NDLI: A duality theory for bilattices

Content Provider	Springer Nature Link
Author	Mobasher, B. Pigozzi, D. Slutzki, G. Voutsadakis, G.
Copyright Year	2000
Abstract	Recent studies of the algebraic properties of bilattices have provided insight into their internal strucutres, and have led to practical results, especially in reducing the computational complexity of bilattice-based multi-valued logic programs. In this paper the representation theorem for interlaced bilattices without negation found in [19] and extended to arbitrary interlaced bilattices without negation in [2] 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 bilattices are characterized in terms of subdirectly irreducible lattices. A known characterization of the join-irreducible elements of the "knowledge" lattice of an interlaced bilattice is used to establish a natural equivalence between the category of finite, distributive bilattices and the category of posets of the form $ {\bf P} \oplus_\perp {\bf Q} $ .
Starting Page	109
Ending Page	125
Page Count	17
File Format	PDF
ISSN	00025240
Journal	algebra universalis
Volume Number	43
Issue Number	2
e-ISSN	14208911
Language	English
Publisher	Birkhäuser Verlag
Publisher Date	2000-08-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
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