On Combinatorial Proofs for Modal Logic

Abstract : In this paper we extend Hughes’ combinatorial proofs to modal logics. The crucial ingredient for modeling the modalities is the use of a self-dual non-commutative operator that has first been observed by Retoré through pomset logic. Consequently, we had to generalize the notion of skew fibration from cographs to Guglielmi’s relation webs. Our main result is a sound and complete system of combinatorial proofs for all normal and non-normal modal logics in the S4-tesseract. The proof of soundness and completeness is based on the sequent calculus with some added features from deep inference.
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Submitted on : Tuesday, December 10, 2019 - 9:39:09 AM
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Matteo Acclavio, Lutz Straßburger. On Combinatorial Proofs for Modal Logic. TABLEAUX 2019 - 28t International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Sep 2019, London, United Kingdom. pp.223-240, ⟨10.1007/978-3-030-29026-9_13⟩. ⟨hal-02390400⟩

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