Abstract
The article investigates the interval modal logic, in which an action of the modal operator ◊ is limited by the boundaries of an interval. In addition, the language of modal logic is extended by the operator 𝐷(𝛼, 𝛽), the truth of which is determined qualitatively: it is true only if the number of points on the interval [𝑐𝑖, 𝑐𝑖+1] where the formula 𝛼 is true is strictly less than the number of points in this segment where the formula 𝛽 is true. The problem of satisfiability of formulas is solved, and as a consequence, the decidability of logic.
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