Authors
Andrzej Indrzejczak
University of Lodz
Abstract
In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form.
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DOI 10.18778/0138-0680.45.2.05
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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.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
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[Omnibus Review].Dag Prawitz - 1991 - Journal of Symbolic Logic 56 (3):1094-1096.
The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.

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Citations of this work BETA

Rule-Generation Theorem and its Applications.Andrzej Indrzejczak - 2018 - Bulletin of the Section of Logic 47 (4):265-281.
Tautology Elimination, Cut Elimination, and S5.Andrezj Indrzejczak - 2017 - Logic and Logical Philosophy 26 (4):461-471.

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