Abstract

In this paper, we obtain axiom systems, bases of identities and quasi-identities for classes of algebras of binary relations with a conjunctive operation, i.e., an operation that can be defined by a logical formula containing only conjunctions. The result of applying such an operation to two binary relations is the Cartesian product of their reflexive projections. Our consideration of these classes leads to the concept of quasi-semilattices as a natural generalization of the notion of semilattices.