A Set Theoretic Approach for Knowledge Representation: the Representation Part

TL;DR

This paper introduces a set theoretic framework for knowledge representation, demonstrating that minimal constructs can express complex logic operators and quantifiers, offering a foundational approach to formalize knowledge.

Contribution

It presents a novel set theoretic method that captures syntax and knowledge with minimal assumptions, extending it with definitions to encompass logic operators and quantifiers.

Findings

Primitive form is expressive enough to define logic operators.

Set theoretic constructs effectively formalize knowledge.

Extensions with definitions enhance expressiveness.

Abstract

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.