The results presented here will interest those studying the decision problems of modal logics. The work has a tenuous link with practice. If data mining is about discovering general properties of databases, this paper does the reverse: it shows how to construct databases to test a given property.

The author presents a new way to construct a finite model of LA-logics. LA-logics have many interdependent modal operators. Each modal operator, by itself, is an S5 mode. Linearly ordered sets of modal operators have Kripke equivalence relations that agree locally (LA). The paper uses restriction in a new way to construct a finite model for a proposition. It shows that LA-logics have the strong finite model property and so are decidable. The author derives the complexity classes for the decision procedures and gives Hilbert-style axiomatizations of certain LA-logics. He shows that the results apply to Pawlak’s information systems [1], graded modalities, and DALLA.

The paper is rigorous and mathematical. It contains one or two unimportant typographical and translation errors.