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Introduces a Gödel modal logic framework, enhancing semantics to ensure finite model properties.
We introduce GW, a Gödel modal logic based on Kripke models in which the value of each modal formula is witnessed by an accessible world.This witnessed semantics eliminates the limit-based phenomena that preclude the finite model property in the usual Kripke semantics for Gödel modal logics, thereby yielding a more constructive semantic framework.We present a sound and complete refutation calculus for GW and design a terminating backward proof-search procedure with countermodel generation.As a direct consequence of this procedure, GW enjoys the finite model property.
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Ferrari et al. (2026) studied this question.
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