Geodesic
Intransitive temporal multi-agent logic with agents' multi-valuations. Decidability
The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 141-150

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We study intransitive temporal multi-agent logic with agents' multi-valuations for letters and formulas. In previous wide accepted research the time and knowledge primarily were modeled by Kripke models with structure looking as simply a single time cluster with multi-relations for agents' accessibility relations. Here we develop this approach and use Kripke models with linear intransitive time and states represented by arbitrary time clusters for agents accessibility multi-relations. This logic is defined in a semantic way, as a set of formulas, which are true at linear models with multi-valued variables by agents' and clusters of states. We propose a background for such approach and a technique for computation truth values of formulas. Main result concerns decidability problem. We prove that the resulting logic is decidable and obtain a sort of finite model property.
Keywords: modal logic, frame and model Kripke, multi-agent logics, decidability problem. 
@article{IIGUM_2025_51_a9,
     author = {K. V. Grekovich and V. V. Rybakov and V. V. Rimatskiy},
     title = {Intransitive temporal multi-agent logic with agents' multi-valuations. {Decidability}},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {141--150},
     publisher = {mathdoc},
     volume = {51},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a9/}
}
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K. V. Grekovich; V. V. Rybakov; V. V. Rimatskiy. Intransitive temporal multi-agent logic with agents' multi-valuations. Decidability. The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 141-150. http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a9/