# The Properties of Sets of Temporal Logic Subformulas

Formalized Mathematics (2012)

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

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topMariusz 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 -

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