Geodesic
Linear step-like logic of knowledge $\mathcal{LTK}.{sl}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1361-1373.

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This paper proposes a description of linear multi-agent logic of knowledge $\mathcal{LTK}.{sl}$ that models a linear non-reflexive non-transitive (step-like) temporal process of transition between information clusters — time points. Using modified techniques, we proved the finite approximability of logic. We proposed an approach for solving the main unification problem in logics of a step-like temporal relation. The projectivity and, as a consequence, unitary type of unification in logic are proved.
Keywords: modal logics, temporal logics, finite model property, linear time, Kripke relational semantics, multi-agent logic
Mots-clés : unification. 
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S. I. Bashmakov; T. Yu. Zvereva. Linear step-like logic of knowledge $\mathcal{LTK}.{sl}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1361-1373. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a15/

[1] Yu.G. Karpov, Model Checking. Verification of parallel and distributed software systems, BHV-Peterburg, Saint Petersburg, 2010

[2] A.V. Kudinov, I.B. Shapirovsky, “Partitioning Kripke frames of finite height”, Izv. Math., 81:3 (2017), 592–617 | DOI | MR | Zbl

[3] V.V. Rybakov, “Nontransitive temporal multiagent logic, information and knowledge, deciding algorithms”, Sib. Math. J., 58:5 (2017), 875–886 | DOI | MR | Zbl

[4] I.B. Shapirovsky, V.B. Shehtman, “Modern modal logic: between mathematics and computer science”, Modern logic: foundations, subject and prospects of development, ID Forum (Moscow, 2018), ed. Zaitsev D.V., 265–305 http://logic.math.msu.ru/wp-content/uploads/shehtman/shsh.pdf

[5] S.I. Bashmakov, “Unification in linear modal logic on non-transitive time with the universal modality”, J. Sib. Fed. Univ. Math. Phys., 11:1 (2018), 3–9 | DOI | MR | Zbl

[6] S.I. Bashmakov, “Unification in pretabular extensions of S4”, Log. Univers., 15:3 (2021), 381–397 | DOI | MR | Zbl

[7] S.I. Bashmakov, T.Yu. Zvereva, “Unification and finite model property for linear step-like temporal multi-agent logic with the universal modality”, Bulletin of the Section of Logic, 51:3 (2022), 345–361 | DOI | MR

[8] A. Chagrov, M. Zacharyaschev, Modal logic, Oxford University Press, Oxford, 1997 | MR | Zbl

[9] W. Dzik, P. Wojtylak, “Projective unification in modal logic”, Log. J. IGPL, 20:1 (2012), 121–153 | DOI | MR | Zbl

[10] S. Ghilardi, “Unification through projectivity”, J. Logic Comput., 7:6 (1997), 733–752 | DOI | MR | Zbl

[11] S. Ghilardi, “Unification in intuitionistic logic”, J. Symb. Log., 62:2 (1999), 859–880 | DOI | MR | Zbl

[12] V. Goranko, S. Passy, “Using the universal modality: Gains and questions”, J. Log. Comput., 2:1 (1992), 5–30 | DOI | MR | Zbl

[13] A. Prior, Time and modality, Oxford University Press, Oxford, 1957 | Zbl

[14] J.A. Robinson, “A machine-oriented logic based on the resolution principle”, J. Assoc. Comput. Mach., 12 (1965), 23–41 | DOI | MR | Zbl

[15] V.V. Rybakov, “Best unifiers in transitive modal logics”, Stud. Log., 99:1-3 (2011), 321–336 | DOI | MR | Zbl

[16] V.V. Rybakov, “Non-transitive linear temporal logic and logical knowledge operations”, J. Log. Comput., 26:3 (2016), 945–958 | DOI | MR | Zbl

[17] R. van der Meyden, Ks. Wong, “Complete axiomatizations for reasoning about knowledge and branching time”, Stud. Log., 75:1 (2003), 93–123 | DOI | MR | Zbl