Proof Theory for Bimodal Provability Logics
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914566973161472 |
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| author | Miranda, Borja Sierra Studer, Thomas |
| author_facet | Miranda, Borja Sierra Studer, Thomas |
| contents | We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of our calculi, and use them to establish a cut-elimination procedure. Finally, we prove the first interpolation results for these logics showing that they all enjoy the uniform Lyndon interpolation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12351 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof Theory for Bimodal Provability Logics Miranda, Borja Sierra Studer, Thomas Logic We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of our calculi, and use them to establish a cut-elimination procedure. Finally, we prove the first interpolation results for these logics showing that they all enjoy the uniform Lyndon interpolation property. |
| title | Proof Theory for Bimodal Provability Logics |
| topic | Logic |
| url | https://arxiv.org/abs/2605.12351 |