Cut-free tableau calculi for some propositional normal modal logics

Studia Logica 57 (2-3):359 - 372 (1996)
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We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G 0(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G 0are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G 0is not compact (and therefore not canonical), and we proof with the tableau-method that G 0is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G 0is decidable and also characterised by the class of all frames for G 0



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Citations of this work

Speaking about transitive frames in propositional languages.Yasuhito Suzuki, Frank Wolter & Michael Zakharyaschev - 1998 - Journal of Logic, Language and Information 7 (3):317-339.
Around provability logic.Leo Esakia - 2010 - Annals of Pure and Applied Logic 161 (2):174-184.

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References found in this work

A companion to modal logic.G. E. Hughes - 1984 - New York: Methuen. Edited by M. J. Cresswell.
A Companion to Modal Logic.G. E. Hughes & M. J. Cresswell - 1995 - Studia Logica 54 (3):411-413.
Modal tableau calculi and interpolation.Wolfgang Rautenberg - 1983 - Journal of Philosophical Logic 12 (4):403 - 423.
An Essay in Classical Modal Logic.Karl Krister Segerberg - 1971 - Dissertation, Stanford University

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