Dual ordered structures of binary relations

Abstract

The theory of ordered structures like a (lattice) ordered semigroups is applied to graphs and automatons as well as to coding, programming and artificial intelligence. In this paper an algebraic structure on an underlying set of binary relations is considered. The structure includes the operations of Boolean algebra, inverse and composition. It is defined a dual semigroup to the binary relations ordered semigroup, and then the general properties of dual operations are studied.