Introduction to Lexical Functional GrammarMary Dalrymple, John Lowe, & Louise Mycock

Centre for Linguistics and PhilologyOxford University

Konstanz, November/December 2012

• “Semantic roles, syntactic constituents, and grammatical functionsbelong to parallel information structures of very different formalcharacter. They are related not by proof-theoretic derivation but bystructural correspondences, as a melody is related to the words of asong. The song is decomposable into parallel melodic and linguisticstructures, which jointly constrain the nature of the whole. In the sameway, the sentences of human language are themselves decomposableinto parallel systems of constraints – structural, functional, semantic,and prosodic – which the whole must jointly satisfy.” (Bresnan, 1990)

LFG

Two aspects of syntactic structure:

• Functional structure is the abstract functional syntactic organisation ofthe sentence, familiar from traditional grammatical descriptions,representing syntactic predicate-argument structure and functionalrelations like subject and object.

• Constituent structure is the overt, more concrete level of linear andhierarchical organisation of words into phrases.

LFG’s c-structure and f-structure

IP

NP

N

David

I′

VP

V′

V

greeted

NP

N

Chris

PRED ‘GREET〈SUBJ,OBJ〉’

SUBJ[

PRED ‘DAVID’]

OBJ[

PRED ‘CHRIS’]

Functional structure

PRED ‘GO〈SUBJ〉’

TENSE PAST

SUBJ

[PRED ‘DAVID’NUM SG

]

• PRED, TENSE NUM: attributes• ‘GO〈SUBJ〉’, DAVID, SG: values• PAST, SG: symbols (a kind of value)• ‘BOY’, ‘GO〈SUBJ〉’: semantic forms

F-structures

PRED ‘GO〈SUBJ〉’

TENSE PAST

SUBJ

[PRED ‘DAVID’NUM SG

]

ADJ{[

PRED ‘QUICKLY’]}

An f-structure can be the value of an attribute. Attributes with f-structurevalues are the grammatical functions: SUBJ, OBJ, OBJθ, COMP, XCOMP, ...

F-structures

PRED ‘GO〈SUBJ〉’

TENSE PAST

SUBJ

[PRED ‘DAVID’NUM SG

]

ADJ{[

PRED ‘QUICKLY’]}

A set of f-structures can also be a value of an attribute.

Sets of f-structures

PRED ‘GO〈SUBJ〉’

TENSE PAST

SUBJ

[PRED ‘DAVID’

]

[PRED ‘GEORGE’

]

ADJ{[

PRED ‘QUICKLY’]}

Sets of f-structures represent:

• adjuncts (there can be more than one adjunct) or• coordinate structures (there can be more than one conjunct)

C- and F-Structure

V

greeted

[PRED ‘GREET〈SUBJ,OBJ〉’

TENSE PAST

]φ

φ function relates c-structure nodes to f-structures.

(Function: Every c-structure node corresponds to exactly one f-structure.)

Constraining the c-structure/f-structure correspondence

V′

V

yawned

[PRED ‘YAWN〈SUBJ〉’

TENSE PAST

]φ

V′ −→ V

Local F-Structure Reference

V′

V

yawned

[PRED ‘YAWN〈SUBJ〉’

TENSE PAST

]φ

V′ −→ V

the current c-structure node (“self”): ∗the immediately dominating node (“mother”): ∗̂

the c-structure to f-structure function: φ

Rule Annotation

V′

V

yawned

[PRED ‘YAWN〈SUBJ〉’

TENSE PAST

]φ

V′ −→ Vφ(∗̂) = φ(∗)

mother’s (V′’s) f-structure = self’s (V’s) f-structure

Simplifying the Notation

φ(∗̂) (mother’s f-structure) = ↑φ(∗) (self’s f-structure) = ↓

V′

V

yawned

[PRED ‘YAWN〈SUBJ〉’

TENSE PAST

]φ

V′ −→ V↑ = ↓

mother’s f-structure = self’s f-structure

Using the Notation

V′ −→ V↑ = ↓

mother’s f-structure = self’s f-structure

V′

V↑ = ↓

Using the Notation

V′ −→ V↑ = ↓

mother’s f-structure = self’s f-structure

V′

V↑ = ↓

Using the Notation

V′ −→ V↑ = ↓

mother’s f-structure = self’s f-structure

V′

V↑ = ↓

Using the Notation

V′ −→ V↑ = ↓

mother’s f-structure = self’s f-structure

V′

V↑ = ↓

[ ]

