Linking Syntax and Semantics • Introduction • Semantics Interpretation and Compositionality • A Simple Grammar with Semantic Interpretation Ch. 9 Linking Syntax and Semantics 1
Introduction • Semantic analysis follows syntactic analysis, in trying to determine what a sentence means. • Aim is to use: • representations of what individual words mean • representation of structure of the sentence (parse tree) and obtain a representation of the sentence meaning. • Ignores context and world knowledge - meaning representation may still leave some things unspecified. (e.g., ``He loves Mary'' - who is ``He''). Ch. 9 Linking Syntax and Semantics 2
Representing Sentence Meaning • Many formalisms have been proposed to represent the meaning of a sentence. • Most common is to use a logic. Predicate logic is a good place to start. • But.. predicate logic not powerful enough to represent all NL sentences (at least not in simple way). • So on the one hand more complex logics have been suggested. • And on the other hand more informal notations have been used (e.g., case frames). Ch. 9 Linking Syntax and Semantics 3
Semantic Interpretation and Compositionality • Determining the meaning of a sentence will be much simpler if we can find the meaning of a constituent solely from the meanings of its sub constituents in the parse tree. • e.g., Find meaning of sentence by combining meaning of noun phrase with meaning of verb phrase. • Rule for combining meanings should be independent of how noun phrase or verb phrase meanings were found. • This is referred to as compositional semantics. • But.. developing a good compositional model is very difficult. Ch. 9 Linking Syntax and Semantics 4
Why Compositional Semantics is Hard • Syntactic structure doesn't always map in any nice way onto semantic structure: – e.g., syntax: s vp np np name v art n John (loves (every dog)) • Semantics (LF): Every d: (DOG1 d) (LOVES1 I1 (NAME j1 “John”) d)) • Un-scoped version is (LOVES1 I1 (NAME j1 “John”)<EVERY d DOG1>) • Presence of idioms e.g Jack kicked the bucket, which means Jack died. Ch. 9 Linking Syntax and Semantics 5
Compositional Semantics: A first Attempt • Consider ``John jumps'', with semantics jumps(john). • How do we give a ``semantics'' to each word (``john'' and ``jumps'') so they may be combined to give the expression above? • A simple answer: Represent the semantics using lambda expressions e.g., ``jumps'' = (Lambda x jumps(x)) . ``John'' = john. • The semantics for jump is now a function with one argument. • When this function is applied to an argument (e.g., john, the value of that argument is substituted for x: jumps(john). Ch. 9 Linking Syntax and Semantics 6
Lambda Calculus (Lambda x .f) is a function with one argument. (Lambda x .f) (v) is equivalent to f , with every occurence of x replaced by v. This is known as lambda reduction . So.. (Lambdax.x +1)(2) =2+1 and (Lambda x.f(x,y))(3)= f(3,y) (Lambda y.f(x,y))(3)= f(x,3) (Lambda x.loves(john,x))(marry)= loves(john,marry) We can also have nested lambda expressions, with the outer most one applied first. (Lambda x.lambda y.f(x,y))(2)= (lambda y. f(2,y)) (Lambda x.lambda y.f(x,y))(2)(3) = f(2,3) Ch. 9 Linking Syntax and Semantics 7
Combining Syntax and Semantics Two ways to combine syntactic and semantic analysis. 1. Parse sentence first. Then use parse tree to guide how semantics of words should be combined. 2. Do both at same time. Work out semantics of constituents while parsing sentences. Ch. 9 Linking Syntax and Semantics 8
