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The structure of interlaced bilattices

Published online by Cambridge University Press:  04 March 2009

A. Avron
A. Avron
Affiliation:
Department of Computer Science, Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel 69978
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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.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 3 , June 1996 , pp. 287 - 299
Copyright
Copyright © Cambridge University Press 1996

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References

Avron, A. (1995) A note on the structure of bilattices. Mathematical Structures in Computer Science 5 431–438.CrossRefGoogle Scholar
Birkhoff, G. (1948) Lattice Theory, A.M.S., Providence.Google Scholar
Fitting, M. (1989) Negation as refutation. In: Proc. 4th Annual Symp. on Logic in Computer Science, IEEE Press 63–70.Google Scholar
Fitting, M. (1990) Bilattices in logic programming. In: Epstein, G. (ed.) The 20th Int. Symp. On Multiple-Valued Logic, IEEE Press 238–246.Google Scholar
Fitting, M. (1991) Bilattices and the semantics of logic programming. Journal of Logic Programming 11 (2) 91–116.CrossRefGoogle Scholar
Fitting, M. (1994) Kleene’s three-valued logics and their children. Fundamenta Informaticae 20 113–131.CrossRefGoogle Scholar
Ginsberg, M. L. (1988) Multivalued logics: a uniform approach to reasoning in AI. Computer Intelligence 4 256–316.CrossRefGoogle Scholar
Jónsson, B (1994) Distributive Bilattices, Vanderbilt University.Google Scholar