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.
@article{bwmeta1.element.doi-10_2478_v10037-012-0027-8,
author = {Mariusz Giero},
title = {Weak Completeness Theorem for Propositional Linear Time Temporal Logic},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {227-234},
zbl = {1285.03011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0027-8}
}
Mariusz Giero. Weak Completeness Theorem for Propositional Linear Time Temporal Logic. Formalized Mathematics, Tome 20 (2012) pp. 227-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0027-8/
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