Abstract: "We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4.3, S4.3.1 and S4.14. When the modality [square] is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear dis...

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Bibliographische Detailangaben

1. Verfasser:	Goré, Rajeev (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge 1993
Schriftenreihe:	Computer Laboratory <Cambridge>: Technical report 288
Schlagworte:	Computer software Logic programming
Zusammenfassung:	Abstract: "We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4.3, S4.3.1 and S4.14. When the modality [square] 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 formulae X the 'superformulae' involved are always bounded by a finite set of formulae X*[subscript L] depending only on X and the logic L. 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. Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these logics. The techniques are due to Hintikka and Rautenberg.
Beschreibung:	19 S.