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Decidability w.r.t. Logical Consecutions of Linear Temporal Logic Extended by Since and Previous
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
International Journal of Intelligent Information Technologies
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The paper concerns the problem of logical consequence in linear temporal logics in terms of logical consecutions. A logical consecution c is an expression ψ1,...,ψn/ψ, where all ψi and ψ are formulas. An informal meaning of c is 'ψ is a logical consequence of assumptions ψ1,...ψn'. We introduce valid and admissible temporal consecutions and prove that the class of admissible consecutions is a proper extension of the class of all valid consecutions. First we describe the admissible consecutions of the intransitive linear temporal Tomorrow/Yesterday logic TYL defined by intervals of natural numbers in a semantic manner -- via consecutions valid on special constructive temporal Kripke/Hintikka models. Then we show that any temporal consecution has a reduced normal form which is given in terms of temporal formulas of temporal degree at most 1. Using this and an enhanced semantic technique we construct an algorithm recognizing consecutions admissible in TYL, i.e. we show that TYL is decidable w.r.t. admissible consecutions.