<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

The Properties of Sets of Temporal Logic Subformulas

Department of Logic, Informatics and Philosophy of Science, University of Białystok, Plac Uniwersytecki 1, 15-420 Białystok, Poland

Formalized Mathematics

{"article-title":"The Properties of Sets of Temporal Logic Subformulas"}

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...

The Properties of Sets of Temporal Logic Subformulas

Online veröffentlicht: 02. Feb. 2013

Seitenbereich: 221 - 226

DOI: https://doi.org/10.2478/v10037-012-0026-9

This content is open access.