A Set Theoretic Approach for Knowledge Representation: the Representation Part
This work addresses knowledge representation for AI systems, but appears incremental as it builds on existing set theory concepts.
The paper tackles the problem of knowledge representation by proposing a set theoretic approach that formalizes knowledge through equality assertions, and demonstrates that the primitive form of this approach can define both propositional connectives and quantifiers.
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.