A basic propositional modal fuzzy logic \({\sf {GK}}_{\Box}\) is defined by combining the Kripke semantics of the modal logic K with the many-valued semantics of Gödel logic G. A sequent of relations calculus is introduced for \({\sf {GK}}_{\Box}\) and a constructive counter-model completeness proof is given. This calculus is used to establish completeness for a Hilbert-style axiomatization and Gentzen-style hypersequent calculus admitting cut-elimination, and to show that the logic is PSPACE-complete.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • George Metcalfe
    • 1
  • Nicola Olivetti
    • 2
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA
  2. 2.LSIS-UMR CNRS 6168Université Paul CézanneMarseille Cedex 20France

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