Compositional Semantics Using Lambda Calculus Let each word in the lexicon have an associated lambda expression as its semantics: • ``jumps'': (lambda x. jumps(x)) • ``Mary'': mary • ``John'': john We now associate, with each grammar rule, a rule for combining the semantics of subconstituents. s(Sem) --> np(NPSem), vp(VPSem), {Apply VPSem to NPSem to get Sem}. np(Sem) --> name(Sem). vp(Sem) --> v(Sem). Now, to find the semantics of ``John jumps'' we apply (lambda x. jumps(x)) to john to get: (lambda x. jumps(x))(john) = jumps ( john ) Ch. 9 Linking Syntax and Semantics 9
A More Complex Example What about ``John loves Mary''? Will the same approach work? Yes, if we make the semantics for ``loves'' a little more complex: ``loves'': (lambda x. lambda y. loves(y,x)) s(Sem) --> np(NPSem), vp(VPSem), {Apply VPSem to NPSem to get Sem}. vp(Sem) --> v(VSem), np(NSem), {Apply VSem to NSem to get Sem} Now semantics for ``loves Mary'' is: (lambda x. lambda y. loves(y,x))(marry) = (lambda y.loves(y,marry) then combining with the semantics for John we get: (lambda y.loves(y,marry))(john) = loves ( john , mary ) Ch. 9 Linking Syntax and Semantics 10
Example Parse Tree with Semantics Ch. 9 Linking Syntax and Semantics 11
Doing it all in Prolog • To do it in Prolog we need a notation for lambda expressions, and a way of combining them (lambda reduction). Notation: X^ loves(X,Y) ==(Lambda x, loves(x,y)). X^Y^loves(X, Y)==(Lambda x.Lambda y.loves(x,y)). Combining: We want to be able to reduce (Lambda x.loves(x,john))(mary) to get loves ( mary , john ). So in Prolog we want: ?- reduce(X ^ loves(X, john), mary, Answer). Answer = loves(mary, john). Exercise: Try writing a reduce predicate to do this! Ch. 9 Linking Syntax and Semantics 12
A First Grammar with Semantics in Prolog Once we have a ``reduce'' predicate we can rely on pattern matching: s(Sem) --> np(NSem), vp(VSem), {reduce(VSem, NSem, Sem)}. vp(VP) --> tv(TV), np(NP), {reduce(TV, NP, VP)}. np(NP) --> propn(NP). tv(X^Y^loves(Y, X)) --> [loves]. propn(john) --> [john]. propn(mary) --> [mary]. Analysis of ``John loves Mary'': loves: TV = X^Y^loves(Y, X) Mary: NP = mary. combine to give: vp: VSem = Y^loves(Y,mary) combined with John: NSem = john gives: s: Sem = loves(john, mary). Ch. 9 Linking Syntax and Semantics 13
A Small Lexicon a(art AGR 3s SEM INDEF1) can(aux SUBCAT base SEM CAN1) car(n SEM CAR1 AGR 3s) cry(v SEM CRY1 VFORM base SUBCAT _none) decide(v SEM DECIDE1 VFORM base S UBCAT _none) decide(v SEM DECIDE-ON1 VFORM base SUBCAT _pp:on) dog(n SEM DOG1 AGR 3s) fish(n SEM FISH1 AGR 3s) fish(n SEM (PLUR FISH1) AGR 3p) he(pro SEM HE1 AGR 3s) man(n SEM MAN1 AGR 3s) men(n SEM (PLUR MAN1) AGR 3p) Jill(name AGR 3s SEM “Jill”) ……. ………. Ch. 9 Linking Syntax and Semantics 14
Morphological Rules with Semantic Interpretation (V VFORM pres AGR 3s SEM <PRES ?semv) � (V VFORM base IRREG-PRES - SEM ?semv) + S (V VFORM ing SEM ?semv) � (V VFORM base SEM ?semv) + ING (V VFORM pastprt SEM ?semv) � (V VFORM base EN-PASTPRT + SEM ?semv) + EN (N AGR 3p SEM (PLUR ?sem)) � (N AGR 3s IRREG-PL – SEM ?semv) Ch. 9 Linking Syntax and Semantics 15
Summary • Semantic analysis will be much easier if we can find a way to compose the semantics of sub-constituents to get the semantics of a constituent. • Hence ultimately composing the semantics of words, given the structure of a sentence, to give the semantics of a sentence. • One way to do this is to use lambda calculus as the language for semantics of words. • Example: combining , john, and mary, to give loves ( john , mary ). Ch. 9 Linking Syntax and Semantics 16
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