A Set Theoretic Approach for Knowledge Representation: the Representation Part

In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by equality assertions. We first present a primitive form that uses minimal assumed knowledge and constructs. Then, assuming naive set theory, we extend it by definitions, which are special kinds of knowledge. Interestingly, we show that the primitive form is expressive enough to define logic operators, not only propositional connectives but also quantifiers.