This article is cited in 1 paper

Algebraic and logical methods in computer science and artificial intelligence

Satisfiability problem in interval FP-logic

Nikita A. Protsenko, Vladimir V. Rybakov, Vitaliy V. Rimatskiy

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: 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.

UDC: 510.665, 510.643

MSC: 03B45, 03H05

Received: 18.01.2023
Revised: 13.03.2023
Accepted: 20.03.2023

Language: English

DOI: 10.26516/1997-7670.2023.44.98