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arXiv · 2606.31906

A G\"odel Modal Logic Over Witnessed Models

Mauro Ferrari·Camillo Fiorentini·Paolo Giardini·Ricardo Oscar Rodriguez
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Abstract

We introduce GW, a G\"odel 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 G\"odel 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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Mauro Ferrari, Camillo Fiorentini, Paolo Giardini, Ricardo Oscar Rodriguez. 2026-06-30. A G\"odel Modal Logic Over Witnessed Models. https://doi.org/10.4204/eptcs.447.20

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