),e∈E→[agent(e,x),theme(e,y)]]]

C12Possessives

(C81) EverybodyreadtwoofChomsky’sbooks.

Markables: m1=everybody, m2=read, m3=two of Chomsky’s works, m4=Chomsky, m5=’s m6=books

QuantMLannotation:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”all” definiteness=”det”/>

<sourceDomain xml:id=”x2” target=”#m1” individuation=”count” pred=”person”/> <event xml:id=”e1” target=”#m2” pred=”read”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” eventScope=”narrow”/>

<entity xml:id=”x3” target=”#m3” domain=”#x4” involvement=”2” definiteness=”indet” /> <qDomain xml:id=”x4” target=”#m4” source=”#x5” restrictions=”#r1”/>

<sourceDomain xml:id=”x5” target=”#m6” individuation=”count” pred=”book”/> <possRestr xml:id=”r1” target=”#m5” distr=”individual” possessor=”#x6” linking=”linear”/> <entity xml:id=”x6” target=”#m4” domain=”#x7” involvement=”single” definiteness=”det”/> <sourceDomain xml:id=”x7” target=”#m4” pred=”Chomsky”/> <scoping arg1=”#x3” arg2=”x1” scopeRel=”wider”/>

Abstractsyntax:A=〈εE,{εP1,εP2,εP3},{LP1,LP2},{sc1}〉 εE=〈m2,read〉,

εP1=〈m1,〈〈m1,〈person,count〉〉,all,det〉〉εP2=〈m3,〈〈〈m5,〈book,count〉〉,〈m4,〈Poss,εP3,individual,linear〉〉〉,2,indef〉〉〉εP3=〈m4,〈〈m4,〈Chomsky,count〉〉,single,det〉〉LP1=〈εE,εP1,Agent,individual,narrow〉,LP2=〈εE,εP2,Theme,individual,narrow〉sc1=〈εP2,εP1,wider〉

ThesemanticinterpretationiscomputedaccordingtoAnnexBsectionsB3.4.4andB3.4.5: IQ(εP1)=[X|x∈X↔person0(x)] IQ(εP3)=[z|chomsky0(z),|chomsky0|=1] IQ(Poss,IQ(εP3))=INA0((IQ(εP3,),λu.λv.Poss(v,u))=λz.[x|chomsky0(x),|chomsky0|=1,Poss(x,z)] IQ(εP2)=[Y⊆book||Y|=2,y∈Y→IQ(Poss,IQ(εP1))(y)] =[Y⊆book||Y|=2,y∈Y→λz.[x|chomsky0(x),|chomsky0|=1,Poss(x,z)](y)] =[Y⊆book||Y|=2,y∈Y→[x|chomsky0(x),|chomsky0|=1,Poss(x,y)]]

IQ(〈εE,{εP1,εP2},{LP1,LP2},{sc1}〉=IQ(LP2)∪*IQ(LP1) =IQ(〈read,〈〈〈m6,〈ook,count〉〉,

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〈〈〈m3,〈〈Poss,〈〈Chomsky,count〉,single,det〉,individual,linear〉〉〉, Theme,individual,narrow,positive〉)∪* IQ(〈read,〈〈〈m1,〈person,count〉,all,det〉〉,Agent,individual,narrow,positive〉) =[Y⊆book||Y|=2,y∈Y→ [z,E⊆read|chomsky0(z),|chomsky0|=1,Poss(z,y),e∈E→theme(e,y]]∪*

[X=person0|x∈X→[E⊆read|e∈E→agent(e,x)] =[Y⊆book,||Y|=2,y∈Y→[z,X=person0|chomsky0(z),|chomsky0|=1,Poss(z,y), x∈X→[E⊆read|e∈E→[agent(e,z),theme(e,y)]]]]

C13Exhaustivequantification

(C91) (Only)TWOdogsbarked.

Markables:m1=Twodogs,m2=dogs,m3=barked

QuantML/XMLannotation:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”two” definiteness=”indet”/>

<sourceDomain xml:id=”x2” target=”#m1” pred=”dog”/> <event xml:id=”e1” target=”#m2” pred=”bark”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow” exhaustivity=”exhaustive”/>

Abstractsyntax:A=〈εE,{εP1},{LP1},{}〉,with:

εE=〈m3,bark〉,εP1=〈m1,〈〈m2,〈dog,count〉〉,two,det〉〉LP1=〈εE,εP1,Agent,individual,narrow,exhaustive,positive〉

Semantics:IQ(〈εE,{εP1},{LP1},{}〉=IQ(LP1)

=IQ(〈εE,εP1,Agent,individual,narrow,exhaustive,positive〉) =[X⊆dog0||X|=2,x∈X↔[E⊆bark|e∈E→agent(e,x)]]]

(C92) (Only)TWOdogsdidnotbark.(Stressed“Two”.)

Markables:m1=Twodogs,m2=dogs,m3=barked

QuantML/XMLannotation:<entity xml:id=”x1” target=”#m1” domain=”#x2” involvement=”two” definiteness=”indet”/>

<sourceDomain xml:id=”x2” target=”#m1” pred=”dog”/> <event xml:id=”e1” target=”#m2” pred=”bark”/> <participation event=”#e1” participant=”#x1” semRole=”agent” distr=”individual” evScope=”narrow”/>

Abstractsyntax:A=〈εE,{εP1},{LP1},{}〉,with: εE=〈m3,bark〉,

εP1=〈m1,〈〈m2,〈dog,count〉〉,two,det〉〉LP1=〈εE,εP1,Agent,individual,narrow,exhaustive,negative〉

Semantics:IQ(〈εE,{εP1},{LP1},{}〉=IQ(LP1)

=IQ(〈εE,εP1,Agent,individual,narrow,exhaustive,neg-narrow〉) =[X⊆dog0||X|=2,x∈X→¬[E⊆bark|e∈E→agent(e,x)]]]

(C93) Atmosttwodogsbarked.

Markables:m1=Atmosttwodogs,m2=dogs,m3=barked

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Annotationstructure:α=〈εE,{εP1},{LP1},{}〉

Semantics:IQ(〈εE,{εP1},{LP1},{}〉=IQ(LP1)=IQ(〈εE,εP1,Agent,individual,narrow,exhaustive,positive〉)

=[Xdog,||X|<3,x∈X↔[dog(x),[E⊆bark|e∈E→agent(e,x)]]]

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