october 2004csa4050 advanced techniques in nlp 1 csa4050: advanced topics in nlp semantics 6...

October 2004 CSA4050 Advanced Techniques in NLP

1

CSA4050: Advanced Topics in NLP

Semantics 6

Semantics of Questions and Assertions involving Quantification


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Classification of Questions

Yes/No Content Answer

Without Quantification

Did Suzie walk?

Did Suzie kick Felix?

Who walked?

Who kicked Felix?

Who did Suzie kick?

With Quantification

Did all the cats sleep?

Did a cat sleep?

Did someone kick Felix?

Which cats slept?

How many children slept?


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Classification of Assertions

Without Quantification Suzie walked

Suzie kicked Felix

With Quantification Suzie kicked a cat.

Every woman kicked Felix.

A woman kicked the cat.

The cat is a mammal


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Issues

• Handling questions ≠ Handling assertions

• Semantic issues:– What LF?– How to process LF

• Syntactic issues– how to parse sentences– how to build LF


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Semantics of Question TypeDid all the cats sleep?

• how to represent meaningq1(all(X,cat(X),sleep(X))

• how to process meaningprovide definition for all(X,R,S)

• intuitively, this succeeds if for every X where R succeeds, S also succeeds

• it fails if there is a single counterexample i.e. cat(X) succeeds and sleep(X) fails.


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Defining all

all(_,R,S) :-\+(R,\+S).

NB• \+ (G) succeeds if G fails.• Goal1,Goal2 succeeds if Goal1, then

Goal2 succeed• What happens if R fails?


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Semantics of Question TypeDid a cat sleep?

• how to represent meaningq1(some(X,cat(X),sleep(X))

• how to process meaningprovide definition for some(X,R,S)

• intuitively, this succeeds if there is an X which satisfies R and S.

• it fails if there is no such X. Only one example need be established.


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Defining some

some(_,R,S) :-

R, S.

NB

• Can this be made more efficient?


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Getting a List of SolutionsWhich cats sleep?

• The built in predicatesetof(X,Goal,L)binds L to a list of X that satisfy Goal

• So for example with a database containingcat(majlo). sleep(majlo). cat(felix). sleep(felix). cat(cobweb).

• ?- setof(X,(cat(X),sleep(X)),L).L = [majlo,felix]


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How many cats slept?

• "How many" questions require a numerical answer that is obtained by counting the number of solutions.

• This can be acheived as follows using setof in conjunction with the built-in length predicate.

howmany(X,Goal,N) :-

setof(X,Goal,L),

length(L,N).


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Assertions with QuantificationUniversal Statements

• Universal statements are those whose LF involves all(<var>,R,S).

• This translates into the Prolog clauseS :- R

• Example– English = Every cat sleeps– LF = all(X,cat(X),sleep(X)).– Prolog = sleep(X) :- cat(X)


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Restrictions on Translationinto Prolog

• Prolog uses the Horn Clause subset of FOL.

• A rule of the forma(X) :- a1(X), ..., an(X)corresponds to the FOL statementx (a1(x) & ... & an(x) a(x))

• Outermost quantifier must be universally quantifed

• Conclusion must be a single predicate


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Assertions with Quantification:Simple existential statements

• With simple assertions like Suzie chased Felixwe simply assert the corresponding LF chased(suzie,felix) into the database.

• This will not work with sentences likeSuzie chased a catwhose LF is some(X,cat(X),chase(suzie,X))


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Establishing the truthof quantified sentences

• In order to find out what has to be asserted, let’s see what happens with corresponding query, given that some(_,R,S) :- R, S.

• Clearly, the query?- some(X,cat(X),chase(suzie,X)).will cause subgoals cat(X), chase(suzie,X) to be tried.

• These will fail


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Anonymous Names

• cat(X) and chased(suzie,felix) will succeed if we have, e.g. cat(felix), chased(suzie,felix) in the database.

• But when we assert some(X,cat(X),chased(suzie,X))no such name is mentioned, so we have to invent an anonymous name.

• The simplest names are integers:cat(100). chased(suzie,100).


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Discourse Referents

• Such names are more properly called discourse referents. Discourse referents are entities that are referred to by different parts of a discourse.

• Some parts introduce new DRs. Others refer back to already established DRs.

• Discourse Representation Theory

• A baby cried. He was hungry


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Interpreting Wh Questions

• Semantically, issue is quite simple• We want the semantic interpretation of the

question to query the database and bind the result to a variable.

• Let SEM be the semantic interpretation of "who sees fido“. We want the following behaviour

?- interpret(SEM,Ans)Ans = [john,mary]

• What does SEM have to look like?


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Representing Meaning

Question Semantic Representation

Who sees Fido? q2(X,setof(Y,see(Y,fido),X))

Who did John see? q2(X,setof(Y,see(john,Y),X))


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How Internal BindingsYield the Answer

interpret(q2(X, ....X....),X)

• The first occurrence of X identifies what the unknown is called.

• The second occurrence identifies where the unknown information is situated in the second arg. position of q2).

• The last occurrence will become bound to the answer.


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Syntax of Wh Questions

• How do we build the right semantic representation from the question?

• Need to look carefully at the syntactic structure of the questions.

• In particular, need to look at the way sentences have been derived.

• Hypothesis: the word who can substitute any noun phrase.

october 2004csa4050 advanced techniques in nlp 1 csa4050: advanced topics in nlp semantics 6...

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