Download presentation

Presentation is loading. Please wait.

Published byKarley Branyon Modified over 3 years ago

1
October 2004CSA4050: Semantics III1 CSA4050: Advanced Topics in NLP Semantics III Quantified Sentences

2
October 2004CSA4050: Semantics III2 Outline Language Sentences Determiners Noun Phrases Syntactic Structure Logic Generalised Quantifiers Higher order functions Translation into Prolog Syntax-Semantics Interface

3
October 2004CSA4050: Semantics III3 Determiners and Quantifiers in Language and Logic A dog barked x dog(x) & bark(x) Every dog barked x dog(x) bark(x) Fido chased a cat x cat(x) & chase(fido,x) Every dog chased a cat x dog(x) ( y cat(x) & chase(x,y)))

4
October 2004CSA4050: Semantics III4 Syntactic Shape vs. Semantic Shape John walks semantics: walk(suzie). Every man talks semantics: all(X, man(X) talk(X)) S NP VP Suzie walks S NP VP Det N talks Every man

5
October 2004CSA4050: Semantics III5 Problem Similar syntactic shape Dissimilar semantic shape How is this possible if the syntax drives the combination of semantic fragments as per rule-to-rule hypothesis? Answer: be creative about logical forms and semantic combination rules

6
October 2004CSA4050: Semantics III6 Montague Solution Reorganising the semantic combination rules operating between VP and NP in rules such as s(S) --> np(NP), vp(VP). We will be considering [NP]([VP]) versus [VP]([NP]). NPs as higher order functions Analyse LF of quantified sentences

7
October 2004CSA4050: Semantics III7 LF of Quantified Sentences LF of quantified sentences has a general shape involving –a restrictor predicate R –a scope predicate S R restricts the set of things we are talking about S says something further about set element(s) –a logical quantifier Q –a bound variable V –a logical operator O connecting R and S

8
October 2004CSA4050: Semantics III8 Examples All lecturers are lazy x lecturer(x) lazy(x) Restrictor = lecturers Scope = lazy Quantifier = All Operator = implies Bound Variable = x

9
October 2004CSA4050: Semantics III9 Examples There is a lazy lecturer x lecturer(x) & lazy(x) Restrictor = lecturers Scope = lazy Quantifier = exist Operator = and Bound Variable = x

10
October 2004CSA4050: Semantics III10 Anatomy of Quantified Sentences LogicQVROS x m(x) w(x) xm(x) w(x) x d(x) & b(x) xd(x)&b(x) x d(x) (h(x) & b(x)) xd(x) h(x) & b(x)

11
October 2004CSA4050: Semantics III11 Generalized Quantifiers We adopt the following generalized quantifier representation for LF in which quantifier is a 3- place predicate: Q(,, ) Operator is omitted. Examples all(X,man(X),walk(X)) exist(X,man(X),walk(X)) the(X,man(X),climbed(X,everest)) most(X,lecturer(X),poor(X))

12
October 2004CSA4050: Semantics III12 NP as higher order function NP Q^all(X,man(X),Q) every man VP Y^walk(Y) walks S all(X,man(X),walk(X))

13
October 2004CSA4050: Semantics III13 Encoding in Prolog The VP remains as before, ie X^walks(X) The quantified NP every man will be of the form Q^all(X,man(X) => Q) The semantic rule for S now ensures that the NP function is applied to the VP function. s(S)--> np(NP),vp(VP), {reduce(NP,VP,S)}

14
October 2004CSA4050: Semantics III14 DCG with Quantification Program 1 % grammar s(S) --> np(NP), vp(VP), {reduce(NP,VP,S)} vp(VP) --> v(V). % lexicon v(X^walk(X)) --> [walks]. np(Q^all(X,man(X),Q)) --> [every,man].

15
October 2004CSA4050: Semantics III15 Result ?- s(X,[every,man,walks],[]). X = all(_G397, man(_G397), _G405^walk(_G405)) all(x, man(x)=> y^walk(y)) What is wrong with this? How can we fix it?

