Interpolation properties for the bimodal provability logic $\mathbf{GR}$
| Autor: | Kogure, Haruka, Kurahashi, Taishi |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 22 pages |
| Databáze: | arXiv |
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