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Logic Programs under Three-Valued Łukasiewicz Semantics

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Logic Programming (ICLP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5649))

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Abstract

If logic programs are interpreted over a three-valued logic, then often Kleene’s strong three-valued logic with complete equivalence and Fitting’s associated immediate consequence operator is used. However, in such a logic the least fixed point of the Fitting operator is not necessarily a model for the program under consideration. Moreover, the model intersection property does not hold. In this paper, we consider the three-valued Łukasiewicz semantics and show that fixed points of the Fitting operator are also models for the program under consideration and that the model intersection property holds. Moreover, we review a slightly different immediate consequence operator first introduced by Stenning and van Lambalgen and relate it to the Fitting operator under Łukasiewicz semantics. Some examples are discussed to support the claim that Łukasiewicz semantics and the Stenning and van Lambalgen operator is better suited to model commonsense and human reasoning.

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Author information

Authors and Affiliations

  1. International Center for Computational Logic, TU Dresden, 01062, Dresden, Germany

    Steffen Hölldobler & Carroline Dewi Puspa Kencana Ramli

Authors
  1. Steffen Hölldobler
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  2. Carroline Dewi Puspa Kencana Ramli
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Editor information

Editors and Affiliations

  1. School of Computing, University of Leeds, LS2 9JT, Leeds, UK

    Patricia M. Hill

  2. Deptartment of Computer Science, Stony Brook University, 11794-4400, Stony Brook, NY, USA

    David S. Warren

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Hölldobler, S., Kencana Ramli, C.D.P. (2009). Logic Programs under Three-Valued Łukasiewicz Semantics. In: Hill, P.M., Warren, D.S. (eds) Logic Programming. ICLP 2009. Lecture Notes in Computer Science, vol 5649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02846-5_37

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  • DOI: https://doi.org/10.1007/978-3-642-02846-5_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02845-8

  • Online ISBN: 978-3-642-02846-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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