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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.
Cited literature [33 references]
https://hal.inria.fr/hal-02390400
Contributor : Lutz Straßburger Connect in order to contact the contributor
Submitted on : Tuesday, December 10, 2019 - 9:39:09 AM
Last modification on : Friday, April 30, 2021 - 10:02:38 AM
Long-term archiving on: : Wednesday, March 11, 2020 - 3:02:23 PM
Contributor : Lutz Straßburger Connect in order to contact the contributor
Submitted on : Tuesday, December 10, 2019 - 9:39:09 AM
Last modification on : Friday, April 30, 2021 - 10:02:38 AM
Long-term archiving on: : Wednesday, March 11, 2020 - 3:02:23 PM
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