Proof Systems for a Gödel Modal Logic

Authors:
George Metcalfe;Nicola Olivetti
Affiliations:
Department of Mathematics, Vanderbilt University, Nashville, USA TN 37240;LSIS-UMR CNRS 6168, Université Paul Cézanne, Marseille Cedex 20, France 13397
Venue:
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Year:
2009

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Abstract

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.