More rules

V′ −→ Vφ(∗̂) = φ(∗)

NP(φ(∗̂) OBJ) = φ(∗)

mother’s f-structure’s OBJ = self’s f-structure

In simpler form:

V′ −→ V↑ = ↓

NP(↑ OBJ) = ↓

Using the Notation

V′ −→ V↑ = ↓

NP(↑ OBJ) = ↓

V′

V NP

[OBJ [ ]

]

Terminal nodes

V

yawned

[PRED ‘YAWN〈SUBJ〉’

TENSE PAST

]

Expressible as:

V −→ yawned(↑ PRED) = ‘YAWN〈SUBJ〉’

(↑ TENSE) = PAST

Standard form:

yawned V (↑ PRED) = ‘YAWN〈SUBJ〉’(↑ TENSE) = PAST

Phrase structure rules: English

IP −→(

NP(↑ SUBJ) = ↓

) (I′

↑ = ↓

)

I′ −→(

I↑ = ↓

) (VP↑ = ↓

)

VP −→(

V↑ = ↓

)

NP −→(

N↑ = ↓

)

Lexical entries: English

yawned V (↑ PRED) = ‘YAWN〈SUBJ〉’(↑ TENSE) = PAST

David N (↑ PRED) = ‘DAVID’

(Standard LFG practice: include only features relevant for analysis underdiscussion.)

Analysis: English

IP

NP(↑ SUBJ) = ↓

N↑ = ↓

David(↑ PRED) = ‘DAVID’

I′

↑ = ↓

VP↑ = ↓

V↑ = ↓

yawned(↑ PRED) = ‘YAWN〈SUBJ〉’

(↑ TENSE) = PAST

Analysis: English

IP

NP(↑ SUBJ) = ↓

N↑ = ↓

David(fn PRED) = ‘DAVID’

I′

↑ = ↓

VP↑ = ↓

V↑ = ↓

yawned(↑ PRED) = ‘YAWN〈SUBJ〉’

(↑ TENSE) = PAST

Analysis: English

IP

NP(↑ SUBJ) = ↓

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

↑ = ↓

VP↑ = ↓

V↑ = ↓

yawned(↑ PRED) = ‘YAWN〈SUBJ〉’

(↑ TENSE) = PAST

Analysis: English

IP

NP(fip SUBJ) = fnp

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

↑ = ↓

VP↑ = ↓

V↑ = ↓

yawned(↑ PRED) = ‘YAWN〈SUBJ〉’

(↑ TENSE) = PAST

Analysis: English

IP

NP(fip SUBJ) = fnp

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

↑ = ↓

VP↑ = ↓

V↑ = ↓

yawned(fv PRED) = ‘YAWN〈SUBJ〉’

(fv TENSE) = PAST

Analysis: English

IP

NP(fip SUBJ) = fnp

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

↑ = ↓

VP↑ = ↓

Vfvp = fv

yawned(fv PRED) = ‘YAWN〈SUBJ〉’

(fv TENSE) = PAST

Analysis: English

IP

NP(fip SUBJ) = fnp

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

↑ = ↓

VPfi′ = fvp

Vfvp = fv

yawned(fv PRED) = ‘YAWN〈SUBJ〉’

(fv TENSE) = PAST

Analysis: English

IP

NP(fip SUBJ) = fnp

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

fip = fi′

VPfi′ = fvp

Vfvp = fv

yawned(fv PRED) = ‘YAWN〈SUBJ〉’

(fv TENSE) = PAST

Solving the Description

(fip SUBJ) = fnpfnp = fn(fn PRED) = ‘DAVID’fip = fi′

fi′ = fvpfvp = fv(fv PRED) = ‘YAWN〈SUBJ〉’(fv TENSE) = PAST

fipfi′

fvpfv

PRED ‘YAWN〈SUBJ〉’

TENSE PAST

SUBJfnpfn

[PRED ‘DAVID’

]

Final result

IP

NP(fip SUBJ) = fnp

Nfnp = fn

David(fn PRED) = ‘DAVID’

I′

fip = fi′

VPfi′ = fvp

Vfvp = fv

yawned(fv PRED) = ‘YAWN〈SUBJ〉’

(fv TENSE) = PAST

PRED ‘YAWN〈SUBJ〉’

TENSE PAST

SUBJ[

PRED ‘DAVID’]

Semantics in LFG

IP

NP

N′

N

John

I′

VP

V′

V

married

NP

N′

N

Rosa

PRED ‘MARRY〈SUBJ,OBJ〉’

SUBJ[

PRED ‘JOHN’]

OBJ[

PRED ‘ROSA’]

Meaning: marry(john, rosa)

How is this meaning composed?

