Advanced Topics in NLP: Partial Execution and Proper Noun Transitive Verb Phrases

CSA4050:Advanced Topics in NLP Semantics IV Partial Execution Proper Noun Transitive Verb Phrase

Partial Execution • Partial execution involves the replacing of certain runtime computations with changes to the source of the Prolog program itself. • For example, we can replace the rule:s(S) --> np(NP), vp(VP) { reduce(NP,VP,S) }.withs(S) --> np(VP^S), vp(S). • This is because the computation of reduce involves only the mutual binding of several variables. CSA4050 Advanced NLP

How it works s(S) --> np(NP), vp(VP) { reduce(NP,VP,S)}. 1. match reduce(A^F,A,F) 2. rewrite s(F) --> np(A^F), vp(A). 3. rename s(S) --> np(VP^S), vp(VP). CSA4050 Advanced NLP

Exercise • What is the result of eliminating the reduce clause by partial execution in the following rule? np(NP) --> d(D), n(N), {reduce(D,N,NP)}. CSA4050 Advanced NLP

Answer np(NP) --> d(D), n(N) { reduce(D,N,NP)}. 1. match reduce(A^F,A,F) 2. rewrite np(F) --> d(A^F), n(A). 3. rename np(NP) --> d(N^NP), n(N). CSA4050 Advanced NLP

DCG with QuantificationProgram 4 % grammar s(S) --> np(VP^S), vp(VP). np(NP) --> d(N^NP), n(N). vp(VP) --> v(VP). % lexicon v(X^walk(X)) --> [walks]. n(X^man(X)) --> [man]. n(suzie) --> [‘Suzie’]. det(RL^SL^all(X,R,S) --> [every], {reduce(RL,X,R), reduce(SL,X,S) }. CSA4050 Advanced NLP

Handling Proper Nouns • The grammar handles every man walksX = all(_G, man(_G), walk(_G)) • Will this grammar parse Suzie walks? • Let’s try it! • ?- s(X,['Suzie',walks],[ ]). CSA4050 Advanced NLP

?- s(X,['Suzie',walks],[ ]). Call: (8) s(_G492, ['Suzie', walks], []) ? Call: (9) np(_L183, ['Suzie', walks], _L184) ? Call: (10) pn(_L183, ['Suzie', walks], _L184) ? Exit: (10) pn(suzie, ['Suzie', walks], [walks]) ? Exit: (9) np(suzie, ['Suzie', walks], [walks]) ? Call: (9) vp(_L185, [walks], _L186) ? Call: (10) iv(_L185, [walks], _L186) ? Exit: (10) iv(_G556^walk(_G556), [walks], []) ? Exit: (9) vp(_G556^walk(_G556), [walks], []) ? Call: (9) reduce(suzie, _G556^walk(_G556), _G492) ? Fail: (9) reduce(suzie, _G556^walk(_G556), _G492)? ........ suzie is not a function

Handling Proper Nouns • Problem is with the “type” of LF of Suzie. • We require that LF of Suzie has the same type as any other NP - such as every man, i.e. • As a lambda expression it would be λp.p(suzie). • In Prolog we can regard this as a function from [VP] to [S] such that reduce(VP,john,S) holds. CSA4050 Advanced NLP

DCG with QuantificationProgram 4 % grammar s(S) --> np(VP^S), vp(VP). np(NP) --> n(NP). np(NP) --> d(N^NP), n(N). vp(VP) --> v(VP). % lexicon v(X^walk(X)) --> [walks]. n(X^man(X)) --> [man]. n(VP^S) --> [‘Suzie’], {reduce(VP,suzie,S)}. det(RL^SL^all(X,R => S) --> [every], {reduce(RL,X,R), reduce(SL,X,S) }. CSA4050 Advanced NLP

