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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2007: Logic Programming and Nonmonotonic Reasoning pp 84–96Cite as

Well-Founded Semantics and the Algebraic Theory of Non-monotone Inductive Definitions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4483))

Abstract

Approximation theory is a fixpoint theory of general (monotone and non-monotone) operators which generalizes all main semantics of logic programming, default logic and autoepistemic logic. In this paper, we study inductive constructions using operators and show their confluence to the well-founded fixpoint of the operator. This result is one argument for the thesis that Approximation theory is the fixpoint theory of certain generalised forms of (non-monotone) induction. We also use the result to derive a new, more intuitive definition of the well-founded semantics of logic programs and the semantics of ID-logic, which moreover is easier to implement in model generators.

Works supported by IWT VLaanderen, FWO Vlaanderen.

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Authors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Belgium

    Marc Denecker & Joost Vennekens

Authors
  1. Marc Denecker
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  2. Joost Vennekens
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Chitta Baral Gerhard Brewka John Schlipf

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Denecker, M., Vennekens, J. (2007). Well-Founded Semantics and the Algebraic Theory of Non-monotone Inductive Definitions. In: Baral, C., Brewka, G., Schlipf, J. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2007. Lecture Notes in Computer Science(), vol 4483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72200-7_9

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  • DOI: https://doi.org/10.1007/978-3-540-72200-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72199-4

  • Online ISBN: 978-3-540-72200-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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