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Set Constraints in Logic Programming

  • Conference paper
Logic Programming and Nonmonotonic Reasoning (LPNMR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2923))

Abstract

We investigate a generalization of weight-constraint programs with stable semantics, as implemented in the ASP solver smodels. Our programs admit atoms of the form \(\langle X,\mathcal{F} \rangle\) where X is a finite set of propositional atoms and \(\mathcal{F}\) is an arbitrary family of subsets of X. We call such atoms set constaints and show that the concept of stable model can be generalized to programs admitting set constraints both in the bodies and the heads of clauses. Natural tools to investigate the fixpoint semantics for such programs are nondeterministic operators in complete lattices. We prove two fixpoint theorems for such operators.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, Lexington, KY, 40506, USA

    Victor W. Marek

  2. Department of Mathematics, University of California, La Jolla, CA, 92093, USA

    Jeffrey B. Remmel

Authors
  1. Victor W. Marek
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  2. Jeffrey B. Remmel
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Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Texas at Austin, USA

    Vladimir Lifschitz

  2. Department of Information and Computer Science, Helsinki University of Technology TKK,  

    Ilkka Niemelä

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Marek, V.W., Remmel, J.B. (2003). Set Constraints in Logic Programming. In: Lifschitz, V., Niemelä, I. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2004. Lecture Notes in Computer Science(), vol 2923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24609-1_16

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  • DOI: https://doi.org/10.1007/978-3-540-24609-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20721-4

  • Online ISBN: 978-3-540-24609-1

  • eBook Packages: Springer Book Archive

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