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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.00445 |
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| _version_ | 1866908741956272128 |
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| author | Mojtahedi, Mojtaba |
| author_facet | Mojtahedi, Mojtaba |
| contents | We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the introduction of a new type of semantics, termed \emph{provability models}, for modal logics extending iGL. This semantics combines elements of standard Kripke semantics with provability in propositional modal logics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_00445 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Provability Logic of HA Mojtahedi, Mojtaba Logic We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the introduction of a new type of semantics, termed \emph{provability models}, for modal logics extending iGL. This semantics combines elements of standard Kripke semantics with provability in propositional modal logics. |
| title | On the Provability Logic of HA |
| topic | Logic |
| url | https://arxiv.org/abs/2206.00445 |