Grammatical Relations and Lexical Functional Grammar

Grammatical Relationsand Lexical Functional Grammar

Grammar Formalisms

Spring Term 2004

Grammatical Relations

• Subject– Sam ate a sandwich.– A sandwich was eaten by Sam.

• Direct object– Sam ate a sandwich.– Sue gave Sam a book.– Sue gave a book to Sam.

• Others that we will define later

Grammatical Relations in Grammar Formalisms

• Tree Adjoining Grammar:– Subject is defined structurally: first NP daughter under S– Object is defined structurally: NP that is a sister to V– But TAG output can be mapped to a dependency grammar tree

that includes subject and object.

• Categorial Grammar:– Grammatical relations are defined structurally if at all.

• Head Driven Phrase Structure Grammar:– Subject is defined indirectly as the first element on the verb’s

subcategorization list.

• Lexical Functional Grammar:– Grammatical relations are labelled explicitly in a feature

structure.

Motivation for Grammatical Relations: Subject-Verb Agreement

– Sam likes sandwiches.– *Sam like sandwiches.– The boys like sandwiches.– *The boys likes sandwiches.

• Hypothesis 1: The verb agrees with the agent.• Hypothesis 2: The verb agrees with the first NP.• Hypothesis 3: The verb agrees with the NP that

is a sister of VP.• Hypothesis 4: The verb agrees with the subject.

– Vacuous unless we have a definition or test for subjecthood.

Checking the hypotheses

• Hypothesis 1:– Can you think of a counterexample in

English.?

• Hypothesis 2:– Can you think of a counterexample in

English?– Can you think of a counterexample in another

language that has subject-verb agreeement?• (not Japanese or Chinese)

Some differences between English and Warlpiri (Australia)

The two small children are chasing that dog.

Aux V NP

NP VP

VP’ S

Wita-jarra-rlu ka-pala wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki.Small-DU-ERG pres-3duSUBJ chase-NPAST that.ABS child-DU-ERG dog.ABS

NP AUX V NP NP NP

S

Some Definitions• Case marking: different word form depending on the

grammatical relation:– She ate a sandwich. (nominative case marking: subject)

– *Her ate a sandwich.– Sam saw her. (accusative or objective case marking: object)

– *Sam saw she.

• Ergative case marking:– Marks the subject, but only if the verb is transitive (has a direct

object).

• Absolutive case marking:– Marks the subject, but only if the verb is intransitive.– Also marks the direct object.

• English has nominative and accusative case markers on pronouns.

• English does not have ergative or absolutive case marking.

Possible word orders in Warlpiri that are not possible in English

• *The two small are chasing that children dog.

• *The two small are dog chasing that children.

• *Chasing are the two small that dog children.

• *That are children chasing the two small dog.

Checking the hypotheses

• Hypothesis 2:– Does it work for Warlpiri?

• Hypothesis 3: – Does it work for Warlpiri?

English and Warlpiri Under Hypothesis 3

NP VP

VP’ S

Aux V NP

Deep structure

NP VP

VP’ S

Aux V NP

Surface Structure

English

English and Warlpiri under Hypothesis 3

NP

VP’ S

Aux V NPDeep structure

Surface Structure

Warlpiri

VP

NP VP

VP’ NP S

Aux V NP

S NP

AUX S

NP S

S

ee ee


NP

VP’ S

Aux V NP

Deep structure

Surface Structure

Warlpiri

VP

NP VP

VP’ NP S

Aux V NP

S NP

AUX S

NP S

S

ee e

Empty categories: represent semantic roles

Adjunctions: represent the real word order

Remnants of the original tree represent gramamtical relations

e


NP VP

VP’ S

Aux V NP

English

Warlpiri S

NP Aux V NP NP NP

Constituent structure: represents word order and grouping of words into constituents

Functional structure: represents grammatical relations and semantic roles

Subject “two small children”

Predicate chase agent theme

Object “that dog”


NP VP

VP’ S

Aux V NP

English

Warlpiri S

NP Aux V NP NP NP

Constituent structure: represents word order and grouping of words into constituents

Functional structure: represents gramamtical relations and semantic roles

Subject “two small children”

Predicate chase agent theme

Object “that dog”

Mapping from c-structure to f-structure

Keeping ScoreHypothesis 3:• One structure contains

a mish-mash of word order, constituency, grammatical relations, and thematic roles

• Adjunctions• Empty categories and

invisible constituents

Hypothesis 4:• Need an extra data

structure for grammatical relations and semantic roles

• Need a mapping between c-structure and f-structure

• Need a reproducible, falsifiable definition of grammatical relations.

Levels of Representation in LFG

[s [np The bear] [vp ate [np a sandwich]]] constituent structure

SUBJ PRED OBJ functional structure

Agent eat patient thematic roles

Grammatical encoding

Lexical mapping

Eat < agent patient > lexical mapping

SUBJ OBJ

SNP

SUBJ

VP

V NP

OBJ

VP

V PP

OBL

Grammatical Encoding

For English!!!

A surprise

• Syntax is not about the form (phrase structure) of sentences.

• It is about how strings of words are associated with their semantic roles.– Phrase structure is only part of the solution.

• Sam saw Sue– Sam: perceiver– Sue: perceived

Surprise (continued)

• Syntax is also about how to tell that two sentences are thematic paraphrases of each other (same phrases filling the same semantic roles).– It seems that Sam ate the sandwich.– It seems that the sandwich was eaten by

Sam.– Sam seems to have eaten the sandwich.– The sandwich seems to have been eaten by

Sam.

