A duality theory for bilattices
type: Item
instance of: scholarly article
title: A duality theory for bilattices
zbMATH Open document ID: 1012.06008
author: George Voutsadakis
author: Bamshad Mobasher
author: Don Pigozzi
author: Giora Slutzki
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: Bilattices are algebras with two separate lattice structures. They have been used as the basis for a denotational semantics for systems of inference that arise in artificial intelligence and knowledge-based programming. Recent studies of the algebraic properties of bilattices have provided insight into their internal structures, and have led to practical results, especially in reducing the computational complexity of bilattice-based multivalued logic programs. In the paper the representation problem for interlaced bilattices without negation raised by \textit{A. Romanowska} and \textit{A. Trakul} [Universal and Applied Algebra, Proc. 5th Symp. Turawa/Pol. 1988, 235-253 (1989; Zbl 0738.06008)] and extended to arbitrary interlaced bilattices without negation by \textit{A. Avron} [Math. Struct. Comput. Sci. 6, 287-299 (1996; Zbl 0856.06005)] is presented. A natural equivalence is then established between the category of interlaced bilattices and the cartesian square of the category of bounded lattices. As a consequence a dual natural equivalence is obtained between the category of distributive bilattices and the coproduct of the category of bounded Priestley spaces with itself. Some applications of these equivalences are given. The subdirectly irreducible interlaced bisemilattices are characterized in terms of subdirectly irreducible lattices.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 08A70
Mathematics Subject Classification ID: 18A23
Mathematics Subject Classification ID: 68N17
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 1899929
zbMATH Keywords: representation of bilattices
zbMATH Keywords: category of bilattices
zbMATH Keywords: logic programming
zbMATH Keywords: interlaced bilattices
zbMATH Keywords: Priestley duality
zbMATH Keywords: natural equivalence
zbMATH Keywords: Priestley spaces
zbMATH Keywords: subdirectly irreducible
MaRDI profile type: Publication
full work available at URL: s000120050149
OpenAlex ID: W2090633591
DOI: 10.1007/S000120050149
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description: scientific article; zbMATH DE number 1899929