Geodesic
Decidability of multi-modal logic $LTK$ of linear time and knowledge
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 220-226.

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The paper investigates modal (temporal-model) logics based at a semantic approach with models combining knowledge and time. We introduce multi-modal logics $LTK_r$ and $LTK_{ir}$ containing modalities for knowledge and time as the sets of all $LTK_r$-valid, and $LTK_{ir}$-valid formulae for a class of special $LTK_r$- frames, $LTK_{ir}$-frames, respectively. The main results of this paper are theorems stating that $LTK_r$ and $LTK_{ir}$ are decidable; we also give an explicit solving algorithm.
Keywords: multi-modal logic, temporal logic, epistemic logic, decidability, effective finite model property. 
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Alexandra N. Lukyanchuk. Decidability of multi-modal logic $LTK$ of linear time and knowledge. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 220-226. http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a8/

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