Axiomatizing logics of finite G\"odel-Kripke models
Logic
2026-05-18 v1
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.
Keywords
Cite
@article{arxiv.2605.15810,
title = {Axiomatizing logics of finite G\"odel-Kripke models},
author = {Amanda Vidal and Ricardo O. Rodriguez},
journal= {arXiv preprint arXiv:2605.15810},
year = {2026}
}