A Class of Finite Boolean Algebras

Abstract

In this chapter we will show that the set of all binary functions defined on a finite Cartesian Product M may be considered as a special case of a more general class of so-called Boolean algebras e.g. systems of events in probability theory or truth function systems used in propositional logic. This is of practical importance because implicants (prime implicants) and implicates (prime implicates) may be also defined in such Boolean algebras. Moreover it will appear that all results concerning implicants and implicates of binary functions may be translated in a simple way into the general model of a certain type of a Boolean algebra.