The structure of interlaced bilattices

Abstract

Bilattices were introduced and applied by Ginsberg and Fitting for a diversity of applications, such as truth maintenance systems, default inferences and logic programming. In this paper we investigate the structure and properties of a particularly important class of bilattices called interlaced bilattices, which were introduced by Fitting. The main results are that every interlaced bilattice is isomorphic to the Ginsberg-Fitting product of two bounded lattices and that the variety of interlaced bilattices is equivalent to the variety of bounded lattices with two distinguishable distributive elements, which are complements of each other. This implies that interlaced bilattices can be characterized using a finite set of equations. Our results generalize to interlaced bilattices some results of Ginsberg, Fitting and Jónsson for distributive bilattices.