16
October 2004CSA4050: Semantics III16 Result ?- s(X,[every,man,walks],[]). X = all(_G397, man(_G397), _G405^walk(_G405)) all(x, man(x)=> y^walk(y)) What is wrong with this? –The variables _G397 and _G405 are distinct. They should be identical. –The consequent of the implication is a λ expression How can we fix it? –We need to force the variables to be identical using reduce

17
October 2004CSA4050: Semantics III17 DCG with Quantification Program 2 % grammar s(S) --> np(NP), vp(VP), {reduce(VP,NP,S)} vp(VP) --> v(V). % lexicon v(X^walk(X)) --> [walks]. np(Q^all(X,man(X) => P)) --> [every,man], {reduce(Q,X,P)}.

18
October 2004CSA4050: Semantics III18 Result ?- s(X,[every,man,walks],[]). X = all(_G397, man(_G397),walk(_G397)) The effect of the reduce clause is –to identify the appropriate variables –to remove the λ variable

19
October 2004CSA4050: Semantics III19 Handling Quantified NPs Before we cheated by having every man as a lexical item. np(Q^all(X,man(X) => P)) --> [every,man], { reduce(Q,X,P)}. Now we see what is involved in analysing the NP from its parts. Step 1 is to write a new syntactic rule np(NP) --> d(D), n(N). How does the semantics work?

20
October 2004CSA4050: Semantics III20 LF of determiners Key idea is determiner has LF of a 2-argument function corresponding to R and S which become bound during processing. λR.λS.Q(V,R,S) where Q is associated with the particular determiner When we apply this function to the adjacent noun, we obtain the LF of the NP.

21
October 2004CSA4050: Semantics III21 How NP is created D R^S^all(X,R,S) every N Y^man(Y) man NP S^all(X,man(X),S)

22
October 2004CSA4050: Semantics III22 Fitting the Semantics Together Handle the quantified NP np(NP) --> d(D), n(N), {reduce(D,N,NP)}. Add lexical entry for every d(RL^SL^all(X,R => S)) -->[every], {reduce(RL,X,R), reduce(SL,X,S) }.

23
October 2004CSA4050: Semantics III23 DCG with Quantification Program 3 % grammar s(S) --> np(NP), vp(VP), {reduce(NP,VP,S)}. np(NP) --> d(D), n(N), {reduce(D,N,NP) }. vp(VP) --> v(VP). % lexicon v(X^walk(X)) --> [walks]. n(X^man(X)) --> [man]. d(RL^SL^all(X,R => S) --> [every], {reduce(RL,X,R), reduce(SL,X,S) }.

24
October 2004CSA4050: Semantics III24 Trace >: (7) s(_G510, [every, man, walks], []) >: (8) np(_L183, [every, man, walks], _L184) >: (9) d(_L205, [every, man, walks], _L206) <: (9) d((X^R)^ (X^S)^all(X, R, S), [every, man, walks], [man, walks]) >: (9) n(_L207, [man, walks], _L208) <: (9) n(Z^man(Z), [man, walks], [walks]) >: (9) reduce((X^R)^ (X^S)^all(X, R, S), Z^man(Z), _L183) <: (9) reduce((X^man(X))^ (X^S)^all(X, man(X), S), X^man(X), (X^S)^all(X, man(X), S)) <: (8) np((X^S)^all(X, man(X), S), [every, man, walks], [walks]) >: (8) vp(_L185, [walks], _L186) >: (9) v(_L185, [walks], _L186) <: (9) v(Y^walk(Y), [walks], []) <: (8) vp(Y^walk(Y), [walks], []) >: (8) reduce((X^S)^all(X, man(X), S), Y^walk(Y), _G510) <: (8) reduce((X^walk(X))^all(X, man(X), walk(X)), X^walk(X), all(X, man(X), walk(X))) <: (7) s(all(X, man(X), walk(X)), [every, man, walks], [])

Similar presentations

OK

CSA2050 Introduction to Computational Linguistics Parsing I.

CSA2050 Introduction to Computational Linguistics Parsing I.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 7 ages by william shakespeare Download ppt on coordinate geometry for class 9th physics Ppt on bluetooth wireless technology Download ppt on acid rain Ppt on power system analysis Ppt on power sharing in democracy power Ppt on condition based maintenance tools Ppt on product advertising Mrna display ppt online Animated ppt on magnetism projects