Bilattices and hyperidentities. (English. Russian original) Zbl 1294.06007
Proc. Steklov Inst. Math. 274, 174-192 (2011); translation from Tr. Mat. Inst. Steklova 274, 191-209 (2011).
Summary: 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, multivalued 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.
MSC:
| 06B20 | Varieties of lattices |
| 06B75 | Generalizations of lattices |
| 08B05 | Equational logic, Mal’tsev conditions |
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