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Distributive bilattices from the perspective of natural duality theory

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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.

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  1. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford, OX2 6GG, UK

    L. M. Cabrer & H. A. Priestley

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  1. L. M. Cabrer
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  2. H. A. Priestley
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Correspondence to H. A. Priestley.

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Presented by M. Haviar.

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Cabrer, L.M., Priestley, H.A. Distributive bilattices from the perspective of natural duality theory. Algebra Univers. 73, 103–141 (2015). https://doi.org/10.1007/s00012-015-0316-5

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