Propositional Linear Temporal Logic with Initial Validity Semantics1

• Autorzy: Mariusz Giero
• Języki publikacji: EN

Abstrakty

EN

In the article [10] a formal system for Propositional Linear Temporal Logic (in short LTLB) with normal semantics is introduced. The language of this logic consists of “until” operator in a very strict version. The very strict “until” operator enables to express all other temporal operators. In this article we construct a formal system for LTLB with the initial semantics [12]. Initial semantics means that we define the validity of the formula in a model as satisfaction in the initial state of model while normal semantics means that we define the validity as satisfaction in all states of model. We prove the Deduction Theorem, and the soundness and completeness of the introduced formal system. We also prove some theorems to compare both formal systems, i.e., the one introduced in the article [10] and the one introduced in this article. Formal systems for temporal logics are applied in the verification of computer programs. In order to carry out the verification one has to derive an appropriate formula within a selected formal system. The formal systems introduced in [10] and in this article can be used to carry out such verifications in Mizar [4].

Słowa kluczowe

EN

temporal logic; very strict until operator; completeness

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 03B70: Logic in computer science

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 4
• Strony: 379-386

Daty

wydano

2015-12-01

otrzymano

2015-10-22

online

2016-03-25

Twórcy

autor

Mariusz Giero

• Faculty of Economics and Informatics, University of Białystok, Kalvariju 135, LT-08221 Vilnius, Lithuania

Bibliografia

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• [4] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.[Crossref]
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• [10] Mariusz Giero. The axiomatization of propositional linear time temporal logic. Formalized Mathematics, 19(2):113–119, 2011. doi:10.2478/v10037-011-0018-1.[Crossref]
• [11] Adam Grabowski. Hilbert positive propositional calculus. Formalized Mathematics, 8(1): 69–72, 1999.
• [12] Fred Kröger and Stephan Merz. Temporal Logic and State Systems. Springer-Verlag, 2008.
• [13] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.
• [14] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics, 8(1):133–137, 1999.
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Identyfikatory

DOI

10.1515/forma-2015-0030

bwmeta1.id-class.MML

LTLAXIO5