A state vector algebra for algorithmic implementation of second-order logic

摘要

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