Characterization of clones of boolean operations by identities

Abstract

In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones by using of identities. For each Boolean clone we obtain a set of equations with the property that an operation \(f\) belongs to this clone if and only if it satisfies these equations.