Satisfiability problem in interval FP-logic

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.