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Lexical-Functional Grammar. A Formal System for Grammatical Representation Kaplan and Bresnan, 1982 Erin Fitzgerald NLP Reading Group October 18, 2006. LFG History. “Syntax is not just structure-based”. Developed by J. Bresnan and R. Kaplan in early 1970’s

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Lexical functional grammar

Lexical-Functional Grammar

A Formal System for Grammatical Representation

Kaplan and Bresnan, 1982

Erin Fitzgerald

NLP Reading Group

October 18, 2006


Lfg history

LFG History

“Syntax is not just structure-based”

  • 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 aboutthat he was sick for days.

      • We talked aboutthe factthat he was sick for days.

Lexical-Functional Grammars


How it s different from chomsky x

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.

Lexical-Functional Grammars


How it s different from hpsg

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

Lexical-Functional Grammars


Generative power of lfg

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

Lexical-Functional Grammars


Correspondence between levels

Correspondence Between Levels

  • C(onstituent)-structure: varies across languages

  • F(unctional)-structure: Universal properties

  • Structures aren’t isomorphic, but related by different correspondences

semantic structure

σ

π

φ

?

δ

string

c-structure

f-structure

discourse structure

Lexical-Functional Grammars


C structure

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

Lexical-Functional Grammars


C structure1

C-Structure

S  NP VP(↑SUBJ)=↓ ↑=↓

NP  DET N

VP  V NP NP(↑OBJ)=↓ (↑OBJ2)=↓

i.e. head

S

NP

VP

DET

N

V

NP

NP

Set specifiers:

S  S CONJ S↓є↑ ↓є↑

Adjuncts also use set indicators

DET

N

DET

N

a

girl

handed

the

baby

a

toy

Immediate Domination Metavariables:

↑: mother f-structure

↓: self f-structure

Lexical-Functional Grammars


F structure

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

Lexical-Functional Grammars


F structure1

F-structure

Lexical-Functional Grammars


F structure attributes and values

F-structure: Attributes and Values

Lexical-Functional Grammars


F structure attributes and values1

F-structure: Attributes and Values

Lexical-Functional Grammars


F structure primitives

F-structure: Primitives

Symbols

Semantic Forms

Embedded Structures

Lexical-Functional Grammars


F structure input to semantic interp

F-structure: Input to Semantic Interp

Agent

Theme

Goal

Lexical-Functional Grammars


C structure to f description

C-Structure to F-Description

S  NP VP(↑SUBJ)=↓ ↑=↓

NP  DET N

VP  V NP NP(↑OBJ)=↓ (↑OBJ2)=↓

S

NP

VP

DET

N

V

NP

NP

a: DET,(↑SPEC) = A

girl: N,(↑NUM) = SG

(↑NUM) = SG

DET

N

DET

N

(↑PRED) = ‘GIRL’

a

girl

handed

the

baby

a

toy

Lexical-Functional Grammars


C structure to f description1

C-Structure to F-Description

S

(f1 SUBJ) = f2

f1= f3

f1

NP; (↑SUBJ)=↓

VP; ↑=↓

f2

f3

(↑NUM) = SG(↑PRED) = ‘GIRL’

N

(↑TENSE) = PAST(↑PRED) = ‘HAND<>’

V

(↑OBJ) = ↓

NP

(↑OBJ) = ↓

NP

(↑SPEC) = A(↑NUM) = SG

DET

f4

f5

(f3 TENSE) = past

Etc.

(↑SPEC) = ↓

DET

(↑NUM) = SG(↑PRED) = BABY

N

(↑SPEC) = ↓(↑NUM) = SG

DET

(↑NUM) = SG(↑PRED) = TOY

N

(f2 SPEC) = A(f2 NUM) = SG

(f2 NUM) = SG(f2 PRED) = ‘GIRL’

(f4 SPEC) = THE

(f4 NUM) = SG(f4 PRED) = ‘BABY’

toy

a

girl

handed

the

baby

a

Lexical-Functional Grammars


F description to f structure

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’

Lexical-Functional Grammars


F structure2

F-structure

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

Lexical-Functional Grammars


F structure equations

F-structure: equations

f2

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

Lexical-Functional Grammars


F structure equations1

F-structure: equations

f2

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’

f4

f1

f3

Lexical-Functional Grammars


F structure equations2

F-structure: equations

f2

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’

f4

f5

f1

f3

Lexical-Functional Grammars


F structure lexically derived eqns

F-structure: lexically derived eqns

f2

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’

f4

f5

f1

f3

Lexical-Functional Grammars


F structure lexically derived eqns1

F-structure: lexically derived eqns

f2

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’

