Building the Signature of Set Theory Using the MathSem Program

TL;DR

This paper presents a method for representing elementary set theory as a semantic net using the MathSem program, aiming to formalize mathematical knowledge for improved knowledge representation.

Contribution

It introduces a novel approach to modeling set theory within a semantic network framework using the MathSem program, enhancing formalization of mathematical knowledge.

Findings

Set theory concepts are effectively represented as semantic nets.

The MathSem program facilitates the formalization process.

The approach improves understanding of mathematical knowledge representation.

Abstract

Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we consider a deductive system that derives mathematical notions, axioms and theorems. All these notions, axioms and theorems can be considered as the part of elementary set theory. This theory will be represented as a semantic net.