Cut-elimination for the alternation-free modal mu-calculus
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917007844179968 |
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| author | Afshari, Bahareh Kloibhofer, Johannes |
| author_facet | Afshari, Bahareh Kloibhofer, Johannes |
| contents | We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The structure of such proofs is exploited to directly transform a cyclic proof with cuts into a cut-free one, without detouring through other logics or relying on intermediate machinery for regularisation. Novel ingredients include the use of multicuts and results from the theory of well-quasi-orders, the later used in the termination argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cut-elimination for the alternation-free modal mu-calculus Afshari, Bahareh Kloibhofer, Johannes Logic in Computer Science Logic We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The structure of such proofs is exploited to directly transform a cyclic proof with cuts into a cut-free one, without detouring through other logics or relying on intermediate machinery for regularisation. Novel ingredients include the use of multicuts and results from the theory of well-quasi-orders, the later used in the termination argument. |
| title | Cut-elimination for the alternation-free modal mu-calculus |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2510.11293 |