Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Handbook of logic in computer science (vol. 2)
Basic simple type theory
The syntactic process
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Wide-coverage efficient statistical parsing with ccg and log-linear models
Computational Linguistics
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Inducing probabilistic CCG grammars from logical form with higher-order unification
EMNLP '10 Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing
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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.