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.
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Metcalfe, G., Olivetti, N. (2009). Proof Systems for a Gödel Modal Logic. In: Giese, M., Waaler, A. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2009. Lecture Notes in Computer Science(), vol 5607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02716-1_20
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DOI: https://doi.org/10.1007/978-3-642-02716-1_20
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