A deep inference system for the modal logic S

Studia Logica 85 (2):199 - 214 (2007)
We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.2307/40210767
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References found in this work BETA
Sara Negri (2005). Proof Analysis in Modal Logic. Journal of Philosophical Logic 34 (5/6):507 - 544.
Gerhard Gentzen (1964). Investigations Into Logical Deduction. American Philosophical Quarterly 1 (4):288 - 306.
Stig Kanger (1957). Provability in Logic. Stockholm, Almqvist & Wiksell.
Melvin Fitting (1999). A Simple Propositional S5 Tableau System. Annals of Pure and Applied Logic 96 (1-3):107-115.

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Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.

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