Rough Pragmatic Description Logic

Abstract

In this chapter, a rough description logic is built on the basis of a pragmatic standpoint of representation of knowledge. The pragmatic standpoint has influenced the acceptance of a broader definition of the semantic network than that appearing in the literature. The definition of the semantic network is a motivation of the introduced semantics of the language of the descriptive logic. First, the theoretical framework of representation of knowledge that was proposed in the papers [24,25] is adjusted to the description of data processing. The pragmatic system of knowledge representation is determined, as well as situations of semantic adequacy and semantic inadequacy for represented knowledge are defined. Then, it is shown that general information systems (generalized information systems in Pawlak’s sense) presented in the paper [5] can be interpreted in pragmatic systems of knowledge representation. Rough sets in the set-theoretical framework proposed in papers [7,8] are defined for the general information systems. The pragmatic standpoint about objects is also a motivation to determine a model of semantic network. This model is considered as a general information system. It determines a formal language of the descriptive logic. The set-theoretical framework of rough sets, which was introduced for general information systems, makes it possible to describe the interpretation of this language in the theory of rough sets. Therefore this interpretation includes situations of semantic inadequacy. At the same time, for the class of all interpretations of this type, there exists a certain descriptive logic, which — in this chapter — is called rough pragmatic description logic.