  We present a mathematical framework for mapping second-order logic relations
onto a simple state vector algebra. Using this algebra, basic theorems of set
theory can be proven in an algorithmic way, hence by an expert system. We
illustrate the use of the algebra with simple examples and show that, in
principle, all theorems of basic set theory can be recovered in an elementary
way. The developed technique can be used for an automated theorem proving in
the 1st and 2nd order logic.
