Provability Models

Mojtaba Mojtahedi; Borja Sierra Miranda

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arXiv · 2510.06696

Provability Models

Mojtaba Mojtahedi·Borja Sierra Miranda

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Abstract

In this paper, we study a new Kripke-style semantics for classical modal logic, named as provability models. We study provability models for the propositional modal logics K, K4, S4 GL, GLP and the interpretability logic ILM. Provability models combine features of Kripke models with the assignment of logics to individual worlds. Originally introduced in [Mojtahedi, 2022], these models allowed the first author to establish arithmetical completeness for intuitionistic provability logic. Interestingly, we show that the ILM is complete for the same provability models of GL. We improve provability models to predicative and decidable provability models in the case of GL and ILM. Furthermore, we prove a soundness and completeness of GLP for provability models.

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BibTeX RIS

Mojtaba Mojtahedi, Borja Sierra Miranda. 2025-11-19. Provability Models. https://arxiv.org/abs/2510.06696

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