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arXiv · 2311.10583

Interpolation properties for the bimodal provability logic $\mathbf{GR}$

Haruka Kogure·Taishi Kurahashi
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Abstract

We study interpolation properties for Shavrukov's bimodal logic $\mathbf{GR}$ of usual and Rosser provability predicates. For this purpose, we introduce a new sublogic $\mathbf{GR}^\circ$ of $\mathbf{GR}$ and its relational semantics. Based on our new semantics, we prove that $\mathbf{GR}^\circ$ and $\mathbf{GR}$ enjoy Lyndon interpolation property and uniform interpolation property.

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Haruka Kogure, Taishi Kurahashi. 2023-11-17. Interpolation properties for the bimodal provability logic $\mathbf{GR}$. https://arxiv.org/abs/2311.10583

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