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Graph-based Decision for Gödel-Dummett Logics

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Abstract

We present a graph-based decision procedure for Gödel-Dummett logics and an algorithm to compute countermodels. A formula is transformed into a conditional bicolored graph in which we detect some specific cycles and alternating chains using matrix computations. From an instance graph containing no such cycle, (resp. no (n + 1)-alternating chain) we extract a countermodel in LC, (resp. LC n ).

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Authors and Affiliations

  1. LORIA – CNRS, Campus Scientifique, BP 239 54 506, Vandœuvre-lès-Nancy, France

    Dominique Larchey-Wendling

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  1. Dominique Larchey-Wendling
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Correspondence to Dominique Larchey-Wendling.

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Larchey-Wendling, D. Graph-based Decision for Gödel-Dummett Logics. J Autom Reasoning 38, 201–225 (2007). https://doi.org/10.1007/s10817-006-9047-9

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  • DOI: https://doi.org/10.1007/s10817-006-9047-9

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