Agent Interpolation for Knowledge
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912402359975936 |
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| author | Bílková, Marta Fussner, Wesley Kuznets, Roman |
| author_facet | Bílková, Marta Fussner, Wesley Kuznets, Roman |
| contents | We define a new type of proof formalism for multi-agent modal logics with S5-type modalities. This novel formalism combines the features of hypersequents to represent S5 modalities with nested sequents to represent the T-like modality alternations. We show that the calculus is sound and complete, cut-free, and terminating and yields decidability and the finite model property for multi-agent S5. We also use it to prove the Lyndon (and hence Craig) interpolation property for multi-agent S5, considering not only propositional atoms but also agents to be part of the common language. Finally, we discuss the difficulties on the way to extending these results to the logic of distributed knowledge and to deductive interpolation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23401 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Agent Interpolation for Knowledge Bílková, Marta Fussner, Wesley Kuznets, Roman Logic in Computer Science Logic 03B45 (Primary) 03B42, 03F03 (Secondary) I.2.4; F.4.1 We define a new type of proof formalism for multi-agent modal logics with S5-type modalities. This novel formalism combines the features of hypersequents to represent S5 modalities with nested sequents to represent the T-like modality alternations. We show that the calculus is sound and complete, cut-free, and terminating and yields decidability and the finite model property for multi-agent S5. We also use it to prove the Lyndon (and hence Craig) interpolation property for multi-agent S5, considering not only propositional atoms but also agents to be part of the common language. Finally, we discuss the difficulties on the way to extending these results to the logic of distributed knowledge and to deductive interpolation. |
| title | Agent Interpolation for Knowledge |
| topic | Logic in Computer Science Logic 03B45 (Primary) 03B42, 03F03 (Secondary) I.2.4; F.4.1 |
| url | https://arxiv.org/abs/2505.23401 |