Grammatical Relations 4i4b5h

Grammatical Relations and 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 Ading 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) S

VP’

NP

VP Aux

The two small children

V

NP

are chasing that dog. S

NP Wita-jarra-rlu Small-DU-ERG

AUX

V

NP

NP

NP

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

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 S

Deep structure VP’

NP

VP

Aux

V

NP

English S

Surface Structure

VP’ NP

VP Aux

V

NP

English and Warlpiri under Hypothesis 3 S

VP’

VP

NP

Aux Warlpiri

V

Deep structure

NP

S NP

S AUX S S

NP

NP

S

Surface Structure

VP’ NP

VP Aux

e

ee

V

NP e

English and Warlpiri under Hypothesis 3 S

VP’

VP

NP

Aux Warlpiri

V

S NP

Deep structure

NP Adjunctions: represent the real word order

S AUX S S

NP

Remnants of the original tree represent gramamtical relations

NP

S

VP’ NP

VP Aux

V

NP

e

ee

Empty categories: represent semantic roles

Surface Structure e

English and Warlpiri under Hypothesis 4 Constituent structure: represents word order and grouping of words into constituents

English S

Subject

VP’ NP

VP

Aux

Warlpiri NP

V

V

NP

NP

NP

“two small children”

Predicate

chase agent theme

Object

“that dog”

NP

S Aux

Functional structure: represents grammatical relations and semantic roles

English and Warlpiri under Hypothesis 4 Constituent structure: represents word order and grouping of words into constituents

English S

Subject

VP’ NP

VP

Aux

Warlpiri NP

V

V

NP

chase agent theme

Object

“that dog”

NP

NP

NP

“two small children”

Predicate

Mapping from c-structure to fstructure

S Aux

Functional structure: represents gramamtical relations and semantic roles

English and Warlpiri under Hypothesis 4 Constituent structure: represents word order and grouping of words into constituents

English S

Subject

VP’ NP

VP

Aux

V

NP

S Aux

V

NP

NP

NP

“two small children”

Predicate

chase agent theme

Object

“that dog”

NP

Mapping from c-structure to f-structure

Warlpiri

Functional structure: represents gramamtical relations and semantic roles

Keeping Score Hypothesis 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]]] SUBJ Agent Eat < agent SUBJ

PRED

SUBJ

OBJ

eat

functional structure Lexical mapping thematic roles

patient

patient >

lexical mapping

OBJ

S NP

constituent structure Grammatical encoding

VP

VP V

NP OBJ

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.

Levels of Representation in LFG [s [np The sandwich ] [vp was eaten [pp by the bear]]]

constituent structure

Grammatical encoding SUBJ

PRED

OBL

patient

eat

agent

Eat < agent OBL

patient >

SUBJ

lexical mapping

SUBJ

S NP

functional structure Lexical mapping thematic roles

VP

VP V

NP OBJ

V

PP OBL

Grammatical Encoding For English!!!

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

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

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

ive 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 ive 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.

Levels of Representation in LFG [s-bar [np what ] [s did

[np the bear]

eat ]]

constituent structure

Grammatical encoding OBJ

SUBJ

patient Eat < agent SUBJ S-bar NP S OBJ

agent patient >

PRED eat

functional structure Lexical mapping thematic roles

lexical mapping

OBJ

VP

S NP SUBJ

V

PP OBL

Grammatical Encoding For English!!!

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 TENSE OBJ

PRED ‘bear’ NUM sg PERS 3 DEF + ‘eat< agent patient > SUBJ OBJ past 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

Each feature has a unique value.

1

2 4

features

3

9

4

16

5

25

Also, another term for grammtical relation is grammatical function. values

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

Give a name to each function f1 SUBJ

PRED ‘bear’ NUM sg f2 PERS 3 DEF + PRED ‘eat< agent patient > SUBJ OBJ TENSE past OBJ PRED ‘sandwich’ NUM sg f3 PERS 3 DEF -

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

SUBJ

PRED TENSE VFORM XCOMP

S NP

N

VP

V

PRED ‘lion’ NUM pl PERS 3 ‘seem < theme > SUBJ’ XCOMP pres fin SUBJ [ ] VFORM INF PRED ‘live< theme loc >’

VP-bar

SUBJ

OBL-loc

COMP VP V

PP P

NP DET

N

Lions seem to live in the forest

CASE PRED OBJ

OBL-loc OBJ

OBL-loc ‘in ’ PRED ‘forest’ NUM sg PERS 3 DEF +

SUBJ

f1

f2 PRED TENSE VFORM XCOMP

S n1 n2

NP

n3

N

VP

V

n5

n4

VP-bar

SUBJ

n6

f4 n7

COMP VP

PRED ‘lion’ NUM pl PERS 3 ‘seem < theme > SUBJ’ XCOMP pres fin SUBJ [ ] f3 VFORM INF PRED ‘live< theme loc >’ OBL-loc

n8

f5 V

PP

n9

P

n10

NP

n11

DET

N

n12 n13

n14

Lions seem to live in the forest

CASE PRED OBJ

f6

OBL-loc OBJ

OBL-loc ‘in ’ PRED ‘forest’ NUM sg PERS 3 DEF +

SUBJ

f1

f2 PRED TENSE VFORM XCOMP

S n1 n2

NP

n3

N

VP

V

n5

n4

VP-bar

SUBJ

n6

f4 n7

COMP VP

PRED ‘lion’ NUM pl PERS 3 ‘seem < theme > SUBJ’ XCOMP pres fin SUBJ [ ] f3 VFORM INF PRED ‘live< theme loc >’ OBL-loc

n8

f5 V

PP

n9

P

n10

NP

n11

DET

N

n12 n13

n14

Lions seem to live in the forest

CASE PRED OBJ

f6

OBL-loc OBJ

OBL-loc ‘in ’ PRED ‘forest’ NUM sg PERS 3 DEF +