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Lexical-Functional Grammar
A Formal System for Grammatical Representation
Kaplan and Bresnan, 1982
Erin FitzgeraldNLP Reading GroupOctober 18, 2006
10/18/2006Lexical-Functional Grammars
LFG History Developed by J. Bresnan and R. Kaplan in
early 1970’s Believed Chomskyan approach doesn’t
model psychological reality of language Other motivations:
Supported in wider variety of languages than other formalisms (ex nonconfigurational languages with ~free word order/ case marks)
Movement paradoxes: That he was sick we talked about __ for days. *We talked about that he was sick for days. We talked about the fact that he was sick for days.
“Syntax is not just structure-based”
10/18/2006Lexical-Functional Grammars
How it’s different from Chomsky X’ Requires a higher level of mathematical precision Subject, Object, etc considered primitives, not
defined from positions in tree Empty categories and funct. projections avoided No movement Unification-based Levels of representation not strictly derived from
each other Not assumed that phonological, etc contents are
derived from syntactic structure in any way.
10/18/2006Lexical-Functional Grammars
How it’s different from HPSG No hierarchical classification to deal with
vertical and horizontal redundancy LFG focuses on the processing and
psychological reality of language HPSG combines all syntactic, phonological,
etc information into a single level
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Generative Power of LFG Not as powerful as general rewriting
system or Turing Machine (LF languages are context-sensitive)
But, greater generative capacity than CFG (lower bound)
Allows anbncn, ωω non-CF languages Sources of generative power:
Functional Composition: Helps encode range of tree properties
Equality Predicate: Enforces a match between properties encoded from different nodes
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Correspondence Between Levels C(onstituent)-structure: varies across
languages F(unctional)-structure: Universal properties
Structures aren’t isomorphic, but related by different correspondences
string c-structure f-structure
discourse structure
semantic structure
φ σπ
δ?
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C-Structure Composed of
Terminal strings Syntactic categories Dominance/precedence relations
Expressed through phrase structure trees Determined by CF phrase structure rules Regulated by a version of X’ theory
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C-Structure
S
NP VP
DET N
NPVNDET
DET N
NP
a girl handed the baby a toy
S NP VP (↑SUBJ)=↓ ↑=↓
NP DET N
VP V NP NP (↑OBJ)=↓ (↑OBJ2)=↓
Immediate Domination Metavariables:↑: mother f-structure
↓: self f-structure
Immediate Domination Metavariables:↑: mother f-structure
↓: self f-structure
i.e. head
Set specifiers:
S S CONJ S ↓є↑ ↓є↑
Adjuncts also use set indicators
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F-structure Composed of
Grammatical function names Semantic forms Feature symbols
Models internal structure of language where grammatical relations are represented
Formalized through matrix of attributes, viewable as mathematical function
Lexical schemata determine content of lexical items
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F-structureSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
10/18/2006Lexical-Functional Grammars
F-structure: Attributes and ValuesSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
10/18/2006Lexical-Functional Grammars
F-structure: Attributes and ValuesSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
10/18/2006Lexical-Functional Grammars
F-structure: PrimitivesSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
Symbols
Semantic Forms
Embedded Structures
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F-structure: Input to Semantic InterpSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
Agent Theme Goal
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C-Structure to F-Description
S
NP VP
DET N
NPVNDET
DET N
NP
a girl handed the baby a toy
S NP VP (↑SUBJ)=↓ ↑=↓
NP DET N
VP V NP NP (↑OBJ)=↓ (↑OBJ2)=↓
a: DET, (↑SPEC) = A
girl: N, (↑NUM) = SG
(↑NUM) = SG
(↑PRED) = ‘GIRL’
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C-Structure to F-Description
S
the baby a toy
NP; (↑SUBJ)=↓ VP; ↑=↓
(↑OBJ) = ↓
NP(↑NUM) = SG
(↑PRED) = ‘GIRL’
N
(↑TENSE) = PAST(↑PRED) = ‘HAND<>’
V(↑SPEC) = A
(↑NUM) = SG
DET
(↑OBJ) = ↓
NP
(↑SPEC) = ↓
DET(↑NUM) = SG
(↑PRED) = BABY
N
(↑SPEC) = ↓ (↑NUM) = SG
DET
(↑NUM) = SG(↑PRED) =
TOY
N
a girl handed
f1
f2
f4 f5
f3
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f3 TENSE) = past
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
Etc.
