Proof Identity and Categorical Models of BV
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910173383098368 |
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| author | Acclavio, Matteo Straßburger, Lutz Zamdzhiev, Vladimir |
| author_facet | Acclavio, Matteo Straßburger, Lutz Zamdzhiev, Vladimir |
| contents | BV-categories are a recent development that aims to give categorical semantics to proofs in the logic BV. However, due to the absence of a coherence theorem on one side and a well-defined notion of proof identity for BV on the other side, the precise relation between BV-categories and the logic BV is still not clear. To improve on this situation, we define in this paper a notion of proof identity for BV, based on the notion of atomic flows, which can be seen as a special form of string diagrams. Based on this notion of proof identity, we then strengthen the existing notion of BV-category and prove that it is sound with respect to the logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25501 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof Identity and Categorical Models of BV Acclavio, Matteo Straßburger, Lutz Zamdzhiev, Vladimir Logic in Computer Science BV-categories are a recent development that aims to give categorical semantics to proofs in the logic BV. However, due to the absence of a coherence theorem on one side and a well-defined notion of proof identity for BV on the other side, the precise relation between BV-categories and the logic BV is still not clear. To improve on this situation, we define in this paper a notion of proof identity for BV, based on the notion of atomic flows, which can be seen as a special form of string diagrams. Based on this notion of proof identity, we then strengthen the existing notion of BV-category and prove that it is sound with respect to the logic. |
| title | Proof Identity and Categorical Models of BV |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2604.25501 |