A Modal Characterization of Indiscernibility and Similarity Relations in Pawlak’s Information Systems

Abstract

In this paper we present a modal logic IND for Pawlak’s information systems giving a modal characterization of 9 informational relations: strong indiscernibility, as well as weak and strong versions of forward and backward informational inclusion, as well as positive and negative similarities. IND extends the logic INF introduced in [4] by adding a modality corresponding to strong indiscernibility relation. The main problem in the modal treating of strong indiscernibility is that its definition is not modally definable. This requires special copying techniques, which in the presence of many interacting modalities presents complications. One of the main aims of the paper is to demonstrate such techniques and to present an information logic complete in the intended semantics and containing almost all natural information relations. It is proved that IND possesses finite model property and hence is decidable.

The work is carried out in the framework of COST Action 274 TARSKI on Theory and Applications of Relational Structures as Knowledge Instruments.