A loop-free decision procedure for modal propositional logics k4, s4 and S

Journal of Philosophical Logic 38 (2):151 - 177 (2009)

Abstract
The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.
Keywords logic of questions  loop-free procedures  the method of Socratic proofs  transitive modal logics
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DOI 10.1007/s10992-008-9089-z
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First-Order Logic.Raymond M. Smullyan - 1968 - New York [Etc.]Springer-Verlag.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Socratic Proofs.Andrzej Wiśniewski - 2004 - Journal of Philosophical Logic 33 (3):299-326.

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