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Counter-Model Search in Gödel-Dummett Logics

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Book cover Automated Reasoning (IJCAR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3097))

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Abstract

We present a new method for deciding Gödel-Dummett logic LC. We first characterize the validity of irreducible sequents of LC by the existence of r-cycles in bi-colored graphs and we propose a linear algorithm to detect r-cycles and build counter-models. Then we characterize the validity of formulae by the existence of r-cycles in boolean constrained graphs. We also give a parallel method to detect r-cycles under boolean constraints. Similar results are given for the finitary versions LC n .

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Author information

Authors and Affiliations

  1. LORIA – CNRS, Campus Scientifique, BP 239, Vandœuvre-lès-Nancy, France

    Dominique Larchey-Wendling

Authors
  1. Dominique Larchey-Wendling
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Editor information

Editors and Affiliations

  1. Information Security Group, Dep. of Computer Science, ETH, Zurich, Switzerland

    David Basin

  2. LORIA & INRIA Lorraine UMR 7503,  

    Michaël Rusinowitch

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© 2004 Springer-Verlag Berlin Heidelberg

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Larchey-Wendling, D. (2004). Counter-Model Search in Gödel-Dummett Logics. In: Basin, D., Rusinowitch, M. (eds) Automated Reasoning. IJCAR 2004. Lecture Notes in Computer Science(), vol 3097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25984-8_19

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  • DOI: https://doi.org/10.1007/978-3-540-25984-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22345-0

  • Online ISBN: 978-3-540-25984-8

  • eBook Packages: Springer Book Archive

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