Weak Completeness Theorem for Propositional Linear Time Temporal Logic

Pole DC	Wartość	Język
dc.contributor.author	Giero, Mariusz	-
dc.date.accessioned	2015-12-06T19:05:56Z	-
dc.date.available	2015-12-06T19:05:56Z	-
dc.date.issued	2012	-
dc.identifier.citation	Formalized Mathematics, Volume 20, Issue 3, 2012, Pages 227-234	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3647	-
dc.description	The author is the winner of the Mizar Prize for Young Researchers in 2012 for this article.	-
dc.description	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.	-
dc.description.abstract	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.	-
dc.description.sponsorship	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).	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.title	Weak Completeness Theorem for Propositional Linear Time Temporal Logic	-
dc.type	Article	-
dc.identifier.doi	10.2478/v10037-012-0027-8	-
dc.description.Affiliation	Department of Logic, Informatics and Philosophy of Science, University of Białystok, Plac Uniwersytecki 1, 15-420 Białystok, Poland	-
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