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

Studia Logica 53 (3):433 - 457 (1994)
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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References found in this work BETA
Krister Segerberg (1971). An Essay in Classical Modal Logic. Uppsala,Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
Wolfgang Rautenberg (1983). Modal Tableau Calculi and Interpolation. Journal of Philosophical Logic 12 (4):403 - 423.

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