A generalized gelfond-lifschitz transformation for logic programs with abstract constraints

  • Authors:

  • Yi-Dong Shen;Jia-Huai You

  • Affiliations:

  • State Key Laboratory of Computer Science, Institute of Software, the Chinese Academy of Sciences, Beijing, China;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada

  • Venue:
  • AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
  • Year:
  • 2007

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Abstract

We present a generalized Gelfond-Lifschitz transformation in order to define stable models for a logic program with arbitrary abstract constraints on sets (c-atoms). The generalization is based on a formal semantics and a novel abstract representation of c-atoms, as opposed to the commonly used power set form representation. In many cases, the abstract representation of a c-atom results in a substantial reduction of size from its power set form representation. We show that any c-atom A = (Ad, Ac) in the body of a clause can be characterized using its satisfiable sets, so that given an interpretation I the c-atom can be handled simply by introducing a special atom θA together with a new clause θA ← A1, ..., An for each satisfiable set {A1, ..., An} of A. We also prove that the latest fixpoint approach presented by Son et al. and our approach using the generalized Gelfond-Lifschitz transformation are semantically equivalent in the sense that they define the same set of stable models.