The Properties of Sets of Temporal Logic Subformulas

Mariusz Giero

Formalized Mathematics (2012)

  • Volume: 20, Issue: 3, page 221-226
  • ISSN: 1426-2630

Abstract

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This is a second preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [17]. We introduce two modified definitions of a subformula. In the former one we treat until-formula as indivisible. In the latter one, we extend the set of subformulas of until-formulas by a special disjunctive formula. This is needed to construct a temporal model. We also define an ordered positive-negative pair of finite sequences of formulas (PNP). PNPs represent states of a temporal model.

How to cite

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Mariusz Giero. "The Properties of Sets of Temporal Logic Subformulas." Formalized Mathematics 20.3 (2012): 221-226. <http://eudml.org/doc/267792>.

@article{MariuszGiero2012,
abstract = {This is a second preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [17]. We introduce two modified definitions of a subformula. In the former one we treat until-formula as indivisible. In the latter one, we extend the set of subformulas of until-formulas by a special disjunctive formula. This is needed to construct a temporal model. We also define an ordered positive-negative pair of finite sequences of formulas (PNP). PNPs represent states of a temporal model.},
author = {Mariusz Giero},
journal = {Formalized Mathematics},
keywords = {basic propositional temporal logic; completeness theorem; temporal model},
language = {eng},
number = {3},
pages = {221-226},
title = {The Properties of Sets of Temporal Logic Subformulas},
url = {http://eudml.org/doc/267792},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Mariusz Giero
TI - The Properties of Sets of Temporal Logic Subformulas
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 3
SP - 221
EP - 226
AB - This is a second preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [17]. We introduce two modified definitions of a subformula. In the former one we treat until-formula as indivisible. In the latter one, we extend the set of subformulas of until-formulas by a special disjunctive formula. This is needed to construct a temporal model. We also define an ordered positive-negative pair of finite sequences of formulas (PNP). PNPs represent states of a temporal model.
LA - eng
KW - basic propositional temporal logic; completeness theorem; temporal model
UR - http://eudml.org/doc/267792
ER -

References

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