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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Volume 20, Issue 3


Weak Completeness Theorem for Propositional Linear Time Temporal Logic

Mariusz Giero
  • Department of Logic, Informatics and Philosophy of Science, University of Białystok, Plac Uniwersytecki 1, 15-420 Białystok, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-02-02 | DOI: https://doi.org/10.2478/v10037-012-0027-8


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.

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About the article

The author is the winner of the Mizar Prize for Young Researchers in 2012 for this article. This work has been supported by the Polish Ministry of Science and Higher Education project “Managing a Large Repository of Computer-verified Mathematical Knowledge” (N N519 385136). 2 would like to thank Prof. Dr. Stephan Merz for valuable hints which helped me to prove the theorem. I would particularly like to thank Dr. Artur Korniłowicz who patiently answered a lot of my questions regarding writing this article. I would like to thank Dr. Josef Urban for discussions and encouragement to write the article. I would like to thank Prof. Andrzej Trybulec, Dr. Adam Naumowicz, Dr. Grzegorz Bancerek and Karol Pak for their help in preparation of the article.

Published Online: 2013-02-02

Published in Print: 2012-12-01

Citation Information: Formalized Mathematics, Volume 20, Issue 3, Pages 227–234, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0027-8.

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