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Algebra universalis

, Volume 73, Issue 2, pp 103–141 | Cite as

Distributive bilattices from the perspective of natural duality theory

  • L. M. Cabrer
  • H. A. Priestley
Article

Abstract

This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of natural duality are employed to give, economically and in a uniform way, categories of structures dually equivalent to these varieties. We relate our dualities to the product representations for bilattices and to pre-existing dual representations by a simple translation process which is an instance of a more general mechanism for connecting dualities based on Priestley duality to natural dualities. Our approach gives us access to descriptions of algebraic/categorical properties of bilattices and also reveals how ‘truth’ and ‘knowledge’ may be seen as dual notions.

2010 Mathematics Subject Classification

Primary: 06D50 Secondary: 08C20 06D30 03G25 

Keywords and phrases

distributive bilattice natural duality Priestley duality De Morgan algebra 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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