Rooted Hypersequent Calculus for Modal Logic S5

Logica Universalis 17 (3):269-295 (2023)
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Abstract

We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are established as well.

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References found in this work

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Display logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
Deep sequent systems for modal logic.Kai Brünnler - 2009 - Archive for Mathematical Logic 48 (6):551-577.

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