Journal of Symbolic Logic 70 (4):1137 - 1149 (2005)

We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit
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DOI 10.2178/jsl/1129642119
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References found in this work BETA

Time and modality.A. N. PRIOR - 1957 - Revue Philosophique de la France Et de l'Etranger 148:114-115.
Foundations of Mathematical Logic.William Craig - 1963 - Journal of Symbolic Logic 45 (2):377-378.

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Citations of this work BETA

KD is Nullary.Philippe Balbiani & Çiğdem Gencer - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):196-205.
Linear Temporal Logic with Until and Next, Logical Consecutions.V. Rybakov - 2008 - Annals of Pure and Applied Logic 155 (1):32-45.
Decidability: Theorems and Admissible Rules.Vladimir Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):293-308.
Projective Formulas and Unification in Linear Temporal Logic LTLU.V. Rybakov - 2014 - Logic Journal of the IGPL 22 (4):665-672.

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