TY - JOUR
T1 - The structure of interlaced bilattices
AU - Avron, A.
N1 - Publisher Copyright:
Copyright © 1996 Cambridge University Press.
PY - 1996/6/16
Y1 - 1996/6/16
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0005979229&partnerID=8YFLogxK
U2 - 10.1017/S0960129500001018
DO - 10.1017/S0960129500001018
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AN - SCOPUS:0005979229
SN - 0960-1295
VL - 6
SP - 287
EP - 299
JO - Mathematical Structures in Computer Science
JF - Mathematical Structures in Computer Science
IS - 3
ER -