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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.10309 |
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| _version_ | 1866909399045373952 |
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| author | Shamkanov, Daniyar |
| author_facet | Shamkanov, Daniyar |
| contents | We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the cut-elimination theorem following the lines of so called continuous cut elimination. Our consideration also covers ordinary proofs of K+ since they correspond to cyclic cut-free proofs of the presented sequent calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10309 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On structural proof theory of the modal logic K+ extended with infinitary derivations Shamkanov, Daniyar Logic We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the cut-elimination theorem following the lines of so called continuous cut elimination. Our consideration also covers ordinary proofs of K+ since they correspond to cyclic cut-free proofs of the presented sequent calculus. |
| title | On structural proof theory of the modal logic K+ extended with infinitary derivations |
| topic | Logic |
| url | https://arxiv.org/abs/2310.10309 |