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

Chitta Baral, Juraj Dzifcak, Marcos A. Gonzalez, Aaron Gottesman

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)775-791
Number of pages17
JournalTheory and Practice of Logic Programming
Volume12
Issue number4-5
DOIs
StatePublished - Jul 1 2012

Keywords

  • answer set programming
  • inverse lambda algorithms
  • lambda calculus
  • natural language understanding

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics
  • Artificial Intelligence

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