Bilattices and hyperidentities

Bilattices as algebras with two lattice structures were introduced by M. Ginsberg and M. Fitting in 1986–1990. They have found wide applications in logic programming, multi-valued logic, and artificial intelligence. We call these bilattices Ginsberg's bilattices. The description of Ginsberg's bilattices was obtained by various authors under the conditions of interlacement (or distributivity) and boundedness. In this paper, we prove that this description remains true without the second condition, while interlacement can be replaced with a weaker form called weak interlacement here. In particular, we prove that every weakly interlaced bilattice is isomorphic to the superproduct of two lattices, while every weakly interlaced Ginsberg bilattice is isomorphic to the Ginsberg superproduct of two equal lattices.