Exercise 2 Using partial execution, eliminate the reduce clause in pn(VP^S) --> [‘Suzie’],{reduce(VP,suzie,S)}. CSA4050 Advanced NLP

s(X, ['Suzie', walks], [ ]) ? Call: (7) s(_G292, ['Suzie', walks], []) ? ↓ Exit: (9) pn((suzie^_G357)^_G357, ['Suzie', walks], [walks]) ? ↓ Exit: (9) iv(_G362^walk(_G362), [walks], []) ? Exit: (8) vp(_G362^walk(_G362), [walks], []) ? : Call: (8) reduce((suzie^_G357)^_G357, _G362^walk(_G362), _G292) ? : Exit: (8) reduce((suzie^walk(suzie))^walk(suzie), suzie^walk(suzie), walk(suzie)) ? Exit: (7) s(walk(suzie), ['Suzie', walks], []) ? creep X = walk(suzie) CSA4050 Advanced NLP

Transitive Verb Phases • Transitive verb phrases take an object, e.g.chased a cat • To handle transitive VPs we need another VP rulevp(VP) --> v(V), np(NP). • In this case we have: V = λx. λy. chased(x,y) NP = λs.some(w,cat(w),s(w)) • Issues: • What is the LF of the resulting VP and • How do the component LFs combine? CSA4050 Advanced NLP

Resulting VP λz.some(y,cat(y),chased(z,y)) • Note that this has the form of a standard VP that is waiting for a subject, so is compatible with the rest of the grammar. CSA4050 Advanced NLP

Making VP VP λz.some(y,cat(y),chased(z,y)) V λx. λy. chased(x,y) chased NP λs.some(w,cat(w),s(w)) some cat CSA4050 Advanced NLP

Apply NP to Vdoesn't work! λs.some(w,cat(w), s(w)) (λx. λy. chased(x,y)) β some(w,cat(w), (λy. λx. chased(x,y))(w)) β some(w,cat(w), λx.chased(x,w)) NP V CSA4050 Advanced NLP

Solution • Need a more complex way of combining V and NP:λNP.λV.λz.NP(V(z)) λs.some(w,cat(w), s(w)) ← NP arg λx. λy. chased(x,y))← V arg CSA4050 Advanced NLP

How it works λNP.λV.λz.NP(V(z)) λs.some(w,cat(w), s(w)) λx. λy. chased(x,y)) λ z.λs.some(w,cat(w), s(w)) λx.λy.chased(x,y)(z) β λ z.λs.some(w,cat(w), s(w)) (λy. chased(z,y)) β λ z. some(cat(w), (λy.chased(z,y))(w)) β λ z. some(cat(w), chased(z,w)) CSA4050 Advanced NLP

VP Rule Revisited vp(VP) --> v(V), np(NP), {instructions}. • The instructions encode the combinationλNP.λV.λz.NP(V(z))vp(Z^P) --> v(V2), np(NP), {reduce(V2,Z,V1), reduce(NP,V1,P)}. CSA4050 Advanced NLP

Program 5 % grammar s(S) --> np(NP), vp(VP), {reduce(NP,VP,S)}. np(NP) --> n(NP). np(NP) --> d(D), n(N), {reduce(D,N,NP) }. vp(VP) --> v(VP). vp(Z^P)--> v(V2), np(NP), {reduce(V2,Z,V1), reduce(NP,V1,P)}. % lexicon v(X^walk(X)) --> [walks]. v(X^Y^chased(X,Y)) --> [chased]. n(X^cat(X)) --> [cat]. n(VP^S) --> [suzie], {reduce(VP,suzie,S)}. d(RL^SL^some(X,R,S)) --> [a], {reduce(RL,X,R),reduce(SL,X,S) }. CSA4050 Advanced NLP

Test ?- s(X,[suzie,chased,a,cat],[]). X = some(_G245, cat(_G245), chased(suzie, _G245)) ?- s(X,[a,cat,chased,a,cat],[]). X = some(_G245, cat(_G245), some(_G266, cat(_G266), chased(_G245, _G266))) ; CSA4050 Advanced NLP

Advanced Topics in NLP: Partial Execution and Proper Noun Transitive Verb Phrases