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)

S VP’ NP VP Some differences between English and Warlpiri (Australia) Aux V NP The two small children are chasing that dog. S NP AUX V NP NP NP 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

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?

S S VP’ VP’ NP VP NP VP Aux V NP Aux V NP English and Warlpiri Under Hypothesis 3 Deep structure English Surface Structure

NP S VP’ NP VP Aux V NP English and Warlpiri under Hypothesis 3 S VP’ VP NP Deep structure Aux V NP S Warlpiri NP S AUX S S NP Surface Structure e e e e

NP S VP’ NP VP Aux V NP English and Warlpiri under Hypothesis 3 S VP’ Deep structure VP NP Aux V NP S Warlpiri Adjunctions: represent the real word order NP S AUX S Remnants of the original tree represent gramamtical relations S NP Empty categories: represent semantic roles e Surface Structure e e e

S VP’ NP VP Aux V NP English and Warlpiri under Hypothesis 4 Functional structure: represents grammatical relations and semantic roles Constituent structure: represents word order and grouping of words into constituents English Subject “two small children” Predicate chase agent theme Object “that dog” Warlpiri S NP Aux V NP NP NP

S VP’ NP VP Aux V NP English and Warlpiri under Hypothesis 4 Functional structure: represents gramamtical relations and semantic roles Constituent structure: represents word order and grouping of words into constituents English Subject “two small children” Predicate chase agent theme Object “that dog” Mapping from c-structure to f-structure Warlpiri S NP Aux V NP NP NP

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.

VP VP V PP V NP OBL OBJ Levels of Representation in LFG [s [np The bear] [vp ate [np a sandwich]]] constituent structure Grammatical encoding SUBJ PRED OBJ functional structure Lexical mapping Agent eat patient thematic roles Eat < agent patient > lexical mapping SUBJ OBJ Grammatical Encoding For English!!! S NP SUBJ

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.

VP VP V PP V NP OBL OBJ Levels of Representation in LFG [s [np The sandwich ] [vp was eaten [pp by the bear]]] constituent structure Grammatical encoding SUBJ PRED OBL functional structure Lexical mapping patient eat agent thematic roles Eat < agent patient > lexical mapping OBL SUBJ Grammatical Encoding For English!!! S NP SUBJ

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 S VP NP NP S V PP SUBJ OBJ OBL Levels of Representation in LFG [s-bar [np what ] [s did [np the bear] eat ]] constituent structure Grammatical encoding OBJ SUBJ PRED functional structure Lexical mapping patient agent eat thematic roles Eat < agent patient > lexical mapping SUBJ OBJ 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 ‘bear’ NUM sg PERS 3 DEF + PRED ‘eat< agent patient > SUBJ OBJ TENSE past OBJ 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 • 4 • 9 • 16 • 25 Each feature has a unique value. Also, another term for grammtical relation is grammatical function. features values

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

Give a name to each function f1 SUBJ PRED ‘bear’ NUM sg PERS 3 DEF + PRED ‘eat< agent patient > SUBJ OBJ TENSE past OBJ PRED ‘sandwich’ NUM sg PERS 3 DEF - 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

SUBJ PRED ‘lion’ NUM pl PERS 3 PRED ‘seem < theme > SUBJ’ XCOMP TENSE pres VFORM fin XCOMP 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 + S NP VP N V VP-bar COMP VP V PP P NP DET N Lions seem to live in the forest

SUBJ PRED ‘lion’ NUM pl PERS 3 PRED ‘seem < theme > SUBJ’ XCOMP TENSE pres VFORM fin XCOMP 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 f2 S n1 f3 n2 NP VP n4 n3 N V VP-bar n5 n6 f4 n7 COMP VP n8 f5 f6 V PP n10 n9 P NP n12 n11 DET N n13 n14 Lions seem to live in the forest

Grammatical Relations and Lexical Functional Grammar