Axiomatizing logics of finite G\"odel-Kripke models

Amanda Vidal; Ricardo O. Rodriguez

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arXiv · 2605.15810

Axiomatizing logics of finite G\"odel-Kripke models

Amanda Vidal·Ricardo O. Rodriguez

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Abstract

We investigate completeness for modal G\"odel logics with respect to finite G\"odel-Kripke models, along with related aspects. It is well known that the logics studied in [4, 11] fail to be complete with respect to finite G\"odel-Kripke models. We show that the natural candidate axiomatic extensions do not restore completeness, thereby resolving a 15 year open problem posed in the aforementioned works. We then provide new axiomatizations that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics.

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BibTeX RIS

Amanda Vidal, Ricardo O. Rodriguez. 2026-05-15. Axiomatizing logics of finite G\"odel-Kripke models. https://arxiv.org/abs/2605.15810

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