Introduction to Lexical Functional Grammar Mary Dalrymple, John - - PowerPoint PPT Presentation

Introduction to Lexical Functional Grammar

Mary Dalrymple, John Lowe, & Louise Mycock Centre for Linguistics and Philology Oxford University Konstanz, November/December 2012

• “Semantic roles, syntactic constituents, and grammatical functions

belong to parallel information structures of very different formal

• character. They are related not by proof-theoretic derivation but by

structural correspondences, as a melody is related to the words of a

• song. The song is decomposable into parallel melodic and linguistic

structures, which jointly constrain the nature of the whole. In the same way, the sentences of human language are themselves decomposable into 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 of

the sentence, familiar from traditional grammatical descriptions, representing syntactic predicate-argument structure and functional relations like subject and object.

• Constituent structure is the overt, more concrete level of linear and

hierarchical 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

‘GREETSUBJ,OBJ’

SUBJ

• PRED

‘DAVID’

• OBJ
• PRED

‘CHRIS’

• 

    

Functional structure

      

PRED

‘GOSUBJ’

TENSE PAST SUBJ

• PRED

‘DAVID’

NUM SG

• 

     

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

F-structures

          

PRED

‘GOSUBJ’

TENSE PAST SUBJ

• PRED

‘DAVID’

NUM SG

• ADJ
• PRED

‘QUICKLY’

• 

         

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

F-structures

          

PRED

‘GOSUBJ’

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

‘GOSUBJ’

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

‘GREETSUBJ,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

‘YAWNSUBJ’

TENSE PAST

• φ

V′

− → V

Local F-Structure Reference

V′ V

yawned

• PRED

‘YAWNSUBJ’

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

‘YAWNSUBJ’

TENSE PAST

• φ

V′

− →

V φ( ∗) = 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

‘YAWNSUBJ’

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′

− →

V φ( ∗) = 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

‘YAWNSUBJ’

TENSE PAST

• Expressible as:

V

− → yawned (↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST Standard form: yawned

V

(↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST

Phrase structure rules: English

IP

− →

• NP

(↑ SUBJ) = ↓

• I′

↑ = ↓

• I′

− →

• I

↑ = ↓

• VP

↑ = ↓

• VP −

→

• V

↑ = ↓

• NP −

→

• N

↑ = ↓

Lexical entries: English yawned

V

(↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST David

N

(↑ PRED) = ‘DAVID’ (Standard LFG practice: include only features relevant for analysis under discussion.)

Analysis: English

IP NP (↑ SUBJ) = ↓ N ↑ = ↓

David (↑ PRED) = ‘DAVID’

I′ ↑ = ↓ VP ↑ = ↓ V ↑ = ↓

yawned (↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST

Analysis: English

IP NP (↑ SUBJ) = ↓ N ↑ = ↓

David (fn PRED) = ‘DAVID’

I′ ↑ = ↓ VP ↑ = ↓ V ↑ = ↓

yawned (↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST

Analysis: English

IP NP (↑ SUBJ) = ↓ N fnp = fn

David (fn PRED) = ‘DAVID’

I′ ↑ = ↓ VP ↑ = ↓ V ↑ = ↓

yawned (↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST

Analysis: English

IP NP (fip SUBJ) = fnp N fnp = fn

David (fn PRED) = ‘DAVID’

I′ ↑ = ↓ VP ↑ = ↓ V ↑ = ↓

yawned (↑ PRED) = ‘YAWNSUBJ’ (↑ TENSE) = PAST

Analysis: English

IP NP (fip SUBJ) = fnp N fnp = fn

David (fn PRED) = ‘DAVID’

I′ ↑ = ↓ VP ↑ = ↓ V ↑ = ↓

yawned (fv PRED) = ‘YAWNSUBJ’ (fv TENSE) = PAST

Analysis: English

IP NP (fip SUBJ) = fnp N fnp = fn

David (fn PRED) = ‘DAVID’

I′ ↑ = ↓ VP ↑ = ↓ V fvp = fv

yawned (fv PRED) = ‘YAWNSUBJ’ (fv TENSE) = PAST

Analysis: English

IP NP (fip SUBJ) = fnp N fnp = fn

David (fn PRED) = ‘DAVID’

I′ ↑ = ↓ VP fi′ = fvp V fvp = fv

yawned (fv PRED) = ‘YAWNSUBJ’ (fv TENSE) = PAST

Analysis: English

IP NP (fip SUBJ) = fnp N fnp = fn

David (fn PRED) = ‘DAVID’

I′ fip = fi′ VP fi′ = fvp V fvp = fv

yawned (fv PRED) = ‘YAWNSUBJ’ (fv TENSE) = PAST

Solving the Description (fip SUBJ) = fnp fnp = fn (fn PRED) = ‘DAVID’ fip = fi′ fi′ = fvp fvp = fv (fv PRED) = ‘YAWNSUBJ’ (fv TENSE) = PAST

fip fi′ fvp fv     

PRED

‘YAWNSUBJ’

TENSE PAST SUBJ

fnp fn

• PRED

‘DAVID’

• 

   

Final result

IP NP (fip SUBJ) = fnp N fnp = fn

David (fn PRED) = ‘DAVID’

I′ fip = fi′ VP fi′ = fvp V fvp = fv

yawned (fv PRED) = ‘YAWNSUBJ’ (fv TENSE) = PAST

    

PRED

‘YAWNSUBJ’

TENSE PAST SUBJ

• PRED

‘DAVID’

• 

   

Semantics in LFG

IP NP N′ N

John

I′ VP V′ V

married

NP N′ N

Rosa

     

PRED

‘MARRYSUBJ,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 assembly and 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 the meaning 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 entities represented by P. Usually, the expression P contains at least one occurrence of the variable X, and we say that these occurrences are bound by the λ lambda

• perator.

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 of X in P with a. Example: [λX.yawn(X)](David) ≡ yawn(David)

Meaning contributions

      

PRED

‘MARRYSUBJ,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 the

following form: When given a meaning x for my subject and a meaning y 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 it

by 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

‘MARRYSUBJ,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 if x marries y

• σ−
• (sσ−
• mσ): If I am provided with the semantic structure of my object

and then the semantic structure of my subject, I produce the semantic structure of the sentence. In the lexicon: λy.λx.marry(x, y):(↑ OBJ)σ−

• ((↑ SUBJ)σ−
• ↑σ)

Proof rules X : fσ P : fσ −

• gσ

P(X) : gσ

Meaning proof for ‘married Rosa’ X : fσ P : 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 : fσ P : 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 and prosody 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 of information structure. We can use abbreviations like the following, where Rosa stands for any reasonable theory of the meaning of Rosa and how it combines with the rest of the sentence: Rosa married married-Rosa John marry(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. CSLI Calendar, 4 October 1990, volume 6:3. Dalrymple, Mary (editor). 1999. Semantics and Syntax in Lexical Functional Grammar: The Resource Logic Approach. Cambridge, MA: The MIT Press. Dalrymple, Mary. 2001. Lexical Functional Grammar, volume 34 of Syntax and Semantics. New York: Academic Press.