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 -tesseract. The proof of soundness and completeness is based on the sequent calculus with some added features from deep inference.
CITATION STYLE
Acclavio, M., & Straßburger, L. (2019). On Combinatorial Proofs for Modal Logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11714 LNAI, pp. 223–240). Springer. https://doi.org/10.1007/978-3-030-29026-9_13
Mendeley helps you to discover research relevant for your work.