Geodesic
Satisfiability problem in interval FP-logic
The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 98-107

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The article investigates the interval modal logic, in which an action of the modal operator $\Diamond$ is limited by the boundaries of an interval. In addition, the language of modal logic is extended by the operator $D (\alpha, \beta)$, the truth of which is determined qualitatively: it is true only if the number of points on the interval $[c_i ; c_{i+1}]$ where the formula $\alpha $ is true is strictly less than the number of points in this segment where the formula $\beta $ is true. The problem of satisfiability of formulas is solved, and as a consequence, the decidability of logic.
Keywords: modal logic, frame and model Kripke, satisfiability problem. 
@article{IIGUM_2023_44_a7,
     author = {Nikita A. Protsenko and Vladimir V. Rybakov and Vitaliy V. Rimatskiy},
     title = {Satisfiability problem in interval {FP-logic}},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {98--107},
     publisher = {mathdoc},
     volume = {44},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_44_a7/}
}
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Nikita A. Protsenko; Vladimir V. Rybakov; Vitaliy V. Rimatskiy. Satisfiability problem in interval FP-logic. The Bulletin of Irkutsk State University. Series Mathematics, Tome 44 (2023), pp. 98-107. http://geodesic.mathdoc.fr/item/IIGUM_2023_44_a7/