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Tableau Methods for Modal and Temporal Logics
, 1995
"... This document is a complete draft of a chapter by Rajeev Gor'e on "Tableau Methods for Modal and Temporal Logics" which is part of the "Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. Hahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrecht. Any comments and correctio ..."
Abstract

Cited by 125 (20 self)
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This document is a complete draft of a chapter by Rajeev Gor'e on "Tableau Methods for Modal and Temporal Logics" which is part of the "Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. Hahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrecht. Any comments and corrections are highly welcome. Please email me at rpg@arp.anu.edu.au The latest version of this document can be obtained via my WWW home page: http://arp.anu.edu.au/ Tableau Methods for Modal and Temporal Logics Rajeev Gor'e Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Syntax and Notational Conventions . . . . . . . . . . . . 3 2.2 Axiomatics of Modal Logics . . . . . . . . . . . . . . . . 4 2.3 Kripke Semantics For Modal Logics . . . . . . . . . . . . 5 2.4 Known Correspondence and Completeness Results . . . . 6 2.5 Logical Consequence . . . . . . . . . . . . . . . . . . . . 8 2....
Cutfree Sequent and Tableau Systems for Propositional Diodorean Modal Logics
"... We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of po ..."
Abstract

Cited by 20 (3 self)
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We present sound, (weakly) complete and cutfree tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 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 cutfree, 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 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 cutfree sequent analogue proving that Gentzen's cutelimination theorem holds for these latter systems. The techniques are due to Hi...