On Consistent and Partially Consistent Extensions of Information Systems

Abstract

Consistent extensions of information systems have been earlier considered in the literature. Informally, a consistent extension of a given information system includes only such objects corresponding to known attribute values which are consistent with the whole knowledge represented by rules extracted from the information system. This paper presents a new look at consistent extensions of information systems focusing mainly on partially consistent extensions and broadening the approach proposed earlier by Z. Suraj. To this end, a notion of a partially consistent extension of an information system is introduced. The meaning, properties and application examples of such extensions are given. In the approach presented, we admit the situation that some objects in an extension are consistent only with a part of the knowledge extracted from the information system. We show how a factor of consistency with the original knowledge for a given object from an extension can be computed. Some coefficients concerning rules in information systems are defined to compute a factor of consistency. The notions presented are crucial for solving different problems. An example is given in the paper to show an application of the proposed approach in modelling of concurrent systems described by information systems.