Weak Completeness Theorem for Propositional Linear Time Temporal Logic

Mariusz Giero

Formalized Mathematics (2012)

  • Volume: 20, Issue: 3, page 227-234
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Mariusz Giero. "Weak Completeness Theorem for Propositional Linear Time Temporal Logic." Formalized Mathematics 20.3 (2012): 227-234. <http://eudml.org/doc/268035>.

@article{MariuszGiero2012,
abstract = {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.},
author = {Mariusz Giero},
journal = {Formalized Mathematics},
keywords = {weak completeness theorem; completeness theorem; temporal logic; temporal model; satisfiability theorem},
language = {eng},
number = {3},
pages = {227-234},
title = {Weak Completeness Theorem for Propositional Linear Time Temporal Logic},
url = {http://eudml.org/doc/268035},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Mariusz Giero
TI - Weak Completeness Theorem for Propositional Linear Time Temporal Logic
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 3
SP - 227
EP - 234
AB - 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.
LA - eng
KW - weak completeness theorem; completeness theorem; temporal logic; temporal model; satisfiability theorem
UR - http://eudml.org/doc/268035
ER -

References

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