f1= f3 (f1 SUBJ) = f2
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F-Description to F-Structure Locate Operator
Obtain value for designator Merge Operator (*Unify*)
If left and right values exist,check if values are equal
Else, create new entity(if properties are compatible)
Similar to taking the union oftwo sets (if conflicts don’t exist)
Start clean; build until full f-description analyzed
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND<>’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
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F-structuref1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
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F-structure: equationsSUBJ ---------- f1= f3
(f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
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F-structure: equationsSUBJ ----------
OBJ ----------
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
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F-structure: equationsSUBJ ----------
OBJ ----------
OBJ2 ----------
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
f5
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F-structure: lexically derived eqnsSUBJ SPEC -------
OBJ ----------
OBJ2 ----------
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
f5
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F-structure: lexically derived eqnsSUBJ SPEC A
OBJ ----------
OBJ2 ----------
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
f5
MERGECONFIRMED
10/18/2006Lexical-Functional Grammars
F-structure: lexically derived eqnsSUBJ SPEC A
NUM SG
PRED ‘GIRL’
OBJ ----------
OBJ2 ----------
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
f5
10/18/2006Lexical-Functional Grammars
F-structure: lexically derived eqnsSUBJ SPEC A
NUM SG
PRED ‘GIRL’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 ----------
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
f5
10/18/2006Lexical-Functional Grammars
F-structure: lexically derived eqnsSUBJ SPEC A
NUM SG
PRED ‘GIRL’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f3
f2
f4
f5
MERGECONFIRMED
10/18/2006Lexical-Functional Grammars
F-structure: lexically derived eqnsSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f2
f4
f5
10/18/2006Lexical-Functional Grammars
F-structure: lexically derived eqnsSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) =‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f2
f4
f5
10/18/2006Lexical-Functional Grammars
A Unique Solution?SUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
OBJ SPEC THE
NUM SG
PRED ‘BABY’
OBJ2 SPEC A
NUM SG
PRED ‘TOY’
TONE SOOTHINGLY
f1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5
(f2 SPEC) = A(f2 NUM) = SG
(f2 NUM) = SG(f2 PRED) = ‘GIRL’
(f3 TENSE) = PAST(f3 PRED) =‘HAND...’
(f4 SPEC) = THE
(f4 NUM) = SG(f4 PRED) = ‘BABY’
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = SG(f5 PRED) = ‘TOY’
f1
f2
f4
f5
Prefer minimal solution
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Principles Regulating F-Structures Uniqueness:
Every attribute has a unique value Completeness:
Every function designated by a PRED must be present in the f-structure of that PRED
Coherence: (converse) Every argument in an f-structure must be
designated by a PRED
A string is grammatical only if it is assigned a complete and coherent f-structure, and its f-struct is consistent and determinate.
10/18/2006Lexical-Functional Grammars
Principles Regulating F-Structures Uniqueness:
Every attribute has a unique value
Note: Uniqueness doesn’t prevent different attributes from sharing values
A girl handed the baby a toys.
(f5 SPEC) = A(f5 NUM) = SG
(f5 NUM) = PL(f5 PRED) = ‘TOYS’
10/18/2006Lexical-Functional Grammars
Principles Regulating F-Structures Completeness:
Every function designated by a PRED must be present in the f-structure of that PRED
An f-structure is locally complete iff it contains all governable grammatical functions that its predicate governs.
