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Typed answer set programming lambda calculus theories and correctness of inverse lambda algorithms with respect to them

Published online by Cambridge University Press:  05 September 2012

CHITTA BARAL ,
JURAJ DZIFCAK ,
MARCOS A. GONZALEZ  and
AARON GOTTESMAN
CHITTA BARAL
Affiliation:
School of Computing, Informatics, and Decision Systems EngineeringArizona State University, Tempe, AZ
JURAJ DZIFCAK
Affiliation:
School of Computing, Informatics, and Decision Systems EngineeringArizona State University, Tempe, AZ
MARCOS A. GONZALEZ
Affiliation:
School of Computing, Informatics, and Decision Systems EngineeringArizona State University, Tempe, AZ
AARON GOTTESMAN
Affiliation:
School of Computing, Informatics, and Decision Systems EngineeringArizona State University, Tempe, AZ
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Abstract

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a dictionary of words and their ASP-lambda formulas. However such an approach is not scalable. In this paper our focus is on two algorithms that allow one to construct ASP-lambda formulas in an inverse manner. In particular the two algorithms take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F such that F with input as G, denoted by F@G, is equal to H; and similarly G@F = H. We present correctness and complexity results about these algorithms. To do that we develop the notion of typed ASP-lambda calculus theories and their orders and use it in developing the completeness results.

Keywords

natural language understandinganswer set programminglambda calculusinverse lambda algorithms
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 12 , Issue 4-5: 28th International Conference on Logic Programming , July 2012 , pp. 775 - 791
Copyright
Copyright © Cambridge University Press 2012

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