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”

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.

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

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

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

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

C-Structure

NPVNDET

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

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

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’

F-structure: Attributes and ValuesSUBJ SPEC A

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

F-structure: Attributes and ValuesSUBJ SPEC A

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

F-structure: PrimitivesSUBJ SPEC A

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

Symbols

Semantic Forms

Embedded Structures

F-structure: Input to Semantic InterpSUBJ SPEC A

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

Agent Theme Goal

C-Structure to F-Description

NPVNDET

a girl handed the baby a toy

NP DET N

VP V NP NP (↑OBJ)=↓ (↑OBJ2)=↓

a: DET, (↑SPEC) = A

girl: N, (↑NUM) = SG

(↑NUM) = SG

(↑PRED) = ‘GIRL’

C-Structure to F-Description

the baby a toy

NP; (↑SUBJ)=↓ VP; ↑=↓

(↑OBJ) = ↓

NP(↑NUM) = SG

(↑PRED) = ‘GIRL’

(↑TENSE) = PAST(↑PRED) = ‘HAND<>’

V(↑SPEC) = A

(↑NUM) = SG

(↑OBJ) = ↓

(↑SPEC) = ↓

DET(↑NUM) = SG

(↑PRED) = BABY

(↑SPEC) = ↓ (↑NUM) = SG

(↑NUM) = SG(↑PRED) =

a girl handed

(f4 SPEC) = THE

(f4 NUM) = SG(f4 PRED) = ‘BABY’

(f3 TENSE) = past

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

(f2 NUM) = SG(f2 PRED) = ‘GIRL’

f1= f3 (f1 SUBJ) = f2

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

(f3 TENSE) = PAST(f3 PRED) = ‘HAND<>’

(f4 SPEC) = THE

(f5 NUM) = SG(f5 PRED) = ‘TOY’

F-structuref1= f3 (f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5

(f3 TENSE) = PAST(f3 PRED) = ‘HAND...’

(f4 SPEC) = THE

F-structure: equationsSUBJ ---------- f1= f3

(f1 SUBJ) = f2 (f3 OBJ) = f4 (f3 OBJ2) = f5

(f4 SPEC) = THE

F-structure: equationsSUBJ ----------

OBJ ----------

(f4 SPEC) = THE

F-structure: equationsSUBJ ----------

OBJ ----------

OBJ2 ----------

(f4 SPEC) = THE

F-structure: lexically derived eqnsSUBJ SPEC -------

OBJ ----------

OBJ2 ----------

(f4 SPEC) = THE

F-structure: lexically derived eqnsSUBJ SPEC A

OBJ ----------

OBJ2 ----------

(f4 SPEC) = THE

MERGECONFIRMED

NUM SG

PRED ‘GIRL’

OBJ ----------

OBJ2 ----------

(f4 SPEC) = THE

NUM SG

PRED ‘GIRL’

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 ----------

(f4 SPEC) = THE

NUM SG

PRED ‘GIRL’

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

(f4 SPEC) = THE

MERGECONFIRMED

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

(f4 SPEC) = THE

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

(f3 TENSE) = PAST(f3 PRED) =‘HAND...’

(f4 SPEC) = THE

A Unique Solution?SUBJ SPEC A

NUM SG

PRED ‘GIRL’

TENSE PAST

OBJ SPEC THE

NUM SG

PRED ‘BABY’

OBJ2 SPEC A

NUM SG

PRED ‘TOY’

TONE SOOTHINGLY

(f3 TENSE) = PAST(f3 PRED) =‘HAND...’

(f4 SPEC) = THE

Prefer minimal solution

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.

Every attribute has a unique value

Note: Uniqueness doesn’t prevent different attributes from sharing values

A girl handed the baby a toys.

(f5 NUM) = PL(f5 PRED) = ‘TOYS’

Principles Regulating F-Structures Completeness:

An f-structure is locally complete iff it contains all governable grammatical functions that its predicate governs.

A girl handed.

Lexical item requires governed functions OBJ and OBJ2

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)>’

Every attribute has a unique value Completeness:

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

Changing structure, but not meaning

NPVNDET

a girl handed a toy the baby

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

PP P NP (↑OBJ)=↓

NP DET N

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

‘BABY’

Dativizing Rule:

(↑ OBJ2) (↑ OBJ)

(↑ OBJ) (↑ TO OBJ)

From (↑(↓PCASE))=↓

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

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’ to VP (↑TO) = ↓ ↑=↓ (↑INF)= ↓ ↑=↓

persuaded: V, (↑ TENSE) = PAST(↑ PRED) = ‘PERSUADE<(↑SUBJ)(↑OBJ)(↑VCOMP)>’(↑ VCOMP TO) =c +(↑ VCOMP SUBJ) = (↑ OBJ)

Raising Verbs The girl promised the baby to go.

The girl promised the baby that the girl (should) go.

VP’ to VP (↑TO) = ↓ ↑=↓ (↑INF)= ↓ ↑=↓

promised: V, (↑ TENSE) = PAST(↑ PRED) = ‘PERSUADE<(↑SUBJ)(↑OBJ)(↑VCOMP)>’(↑ VCOMP TO) =c +(↑ VCOMP SUBJ) = (↑ SUBJ)

(↑ 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

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

Long Distance Dependencies The girl wondered [who the baby saw __].

Instance of constituent control Decompose into chain of functional

identities

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

C-Structure for Long-Distance Dependencies

the baby saw

(↑Q-FOCUS)=↓↓=▼

↑=↓ S

(↑OBJ) = ↓

NP(↑PRED) = WHO

N↑= ↓

(↑SPEC) = ↓

DET(↑NUM) = SG

(↑PRED) = BABY

(↑TENSE) = PAST (↑PRED) = ‘SEE<>’

(↑OBJ) = ↓

(↑SCOMP)=↓ S’

↑=▲

Bounded Domination Metavariables:▲: bounded above (longer path)

▼: bounding node

Bounded Domination Metavariables:▲: bounded above (longer path)

▼: bounding node

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!

More (unfinished) slides

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

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

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”

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.

Proper Instantiation Pg 246

Lexical-Functional Grammar

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