Towards a Proof Theory of G\"odel Modal Logics
George Metcalfe (University of Bern), Nicola Olivetti (Paul Cezanne, University)
TL;DR
This paper develops proof calculi for G"odel modal logics combining Kripke semantics with many-valued logic, establishing their completeness and complexity results.
Contribution
It introduces analytic proof calculi for G"odel modal logics' box and diamond fragments, connecting modal and fuzzy logic semantics.
Findings
Proof calculi for G"odel modal logics are established.
Completeness and complexity results are proven for these fragments.
The work bridges modal logic with fuzzy logic semantics.
Abstract
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments.
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