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  • Han Gao (ICS CAS):

    Relevance and interpolation via binary nested sequents

    21.10.2026 16:00Velká zasedačka (č. 318, 2. poschodí) Ústavu informatiky AV ČR, v.v.i. Seminář aplikované matematické logiky

    The variable-sharing property (VSP) is regarded as a key feature of relevant logic, while the Craig interpolation property (CIP), formulated with respect to relevant implication, implies the VSP in constant-free propositional languages. However, to the best of our knowledge, no constant-free distributive relevant logic has previously been shown to enjoy the CIP. This absence of positive results has contributed to a widespread impression among relevant logicians that relevance and Craig interpolation are incompatible. In this work, we address this tension by proving that the negation-free fragment of basic relevant logic B, denoted B+, enjoys both properties. Our proofs are purely syntactic and is based on a novel nested sequent calculus featuring binary relevant blocks as primitive structural constructs. Unlike conventional nested sequent calculi, where unary nesting reflects the binary accessibility relation of Kripke semantics, our calculus employs a binary nesting operator that directly reflects the ternary relational structure of Routley–Meyer semantics. We establish soundness and cut-free completeness of the calculus, and then provide syntactic proofs of both the VSP and the CIP using a structural notion internalized in the nested sequents. The talk is based on joint work with Fabio De Martin Polo.

  • Luca Carai (ICS CAS):

    TBA

    04.11.2026 16:00Velká zasedačka (č. 318, 2. poschodí) Ústavu informatiky AV ČR, v.v.i. Seminář aplikované matematické logiky

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