A girl handed.
PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’
Lexical item requires governed functions OBJ and OBJ2
10/18/2006Lexical-Functional Grammars
Principles Regulating F-Structures Coherence:
Every argument in an f-structure must be designated by a PRED
An f-structure is locally coherent iff all governable functions are governed.
The girl fell the apple the dog.
PRED ‘FELL<(↑ SUBJ)>’
10/18/2006Lexical-Functional Grammars
Principles Regulating F-Structures Uniqueness:
Every attribute has a unique value Completeness:
Every function designated by a PRED must be present in the f-structure of that PRED
Coherence: (converse) Every argument in an f-structure must be
designated by a PRED
A string is grammatical only if it is assigned a complete and coherent f-structure, and its f-struct is consistent and determinate.
Exception: Adjunct grammatical functions are not specified in PRED and no reqmt of mutual syntactic compatibility, so excluded from Uniqueness and Coherence Conditions
Exception: Adjunct grammatical functions are not specified in PRED and no reqmt of mutual syntactic compatibility, so excluded from Uniqueness and Coherence Conditions
10/18/2006Lexical-Functional Grammars
Changing structure, but not meaning
S
NP VP
DET N
NPVNDET
DET N
NP
a girl handed a toy the baby
VP V NP NP PP* (↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓
PP P NP (↑OBJ)=↓
NP DET N
S NP VP (↑SUBJ)=↓ ↑=↓
PP
to
P
10/18/2006Lexical-Functional Grammars
Changing structure, but not meaningSUBJ SPEC A
NUM SG
PRED ‘GIRL’
TENSE PAST
PRED ‘HAND<(↑ SUBJ)(↑ OBJ)(↑ TO OBJ)>’
OBJ SPEC A
NUM SG
PRED ‘TOY’
TO PCASE TO
OBJ SPEC
NUM
PRED
THE
SGSG
‘BABY’
Dativizing Rule:
(↑ OBJ2) (↑ OBJ)
(↑ OBJ) (↑ TO OBJ)
From (↑(↓PCASE))=↓
10/18/2006Lexical-Functional Grammars
Defining vs. Constraining Schema Consider:
The girl is handing the baby the toy.
*The girl is hands the baby the toy.
VP V NP NP PP* VP’ (↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ (↑VCOMP)=↓
VP’ (to) VP ↑=↓
is: V, (↑ TENSE) = PRESENT(↑ SUBJ NUM) = SG(↑ PRED) = ‘PROG<(↑ VCOMP)>’(↑ VCOMP PARTICIPLE) = PRESENT(↑ VCOMP SUBJ) = (↑ SUBJ)
(↑ VCOMP PARTICIPLE) =c PRESENT
Single, progressive arg
Functional control
Constraint Schema
10/18/2006Lexical-Functional Grammars
Raising Verbs The girl persuaded the baby to go.
The girl persuaded the baby that the baby (should) go.
Link via co-indexing, or arguments assumed distinct
VP V NP NP PP* VP’ (↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ (↑VCOMP)=↓
VP’ to VP (↑TO) = ↓ ↑=↓ (↑INF)= ↓ ↑=↓
persuaded: V, (↑ TENSE) = PAST(↑ PRED) = ‘PERSUADE<(↑SUBJ)(↑OBJ)(↑VCOMP)>’(↑ VCOMP TO) =c +(↑ VCOMP SUBJ) = (↑ OBJ)
10/18/2006Lexical-Functional Grammars
Raising Verbs The girl promised the baby to go.
The girl promised the baby that the girl (should) go.
