A Class of Decidable Information Logics

For a class of propositional information logics defined from Pawlak’s information systems, the validity problem is proved to be decidable using a significant variant of the standard filtration technique. Decidability is proved by showing that each logic has the strong finite model property and by bounding the size of the models. The logics in the scope of this paper are characterized by classes of Kripke-style structures with interdependent relations pairwise satisfying the Gargov’s local agreement condition and closed under the so-called restriction operation. They include Gargov’s data analysis logic with local agreement and Nakamura’s logic of graded modalities. The last part of the paper is devoted to the definition of complete Hilbert-style axiomatizations for subclasses of the introduced logics, thus providing evidence that such logics are subframe logics in Wolter’s sense.