Topics in Lexical-Functional Grammar. Ronald M. Kaplan and Mary Dalrymple. Xerox PARC. August 1995

Transcription

1 Projections and Semantic Interpretation Topics in Lexical-Functional Grammar Ronald M. Kaplan and Mary Dalrymple Xerox PARC August 199 Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

2 Constituent structure (c-structure): NP S VP V Bill left Functional structure (f-structure): PRED SUBJ `leave< SUBJ >' h i PRED `Bill' Semantic structure: leave (bill) Kaplan and Dalrymple, ESSLLI 9, Barcelona

3 Halvorsen (198): \F-structures provide a universal format for representing the meaningful grammatical relations in a sentence." Kaplan and Dalrymple, ESSLLI 9, Barcelona

4 Problem: Find a way of determining the meaning of a sentence based on the meanings of the words in the sentence; and the f-structure for the sentence. Kaplan and Dalrymple, ESSLLI 9, Barcelona

5 Halvorsen (198): obtain translation by applying principles for generating semantic structures based on f-structure congurations (II) Pred-Arg Conguration: if f k is an f-structure of the form s 1 v 1. s n v n containing some v i with an argument list, then M k is a semantic structure such that (M k PREDICATE) = M si... Kaplan and Dalrymple, ESSLLI 9, Barcelona

6 Halvorsen (1988), Halvorsen and Kaplan (1988): extension of rule language of LFG to permit simultaneous characterization of multiple levels NP S VP PRED SUBJ `leave' h PRED `Bill' i V Bill left leave(bill) Kaplan and Dalrymple, ESSLLI 9, Barcelona

7 Guiding principles: Each word contributes to the meaning of the sentence. { It can't be ignored. { Multiplicities matter. The f-structure is a scaolding that guides the assembly of meaning. { It doesn't necessarily specify each step. Kaplan and Dalrymple, ESSLLI 9, Barcelona

8 Bill appointed Hillary. PRED SUBJ OBJ `appoint' h i PRED `Bill' h PRED `Hillary' i \Appoint" contributes: SUBJ appoints OBJ or 8X:8Y: if my SUBJ means X and my OBJ means Y then my f-structure means \X appointed Y ". 8X; Y:(" SUBJ) ; X (" OBJ) ; Y " ; appoint(x; Y ) Kaplan and Dalrymple, ESSLLI 9, Barcelona 8

9 Solution: Obtain the meaning of the sentence via deduction in linear logic, starting with the meanings of the words as premises and making use of f-structural syntactic information. Kaplan and Dalrymple, ESSLLI 9, Barcelona 9

10 Bill appointed Hillary. Lexical entries: Bill NP (" PRED) = `Bill' " ; bill Hillary NP (" PRED) = `Hillary' " ; hillary appointed V (" PRED)= `appoint' 8X; Y:(" SUBJ) ; X (" OBJ) ; Y " ; appoint(x; Y ) PRED SUBJ OBJ `appoint' h i PRED `Bill' h PRED `Hillary' i Kaplan and Dalrymple, ESSLLI 9, Barcelona 10

11 f: PRED `appoint' SUBJ g: h PRED `Bill' i OBJ h: h PRED `Hillary' i bill: hillary: g ; bill h ; hillary appointed: 8X; Y: g ; X h ; Y f ; appoint(x; Y ) bill hillary appointed (Premises.) ` ` ` bill hillary 8X: g ; X (8Y: h ; Y f ; appoint(x; Y )) hillary 8Y: h ; Y f ; appoint(bill; Y )) f ; appoint(bill; hillary) Kaplan and Dalrymple, ESSLLI 9, Barcelona 11

12 Composing meanings via deduction: 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 Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

13 Completeness: an f-structure must contain all the governable grammatical functions that its predicates govern *Bill devoured. Coherence: all the governable grammatical functions that an f-structure contains must be governed by its predicates *Bill congratulated Hillary the sink. Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

14 Linear logic: A resource-oriented logic Girard 198 Technically: Removal of rules of weakening and contraction: ` B ; A ` Weakening B ; A; A ` B ; A ` B Contraction Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

15 Linear logic: Accounting for premises multiplicative conjunction: linear implication: INCORRECT: A ` (A A) INCORRECT: (A B) ` A CORRECT: (A (A B)) ` B INCORRECT: (A (A B)) ` (A B) INCORRECT: (A (A B)) ` (A B) B Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

16 Completeness and Coherence: T h ` f ; t (for some term t) Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

17 Our approach: exploits the ability of the logic to name things, to capture the f-structural syntactic constraints on semantic composition exploits the resource-conscious properties of linear logic to allow modication exploits the resource-conscious properties of linear logic to ensure that each word contributes exactly once to the meaning Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

18 Bill convinced every voter. PRED `convince' TENSE PAST SUBJ h PRED i `Bill' OBJ SPEC PRED `every' `voter' every(z; voter(z); convince(bill; z)) Kaplan and Dalrymple, ESSLLI 9, Barcelona 18

19 f: PRED `convince' TENSE PAST SUBJ g: h PRED `Bill' i OBJ h: SPEC `every' PRED `voter' bill: g ; Bill every-voter: 8F; S:(8x:h ; x F ; t Sx) F ; every(z; voter(z); Sz) convince: 8X; Y: (g ; X h ; Y ) f ; t convince(x; Y ) Kaplan and Dalrymple, ESSLLI 9, Barcelona 19

20 bill every-voter convince (Premises.) ` bill convince 8F; S: (8x: h ; x F ; t Sx) F ; t every(z; voter(z); Sz) ` 8Y: (h ; Y f ; t convince(bill; Y )) 8F; S: (8x: h ; x F ; t Sx) F ; t every(z; voter(z); Sz) ` f ; t every(z; voter(z); convince(bill; z)) Kaplan and Dalrymple, ESSLLI 9, Barcelona 0

21 f: PRED `convince' TENSE PAST SUBJ g: h PRED `Bill' i OBJ h: SPEC `every' PRED `voter' every: 8F; R; S:( (8x:(h VAR);x (h RESTR);Rx) (8x:h ; x F ; t Sx)) F ; every(z; Rz; Sz) voter: 8X: (h VAR);X (h RESTR);voter(X) every-voter: 8F; S:(8x:h ; x F ; t Sx) F ; every(z; voter(z); Sz) Kaplan and Dalrymple, ESSLLI 9, Barcelona 1

22 The use of linear logic in a deduction framework enables a simple and formally well-dened treatment of: completeness and coherence modication complex predicates (Dalrymple, Hinrichs, Lamping, and Saraswat 199) quantication (Dalrymple, Lamping, Pereira, and Saraswat 199, 199) intensional verbs (Dalrymple, Lamping, Pereira, and Saraswat 199) Kaplan and Dalrymple, ESSLLI 9, Barcelona