VP V NP NP PP* VP’ (↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ (↑VCOMP)=↓
VP’ to VP (↑TO) = ↓ ↑=↓ (↑INF)= ↓ ↑=↓
promised: V, (↑ TENSE) = PAST(↑ PRED) = ‘PERSUADE<(↑SUBJ)(↑OBJ)(↑VCOMP)>’(↑ VCOMP TO) =c +(↑ VCOMP SUBJ) = (↑ SUBJ)
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(↑ PARTICLE) = PASSIVE(↑ PRED) = ‘PROMISE<(↑BY OBJ)(↑SUBJ)(↑VCOMP)>’(↑ VCOMP TO) =c +(↑ VCOMP SUBJ) = (↑ BY OBJ)
Raising Verbs: Passivization The baby was persuaded to go by the girl. *The baby was promised to go by the girl.
persuaded: V,
promised: V,
(↑ PARTICLE) = PASSIVE(↑ PRED) = ‘PERSUADE<(↑BY OBJ)(↑SUBJ)(↑VCOMP)>’(↑ VCOMP TO) =c +(↑ VCOMP SUBJ) = (↑ SUBJ)
Doesn’t conform to Fn Control Restrictions
10/18/2006Lexical-Functional Grammars
F-Level Distinct from Semantics No quantifier or VP scope specification Raising vs. Equi Verbs (All have semantic role)
The girl persuaded the baby to go. The girl expected the baby to go.Same f-structure, very different semantics
10/18/2006Lexical-Functional Grammars
Long Distance Dependencies The girl wondered [who the baby saw __].
Instance of constituent control Decompose into chain of functional
identities
10/18/2006Lexical-Functional Grammars
Bound Domination Metavariables Aim to provide a formal mechanism to
represent long-dist constituent dependencies No unmotivated grammatical functions or
features Allow unbounded # of controllees for single
constituent Succinctly show generalizations
10/18/2006Lexical-Functional Grammars
C-Structure for Long-Distance Dependencies
the baby saw
(↑Q-FOCUS)=↓↓=▼
NP
↑=↓ S
(↑OBJ) = ↓
NP(↑PRED) = WHO
N↑= ↓
VP
(↑SPEC) = ↓
DET(↑NUM) = SG
(↑PRED) = BABY
N
(↑TENSE) = PAST (↑PRED) = ‘SEE<>’
V
(↑OBJ) = ↓
NP
who
f1
(↑SCOMP)=↓ S’
e
↑=▲
NP
Bounded Domination Metavariables:▲: bounded above (longer path)
▼: bounding node
Bounded Domination Metavariables:▲: bounded above (longer path)
▼: bounding node
10/18/2006Lexical-Functional Grammars
More Precisely She’ll grow that tall/*height. She’ll reach that *tall/height. The girl wondered how tall she would
grow/*reach ___. The girl wondered what height she would
*grow/reach ___.
These examples show that some bounding should be further constrained to specify POS
Follow by AP
Follow by NP
(e: ↓=▼AP)
(e: ↓=▼NP)
Thanks!
10/18/2006Lexical-Functional Grammars
More (unfinished) slides
10/18/2006Lexical-Functional Grammars
Bounding Convention A node M belongs to a control domain with
root node R iff R dominates M and there are no bounding nodes on the path from M up to but not including R
Pg 245
10/18/2006Lexical-Functional Grammars
Unification with Complex Expressions See packet pg 10/22 Outside-in
Combine feature structures at their roots and work top-down
Inside-out Begin with two distinct f-structs sharing a
substructure, and recursively combine up Req’d for analyses like topicalization and
anaphoric binding
10/18/2006Lexical-Functional Grammars
Subject-Auxiliary Inversion in LFG Pg 228
A girl is handing the baby a toy. Is a girl handing the baby a toy? *Is a girl is handing the baby a toy.
Prevented by “distinctiveness of semantic form instances”
10/18/2006Lexical-Functional Grammars
Generative Power of LFG A c-structure derivation is valid iff
No category appears twice in non-branching dominance chain
No NT exhaustively dominates an optionality e At least one lexical item (or controlled e)
appears between two optionality e’s derived by same rule element.
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Proper Instantiation Pg 246