Geodesic
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

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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. 
@article{IIGUM_2024_47_a5,
     author = {Stepan I. Bashmakov and Kirill A. Smelykh},
     title = {Relational version of the multi-agent computation tree logic $\mathcal{CTLK}$},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {78--92},
     publisher = {mathdoc},
     volume = {47},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2024_47_a5/}
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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/