Weak Completeness Theorem for Propositional Linear Time Temporal Logic

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We prove weak (finite set of premises) completeness theorem for extended propositional linear time temporal logic with irreflexive version of until-operator. We base it on the proof of completeness for basic propositional linear time temporal logic given in [20] which roughly follows the idea of the Henkin-Hasenjaeger method for classical logic. We show that a temporal model exists for every formula which negation is not derivable (Satisfiability Theorem). The contrapositive of that theorem leads to derivability of every valid formula. We build a tree of consistent and complete PNPs which is used to construct the model.

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SCImago Journal Rank (SJR) 2017: 0.119
Source Normalized Impact per Paper (SNIP) 2017: 0.237

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researchers in the fields of formal methods and computer-checked mathematics


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