Glue: Composing meanings via deduction

Glue (Asudeh, 2004, 2012; Dalrymple, 1999, 2001): Meaning assemblyand linear logic

• Logic of meanings (semantic level):the level of meanings of utterances and phrases

• Logic for composing meanings (‘glue’ level):the level responsible for assembling the meanings of parts to get themeaning of the whole

Meanings

Meanings are expressions like David, yawn(David), yawn ...

Function: when applied to an argument, yields a unique value.

yawn: applied to David, yields “true”.applied to Fred, yields “true”.applied to George, yields “false”....

Function application:

yawn applied to David = yawn(David)

Application and abstraction

Lambda abstraction:

λX.P represents a function from entities represented by X to entitiesrepresented by P .

Usually, the expression P contains at least one occurrence of the variableX, and we say that these occurrences are bound by the λ lambdaoperator.

Function application:

[λX.P ](a)

The function λX.P is applied to the argument a.

Equivalent to the expression that results from replacing all occurrences ofX in P with a.

Example: [λX.yawn(X)](David) ≡ yawn(David)

Meaning contributions

PRED ‘MARRY〈SUBJ,OBJ〉’

SUBJ[

PRED ‘JOHN’]

OBJ[

PRED ‘ROSA’]

• The word John contributes the meaning john.

• The word Rosa contributes the meaning rosa.

• The word married contributes meaning assembly instructions of thefollowing form: When given a meaning x for my subject and a meaningy for my object, I produce a meaning marry(x, y) for my sentence.

Contribution of ‘John’

NP

N′

N

John

[PRED ‘JOHN’

]john:[ ]

• Every f-structure has a corresponding semantic structure, related to itby the projection function σ (represented by a dotted line).

• john:[ ] is a meaning constructor.

• In the lexicon: john:↑σ

Meaning assembly: Gluing meanings together

PRED ‘MARRY〈SUBJ,OBJ〉’

SUBJ [ ]

OBJ [ ]

λy .λx .marry(x, y):oσ−◦(sσ−◦mσ)

λy .λx .marry(x, y): a relation between two individuals x and y that holds ifx marries y

oσ−◦(sσ−◦mσ): If I am provided with the semantic structure of my objectand then the semantic structure of my subject, I produce the semanticstructure of the sentence.

In the lexicon: λy .λx .marry(x, y):(↑ OBJ)σ−◦((↑ SUBJ)σ−◦↑σ)

Proof rules

X : fσP : fσ −◦ gσ

P (X) : gσ

Meaning proof for ‘married Rosa’

X : fσP : fσ −◦ gσ

P (X) : gσ

rosa:oσ λy .λx .marry(x, y):oσ−◦(sσ−◦mσ)λx .marry(x, rosa):sσ−◦mσ

Meaning proof for ‘John married Rosa’

X : fσP : fσ −◦ gσ

P (X) : gσ

rosa:oσ λy .λx .marry(x, y):oσ−◦(sσ−◦mσ)λx .marry(x, rosa):sσ−◦mσ john:sσ

marry(john, rosa): mσ

Details are not important for theory of information structure andprosody

Our theory of meaning composition, to be explained in the following:

rosa:oσ λy .λx .marry(x, y):oσ−◦(sσ−◦mσ)λx .marry(x, rosa):sσ−◦mσ john:sσ

marry(john, rosa): mσ

In fact, however, the details won’t be important for our discussion ofinformation structure. We can use abbreviations like the following, whereRosa stands for any reasonable theory of the meaning of Rosa and how itcombines with the rest of the sentence:

Rosa marriedmarried-Rosa Johnmarry(john, rosa): mσ

Bibliography

Asudeh, Ash. 2004. Resumption as Resource Management . Ph.D.thesis, Stanford University.

Asudeh, Ash. 2012. The Logic of Pronominal Resumption. Oxford:Oxford University Press.

Bresnan, Joan. 1990. Parallel constraint grammar project. CSLICalendar, 4 October 1990, volume 6:3.

Dalrymple, Mary (editor). 1999. Semantics and Syntax in LexicalFunctional Grammar: The Resource Logic Approach. Cambridge, MA:The MIT Press.

Dalrymple, Mary. 2001. Lexical Functional Grammar , volume 34 ofSyntax and Semantics. New York: Academic Press.