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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1158–1170 (Mi semr1120)  

Mathematical logic, algebra and number theory

Branching time agents' logic, satisfiability problem by rules in reduced form

V. V. Rybakovab

a Institute of Mathematics and Computer Science Siberian Federal University, 79, Svobodny ave., Krasnoyarsk, 660041, Russia
b A.P. Ershov Institute of informatics systems SB RAS 6, Acad. Lavrentjev ave., Novosibirsk, 630090, Russia

Abstract: This paper considers the branching time logic on non-transitive intervals of agents' accessibility relations. The agents' accessibility relations are defined inside transitivity intervals and via neighboring limit points, they may be not complete and lose some states — the lacunas of forgotten time thought they may interfere. This approach is used for modeling computational processes and analysis of incomplete information for individual agents. A logical language for reasoning about models' properties which includes temporal and modal logical operations is suggested. Illustrative examples are provided. Mathematical part of the paper is devoted to the satisfiability and decidability problems for the suggested logic. We use instruments of reduced normal forms for rules and algorithms converting rules to such forms. We find algorithms solving the satisfiability problem. Some open problems are suggested.

Keywords: temporal logic, branching time logic, multi-agent logic, computability, information, satisfiability, decidability.

DOI: https://doi.org/10.33048/semi.2019.16.079

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Bibliographic databases:

UDC: 510.64
MSC: 03F99
Received January 4, 2019, published August 26, 2019
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Citation: V. V. Rybakov, “Branching time agents' logic, satisfiability problem by rules in reduced form”, Sib. Èlektron. Mat. Izv., 16 (2019), 1158–1170

Citation in format AMSBIB
\Bibitem{Ryb19}
\by V.~V.~Rybakov
\paper Branching time agents' logic, satisfiability problem by rules in reduced form
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1158--1170
\mathnet{http://mi.mathnet.ru/semr1120}
\crossref{https://doi.org/10.33048/semi.2019.16.079}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000483863600001}


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