Knowledge and approximations: A formal study under the perspective of information systems and rough set theory

Abstract

In this article, we aim to bring together the operators of epistemic logic and approximation operators of rough set theory by combining the ideas from epistemic logic and rough set logics. The possible world semantics of epistemic logic is extended to capture a situation where we have a set of states, each representing a possible state of affairs and carrying information about a set of objects regarding a set of attributes. We propose a logic that can be used to reason about the knowledge operator as well as the approximation operators generated from the constituent information systems relative to different set of attributes. The important issues of the proposed logic viz. sound and complete deductive systems with respect to various classes of models are also addressed.