Cut-free sequent and tableau systems for propositional diodorean modal logics

Studia Logica 53 (3):433 - 457 (1994)

Abstract
We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logicsS4.3, S4.3.1 andS4.14. When the modality is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points.Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulaeX the superformulae involved are always bounded by a finite set of formulaeX* L depending only onX and the logicL. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive.
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DOI 10.1007/BF01057938
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An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
Logics of Time and Computation.Robert Goldblatt - 1990 - Studia Logica 49 (2):284-286.

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Multiple-Conclusion Rules, Hypersequents Syntax and Step Frames.Nick Bezhanishvili & Silvio Ghilardi - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 54-73.

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