How to associate phrases with their semantic roles in LFG

• Starting from a constituent structure tree:• Grammatical encoding tells you how to

find the subject.– The bear is the subject.

• Lexical mapping tells you what semantic role the subject has.– The subject is the agent.– Therefore, the bear is the agent.


[s [np The sandwich ] [vp was eaten [pp by the bear]]] constituent structure

SUBJ PRED OBL functional structure

patient eat agent thematic roles


Lexical mapping


OBL SUBJ

SNP

SUBJ

VP

V NP

OBJ

VP

V PP

OBL


For English!!!

Active and Passive

• Active:– Patient is mapped to OBJ in lexical mapping.

• Passive– Patient is mapped to SUBJ in lexical mapping.

• Notice that the grammatical encodings are the same for active and passive sentences!!!

Passive mappings• Starting from the constituent structure tree.• The grammatical encoding tells you that the

sandwich is the subject.• The lexical mapping tells you that the subject

is the patient.– Therefore, the sandwich is the patient.

• The grammatical encoding tells you that the bear is oblique.

• The lexical mapping tells you that the oblique is the agent.– Therefore, the bear is the agent.

How you know that the active and passive have the same meaning

• In both sentences, the mappings connect the bear to the agent role.

• In both sentences, the mappings connect the sandwich to the patient role (roll?)

• In both sentences, the verb is eat.


[s-bar [np what ] [s did [np the bear] eat ]] constituent structure

OBJ SUBJ PRED functional structure

patient agent eat thematic roles


Lexical mapping


SUBJ OBJ

VP

V PP

OBL


For English!!!

SNP

SUBJ

S-barNP

OBJ

S

Wh-question

• Different grammatical encoding:– In this example, the OBJ is encoded as the

NP immediately dominated by S-bar

• Same lexical mappings are used for:– What did the bear eat?– The bear ate the sandwich.

Functional Structure

SUBJ PRED ‘bear’ NUM sg PERS 3 DEF +PRED ‘eat< agent patient > SUBJ OBJTENSE pastOBJ PRED ‘sandwich’ NUM sg PERS 3 DEF -

Functional Structure

• Pairs of attributes (features) and values– Attributes (in this example): SUBJ, PRED,

OBJ, NUM, PERS, DEF, TENSE– Values:

• Atomic: sg, past, +, etc.• Feature structure:

[num sg, pred `bear’, def +, person 3]• Semantic form: ‘eat<subj ob>’, ‘bear’, ‘sandwich’

Semantic Forms

• Why are they values of a feature called PRED?– In some approaches to semantics, even

nouns like bear are predicates (function) that take one argument and returns true or false.

– Bear(x) is true when the variable x is bound to a bear.

– Bear(x) is false when x is not bound to a bear.

Why is it called a Functional Structure?

X squared

1 1

2 4

3 9

4 16

5 25

Each feature has a unique value.

features values

Also, another term for grammtical relation is grammatical function.

We will use the terms functional structure, f-structure and feature structure interchangeably.

Give a name to each function

SUBJ PRED ‘bear’ NUM sg PERS 3 DEF +PRED ‘eat< agent patient > SUBJ OBJTENSE pastOBJ PRED ‘sandwich’ NUM sg PERS 3 DEF -

f1

f2

f3

How to describe an f-structure

• F1(TENSE) = past– Function f1 applied to TENSE gives the value past.

• F1(SUBJ) = [PRED ‘bear’, NUM sg, PERS 3, DEF +]

• F2(NUM) = sg

Descriptions can be true or false

• F(a) = v – Is true if the feature-value pair [a v] is in f.– Is false if the feature-value pair [a v] is not in f.

This is the notation we really use

• (f1 TENSE) = past

• Read it this way:

f1’s tense is past.

• (f1 SUBJ) = [PRED ‘bear’, NUM sg, PERS 3, DEF +]

• (f2 NUM) = sg

Chains of function application

• (f1 SUBJ) = f2

• (f2 NUM) = sg

• ((f1 SUBJ) NUM) = sg

• Write it this way.

(f1 SUBJ NUM) = sg

• Read it this way.

“f1’s subject’s number is sg.”

More f-descriptions

• (f a) = v– f is something that evaluates to a function.– a is something that evaluates to an attribute.– v is something that evaluates to a function, symbol,

or semantic form.

• (f1 subj) = (f1 xcomp subj)– Used for matrix coding as subject. A subject is

shared by the main clause and the complement clause (xcomp).

• (f1 (f6 case)) = f6– Used for obliques

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

Lions seem to live in the forest

DET N

P NP

V PP

COMP VP

N V VP-bar

NP VP

S

SUBJ PRED ‘lion’ NUM pl PERS 3PRED ‘seem < theme > SUBJ’ XCOMPTENSE presVFORM finXCOMP SUBJ [ ] VFORM INF PRED ‘live< theme loc >’ SUBJ OBL-loc OBJ

OBL-loc CASE OBL-loc PRED ‘in<OBJ>’ OBJ PRED ‘forest’ NUM sg PERS 3 DEF +

f1

f3

f2

f4

f5 f6

n7

n6n5

n4

n3

n2

n1

n10n9

n8

n11n13

n12

n14

Grammatical Relations and Lexical Functional Grammar

Documents

Transcript of Grammatical Relations and Lexical Functional Grammar