Formulas expressing totally nonstable truth values of formulas

Vladimir V. Rybakov ; Vladimir R. Kiyatkin ; Konstantin V. Grekovich

The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 108-115

Résumé

In this short paper we consider problem of nonstable truth values of formulas. We investigate temporal-modal logic for description of reliability information. The logic itself is generated by rather standard models on linear time. We consider intervals of nonstable truth values of formulas. This mean that the formula permanently and for a reasonably big time change its truth from true to false and vice versa. We aim to construct some technique and to find an algorithm which may recognize permanently nonstable formulas.

Détail

Keywords: modal logic, frame and model Kripke, satisfiability problem, decidability of logic.

Bibliographie

[1] Babenyshev S., Rybakov V., “Linear Temporal Logic LTL: Basis for Admissible Rules”, J. Logic and Computation, 21:2 (2011), 157–177 | DOI

[2] Gabbay D.M., Hodkinson I.M., “An axiomatization of the temporal logic with Until and Since over the real numbers”, Journal of Logic and Computation, 1:1 (1990), 229–260

[3] Gabbay D.M., Hodkinson I.M., Reynolds M.A., Temporal Logic: Mathematical foundations and computational aspects, v. 1, Clarendon Press, Oxford, 1994, 653 pp.

[4] Goldblatt R., Logics of Time and Computations, Chapter 6, CSLI pubblications, Stanford University, 1992

[5] Goranko V., “Hierarchies of Modal and Temporal Logics with Reference Pointers”, Journal of Logic, Language and Information, 5:1 (1996), 1–24

[6] Rybakov V., “Logical Consecutions in Discrete Linear Temporal Logic”, J. of Symbolic Logic, 70:4 (2005), 1137–1149

[7] Rybakov V., “Linear temporal logic with until and next, logical consecutions”, Annals of Pure and Applied Logic, 155 (2008), 32–45

[8] Rybakov V., “Logic of knowledge and discovery via interacting agents decision algorithm for true and satisfiable statements”, Information Sciences, 179:11 (2009), 1608–1614

[9] Rybakov V., “Linear Temporal Logic $LTL_{K_n}$ extended by Multi-Agent Logic $K_n$ with Interacting Agents”, Journal of logic and Computation, 19:6 (2009), 989–1017

[10] Rybakov V., “Logical Analysis for Chance Discovery in Multi-Agents' Environment”, Conference Proceedings, KES-2012, Springer, 2012, 1593–1601

[11] Rybakov V., “Writing out unifiers in linear temporal logic”, Journal of Logic and Computation, 22:5 (2012), 1199–1206

[12] Rybakov V., “Non-transitive linear temporal logic and logical knowledge operations”, J. Logic and Computation, 26:3 (2016), 945–958

[13] Rybakov V., “Multiagent temporal logics with multivaluations”, Siberian Mathematical Journal, 59:4 (2018), 710–720

[14] Rybakov V., “Temporal multi-valued logic with lost worlds in the past”, Siberian Electronic mathematical Reports, 15:1 (2018), 436–449

[15] Rybakov V., “Branching time agents' logic, satisfiability problem by rules in reduced form”, Siberian Electronic mathematical Reports, 16:1 (2019), 1158–1170 | DOI

[16] van Benthem J., “Tense logic and time”, Notre Dame J. Formal Logic, 25:1 (1984), 1–16

[17] Vardi M.Y., “An automata-theoretic approach to linear temporal logic”, Y. Banff Higher Order Workshop, 1995, 238–266

[18] Vardi M.Y., “Reasoning about the past with two-way automata”, ICALP, LNCS, 1443, eds. Larsen K.G., Skyum S., Winskel G., Springer, 1998, 628–641

[19] Venema Yde, “Temporal Logic”, Blackwell Guide on Philosophical Logic, ed. Lou Goble, Blackwell Publishers, 2001, 203–211