MERGECONFIRMED

f4

f5

f1

f3

Lexical-Functional Grammars


F structure lexically derived eqns2

F-structure: lexically derived eqns

f2

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’

f4

f5

f1

f3

Lexical-Functional Grammars


F structure lexically derived eqns3

F-structure: lexically derived eqns

f2

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’

f4

f5

f1

f3

Lexical-Functional Grammars


F structure lexically derived eqns4

F-structure: lexically derived eqns

f2

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’

f4

f5

f1

f3

MERGECONFIRMED

Lexical-Functional Grammars


F structure lexically derived eqns5

F-structure: lexically derived eqns

f2

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’

f4

f5

f1

Lexical-Functional Grammars


F structure lexically derived eqns6

F-structure: lexically derived eqns

f2

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’

f4

f5

f1

Lexical-Functional Grammars


A unique solution

A Unique Solution?

f2

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’

f4

f5

f1

Prefer minimal solution

Lexical-Functional Grammars


Principles regulating f structures

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.

Lexical-Functional Grammars


Principles regulating f structures1

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’

Lexical-Functional Grammars


Principles regulating f structures2

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

Lexical-Functional Grammars


Principles regulating f structures3

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)>’

Lexical-Functional Grammars


Principles regulating f structures4

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

Lexical-Functional Grammars


Changing structure but not meaning

Changing structure, but not meaning

VP  V NP NP PP*(↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓

PP  P NP (↑OBJ)=↓

NP  DET N

S  NP VP(↑SUBJ)=↓ ↑=↓

S

NP

VP

DET

N

V

NP

PP

DET

N

P

NP

DET

N

a

girl

handed

a

toy

to

the

baby

Lexical-Functional Grammars


Changing structure but not meaning1

Changing structure, but not meaning

Dativizing Rule:

(↑OBJ2)  (↑ OBJ)

(↑ OBJ)  (↑ TO OBJ)

From (↑(↓PCASE))=↓

THE

SG

SG

‘BABY’

Lexical-Functional Grammars


Defining vs constraining schema

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)

Single, progressive arg

Functional control

(↑ VCOMP PARTICIPLE) =c PRESENT

Lexical-Functional Grammars

Constraint Schema


Raising verbs

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)

Lexical-Functional Grammars


Raising verbs1

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)

Lexical-Functional Grammars


Raising verbs passivization

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)

(↑ PARTICLE) = PASSIVE

(↑ PRED) = ‘PROMISE<(↑BY OBJ)(↑SUBJ)(↑VCOMP)>’

(↑ VCOMP TO) =c +

(↑ VCOMP SUBJ) = (↑ BY OBJ)

Doesn’t conform to Fn Control Restrictions

Lexical-Functional Grammars


F level distinct from semantics

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

Lexical-Functional Grammars


Long distance dependencies

Long Distance Dependencies

  • The girl wondered [who the baby saw __].

  • Instance of constituent control

  • Decompose into chain of functional identities

Lexical-Functional Grammars


Bound domination metavariables

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

Lexical-Functional Grammars


C structure for long distance dependencies

C-Structure for Long-Distance Dependencies

Bounded Domination Metavariables:

▲: bounded above (longer path)

▼: bounding node

(↑SCOMP)=↓ S’

f1

(↑Q-FOCUS)=↓↓=▼NP

↑=↓S

(↑PRED) = WHO

N

(↑OBJ) = ↓

NP

↑= ↓

VP

(↑SPEC) = ↓

DET

(↑NUM) = SG(↑PRED) = BABY

N

(↑TENSE) = PAST(↑PRED) = ‘SEE<>’

V

(↑OBJ) = ↓ NP

↑=▲ NP

who

the

baby

saw

e

Lexical-Functional Grammars


More precisely

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)

Lexical-Functional Grammars


Thanks

Thanks!


More unfinished slides

More (unfinished) slides

Lexical-Functional Grammars


Bounding convention

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

Lexical-Functional Grammars


Unification with complex expressions

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

Lexical-Functional Grammars


Subject auxiliary inversion in lfg

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”

Lexical-Functional Grammars


Generative power of lfg1

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.

Lexical-Functional Grammars


Proper instantiation

Proper Instantiation

  • Pg 246

Lexical-Functional Grammars


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