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Relational version of the multi-agent computation tree logic $\mathcal{CTLK}$
The Bulletin of Irkutsk State University. Series Mathematics, Tome 47 (2024), pp. 78-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper deals with multi-agent computation tree logic — $\mathcal{CTLK}$ (Computation Tree Logic with Knowledge). Each agent represents its own computational route of the initial problem, and new branches of possible computational routes spawn new agents. The logic $\mathcal{CTLK}$ is a natural enrichment of $\mathcal{CTL}$ by new knowledge operators. We introduce alternative to automata Kripke's relational semantics, describes properties of $\mathcal{CTLK}^{Rel}$-frame and proves finite approximability.
Keywords: multi-agent logic, branching temporal logic, Kripke relational semantics, filtration method, finite approximability. 
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Stepan I. Bashmakov; Kirill A. Smelykh. Relational version of the multi-agent computation tree logic $\mathcal{CTLK}$. The Bulletin of Irkutsk State University. Series Mathematics, Tome 47 (2024), pp. 78-92. http://geodesic.mathdoc.fr/item/IIGUM_2024_47_a5/

[1] Vityaev E.E., “Semantic probabilistic inference of predictions”, The Bulletin of Irkutsk State University. Series Mathematics, 21 (2017), 33–50 | DOI | MR | Zbl

[2] Karpov Yu.G., Model checking. Verification of parallel and distributed program systems, BHV-St. Petersburg Publ., St. Petersburg, 2010, 560 pp.

[3] Mantsivoda A.V., Ponomaryov D.K., “Towards Semantic Document Modelling of Business Processes”, The Bulletin of Irkutsk State University. Series Mathematics, 29 (2019), 52–67 | DOI | MR | Zbl

[4] “Kripke-style models for logics of evidence and truth / H. Antunes, W. Carnielli, A. Kapsner, A. Rodrigues”, Axioms, 9:3 (2020), 100 | DOI

[5] Bashmakov S. I., Zvereva T. Yu., “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

[6] Bashmakov S. I., Zvereva T. Yu., “Linear Step-like Logic of Knowledge LTK.sl”, Siberian Electronic Mathematical Reports, 20:2 (2023), 1361–1373 | DOI | MR

[7] Chagrov A., Zacharyaschev M., Modal Logic, Oxford University Press, 1997, 605 pp. | MR

[8] Clarke E. M., Emerson E. A., “Design and synthesis of synchronization skeletons using branching time temporal logic” (1981), Logics of Programs, Lecture Notes in Computer Science, 131, 1982, 52–71 | DOI | MR | Zbl

[9] Dima C., “Revisiting satisfiability and model-checking for CTLK with synchrony and perfect recall”, Computational Logic in Multi-Agent Systems, CLIMA 2008, Lecture Notes in Computer Science, 5405, 2008, 117–131 | DOI

[10] Guelev D. P., Dima C., Enea C., “An alternating-time temporal logic with knowledge, perfect recall and past: axiomatisation and model-checking”, Journal of Applied Non-Classical Logics, 21:1 (2011), 93–131 | DOI | MR | Zbl

[11] Halpern J. Y., Vardi M. Y., “The complexity of reasoning about knowledge and time. I. Lower bounds”, J. Computer and System Sciences, 38:1 (1989), 195–237 | DOI | MR | Zbl