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A note on the structure of bilattices

Published online by Cambridge University Press:  04 March 2009

A. Avron
A. Avron
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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Abstract

A notion of bilattice was first proposed by Ginsberg as a general framework for many applications. Related notions were further investigated and applied for various goals by Fitting. In the present paper a general definition of bilattices is proposed, which covers all particular cases that have actually been used in the literature. It is shown also that in the finite case every bilattice in our sense is graphically representable by a special type of a two-dimensional diagram.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 3 , September 1995 , pp. 431 - 438
Copyright
Copyright © Cambridge University Press 1995

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References

Belnap, N. D. (1977a) A useful four-valued logic. In: Epstein, G. and Dunn, J. M. (eds.) Modern Uses of Multiple-Valued Logic, D. Reidel 8–37.Google Scholar
Belnap, N. D. (1977b) How computers should think. In: Ryle, G. (ed.). Contemporary Aspects of Philosophy, Oriel Press 30–56.Google Scholar
Fitting, M. C. (1989) Negation as Refutation. Proc. 4th Annual Symp. on Logic in Computer Science, IEEE Press 63–70.Google Scholar
Fitting, M. C. (1990a) Kleene’s logic, generalized. Journal of Logic and Computation 1 797–810.CrossRefGoogle Scholar
Fitting, M. C. (1990b) Modal/multiple valued logics. (To be published in Handbook of Logic in AI and Logic Programming, Oxford University Press.)Google Scholar
Fitting, M. C. (1991) Bilattices and the semantics of logic programming. Journal of Logic Programming 11 (2) 91–116.CrossRefGoogle Scholar
Fitting, M. C. (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