DOT : a Knowledge Representation System Using Dot Notation and IS-A Relation

Abstract

Although the concepts of IS-A relation and inheritance are used in a wide variety of areas in computer science, it has been pointed out that their semantics as well as their expressive and reasoning capabilities lack mathematical foundation. In this paper, we propose a framework for knowledge representation and reasoning, called DOT, whose two main components are dot notations and IS-A relations. In DOT, roles or attributes are semantically included in the domain of IS-A relation using dot notations, and then relationships between objects are represented by a description of IS-A relation between two dot notations. We formalize the DOT framework in an algebraic way, and show that the upper and/or the lower bounds of each element in the domain concerning the IS-A relation can be represented by regular expressions in automata theory. Furthermore, it is proved that whether a pair of elements in the domain is included in the IS-A relation specified by the DOT framework is decided in polynomial time. In this way, the expressive and reasoning capabilities of IS-A relation and inheritance are mathematically well formalized without losing simplicity of the framework.