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Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics

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Logic Programming and Nonmotonic Reasoning (LPNMR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2173))

Abstract

In this paper, we continue to explore many-valued disjunctive logic programs with probabilistic semantics. In particular, we newly introduce the least model state semantics for such programs. We show that many-valued disjunctive logic programs under the semantics of minimal models, perfect models, stable models, and least model states can be unfolded to equivalent classical disjunctive logic programs under the respective semantics. Thus, existing technology for classical disjunctive logic programming can be used to implement many-valued disjunctive logic programming. Using these results on unfolding many-valuedness, we then give many-valued fixpoint characterizations for the set of all minimal models and the least model state. We also describe an iterative fixpoint characterization for the perfect model semantics under finite local stratification.

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Authors and Affiliations

  1. Institut und Ludwig Wittgenstein Labor für Informationssysteme, TU Wien Favoritenstraße 9-11, A-1040, Vienna, Austria

    Thomas Lukasiewics

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  1. Thomas Lukasiewics
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Editors and Affiliations

  1. Institut für Informationssysteme, Vienna University of Technology, 1040, Wien, Austria

    Thomas Eiter

  2. Institut für Informationssysteme, Vienna University of Technology, 1040, Wien, Austria

    Wolfgang Faber

  3. Department of Computer Science Lexington, University of Kentucky, KY, 40506-0046, USA

    Miros law Truszczyński

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© 2001 Springer-Verlag Berlin Heidelberg

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Lukasiewics, T. (2001). Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics. In: Eiter, T., Faber, W., Truszczyński, M.l. (eds) Logic Programming and Nonmotonic Reasoning. LPNMR 2001. Lecture Notes in Computer Science(), vol 2173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45402-0_25

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  • DOI: https://doi.org/10.1007/3-540-45402-0_25

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  • Print ISBN: 978-3-540-42593-9

  • Online ISBN: 978-3-540-45402-1

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