October 2004CSA4050 Advanced Techniques in NLP 1 CSA4050: Advanced Topics in NLP Semantics 6 Semantics of Questions and Assertions involving Quantification

October 2004CSA4050 Advanced Techniques in NLP 2 Classification of Questions Yes/NoContent 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?

October 2004CSA4050 Advanced Techniques in NLP 3 Classification of Assertions Without QuantificationSuzie walked Suzie kicked Felix With QuantificationSuzie kicked a cat. Every woman kicked Felix. A woman kicked the cat. The cat is a mammal

October 2004CSA4050 Advanced Techniques in NLP 4 Issues Handling questions ≠ Handling assertions Semantic issues: –What LF? –How to process LF Syntactic issues –how to parse sentences –how to build LF

October 2004CSA4050 Advanced Techniques in NLP 5 Semantics of Question Type Did all the cats sleep? how to represent meaning q1(all(X,cat(X),sleep(X)) how to process meaning provide 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.

October 2004CSA4050 Advanced Techniques in NLP 6 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?

October 2004CSA4050 Advanced Techniques in NLP 7 Semantics of Question Type Did a cat sleep? how to represent meaning q1(some(X,cat(X),sleep(X)) how to process meaning provide 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.

October 2004CSA4050 Advanced Techniques in NLP 8 Defining some some(_,R,S) :- R, S. NB Can this be made more efficient?

October 2004CSA4050 Advanced Techniques in NLP 9 Getting a List of Solutions Which cats sleep? The built in predicate setof(X,Goal,L) binds L to a list of X that satisfy Goal So for example with a database containing cat(majlo). sleep(majlo). cat(felix). sleep(felix). cat(cobweb). ?- setof(X,(cat(X),sleep(X)),L). L = [majlo,felix]

October 2004CSA4050 Advanced Techniques in NLP 10 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).

October 2004CSA4050 Advanced Techniques in NLP 11 Assertions with Quantification Universal Statements Universal statements are those whose LF involves all(,R,S). This translates into the Prolog clause S :- R Example –English= Every cat sleeps –LF= all(X,cat(X),sleep(X)). –Prolog = sleep(X) :- cat(X)

October 2004CSA4050 Advanced Techniques in NLP 12 Restrictions on Translation into Prolog Prolog uses the Horn Clause subset of FOL. A rule of the form a(X) :- a1(X),..., an(X) corresponds to the FOL statement  x (a1(x) &... & an(x)  a(x)) Outermost quantifier must be universally quantifed Conclusion must be a single predicate

October 2004CSA4050 Advanced Techniques in NLP 13 Assertions with Quantification: Simple existential statements With simple assertions like Suzie chased Felix we simply assert the corresponding LF chased(suzie,felix) into the database. This will not work with sentences like Suzie chased a cat whose LF is some(X,cat(X),chase(suzie,X))

October 2004CSA4050 Advanced Techniques in NLP 14 Establishing the truth of 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

October 2004CSA4050 Advanced Techniques in NLP 15 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).

October 2004CSA4050 Advanced Techniques in NLP 16 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

October 2004CSA4050 Advanced Techniques in NLP 17 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?

October 2004CSA4050 Advanced Techniques in NLP 18 Representing Meaning QuestionSemantic Representation Who sees Fido?q2(X,setof(Y,see(Y,fido),X)) Who did John see?q2(X,setof(Y,see(john,Y),X))

October 2004CSA4050 Advanced Techniques in NLP 19 How Internal Bindings Yield 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.

October 2004CSA4050 Advanced Techniques in NLP 20 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.