Every deep-inference derivation decomposes into an up-fragment then a down-fragment around a Lyndon interpolant, generalizing both interpolation and cut elimination.
Proof Identity and Categorical Models of BV
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abstract
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.
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cs.LO 1years
2026 1verdicts
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Interpolation via Generalized Splitting
Every deep-inference derivation decomposes into an up-fragment then a down-fragment around a Lyndon interpolant, generalizing both interpolation and cut elimination.