Building the Signature of Set Theory Using the MathSem Program

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 a small mathematical theory. This theory will be represented as a semantic net. We start with the signature where Set is the support set, is the membership predicate. Using the MathSem program we build the signature <Set;  where is set intersection,  is set union, -is the Cartesian product of sets, and is the subset relation.