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.
Distributive bilattices from the perspective of natural duality theory / Leonardo Manuel Cabrer; Hilary Priestley. - In: ALGEBRA UNIVERSALIS. - ISSN 0002-5240. - STAMPA. - 73:(2015), pp. 103-141. [10.1007/s00012-015-0316-5]
Distributive bilattices from the perspective of natural duality theory
CABRER, LEONARDO MANUEL;
2015
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.File | Dimensione | Formato | |
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