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http://hdl.handle.net/11320/3647
Tytuł: | Weak Completeness Theorem for Propositional Linear Time Temporal Logic |
Autorzy: | Giero, Mariusz |
Data wydania: | 2012 |
Data dodania: | 6-gru-2015 |
Wydawca: | De Gruyter Open |
Źródło: | Formalized Mathematics, Volume 20, Issue 3, 2012, Pages 227-234 |
Abstrakt: | 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. |
Afiliacja: | Department of Logic, Informatics and Philosophy of Science, University of Białystok, Plac Uniwersytecki 1, 15-420 Białystok, Poland |
Sponsorzy: | 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). |
Opis: | The author is the winner of the Mizar Prize for Young Researchers in 2012 for this article. I 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. |
URI: | http://hdl.handle.net/11320/3647 |
DOI: | 10.2478/v10037-012-0027-8 |
ISSN: | 1426-2630 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2012, Volume 20, Issue 3 |
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