2-Sequent calculus: a proof theory of modalities

Annals of Pure and Applied Logic 58 (3):229-246 (1992)

Abstract
Masini, A., 2-Sequent calculus: a proof theory of modalities, Annals of Pure and Applied Logic 58 229–246. In this work we propose an extension of the Getzen sequent calculus in order to deal with modalities. We extend the notion of a sequent obtaining what we call a 2-sequent. For the obtained calculus we prove a cut elimination theorem.
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DOI 10.1016/0168-0072(92)90029-y
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References found in this work BETA

Proofs and Types.Jean-Yves Girard - 1989 - Cambridge University Press.
Intuitionistic Tense and Modal Logic.W. B. Ewald - 1986 - Journal of Symbolic Logic 51 (1):166-179.
Constructive Modal Logics I.Duminda Wijesekera - 1990 - Annals of Pure and Applied Logic 50 (3):271-301.

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Citations of this work BETA

Proof Theory for Functional Modal Logic.Shawn Standefer - 2018 - Studia Logica 106 (1):49-84.
A Proof-Theoretic Investigation of a Logic of Positions.Stefano Baratella & Andrea Masini - 2003 - Annals of Pure and Applied Logic 123 (1-3):135-162.
An Approach to Infinitary Temporal Proof Theory.Stefano Baratella & Andrea Masini - 2004 - Archive for Mathematical Logic 43 (8):965-990.
Causality, Modality, and Explanation.Graham White - 2008 - Notre Dame Journal of Formal Logic 49 (3):313-343.
Temporal Gödel-Gentzen and Girard Translations.Norihiro Kamide - 2013 - Mathematical Logic Quarterly 59 (1-2):66-83.

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