A purely syntactic and cut-free sequent calculus for the modal logic of provability

Review of Symbolic Logic 2 (4):593-611 (2009)

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Abstract
In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. No explicit semantic element is used in the sequent calculus and all the results are proved in a purely syntactic way.
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DOI 10.1017/s1755020309990244
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References found in this work BETA

Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Cut-Free Sequent Calculi for Some Tense Logics.Ryo Kashima - 1994 - Studia Logica 53 (1):119 - 135.
The Modal Logic of Provability: Cut-Elimination. [REVIEW]Silvio Valentini - 1983 - Journal of Philosophical Logic 12 (4):471 - 476.

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Citations of this work BETA

Proofs and Countermodels in Non-Classical Logics.Sara Negri - 2014 - Logica Universalis 8 (1):25-60.
Labelled Tree Sequents, Tree Hypersequents and Nested Sequents.Rajeev Goré & Revantha Ramanayake - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 279-299.
Embedding Formalisms: Hypersequents and Two-Level Systems of Rule.Agata Ciabattoni & Francesco A. Genco - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 197-216.

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