Distributive bilattices from the perspective of natural duality theory

TL;DR

This paper employs natural duality theory to provide a unified and economical representation of distributive bilattices, linking their algebraic properties to dual categorical structures and interpreting 'truth' and 'knowledge' as dual concepts.

Contribution

It introduces a novel natural duality framework for distributive bilattices, connecting existing product representations and dualities through a simple translation process.

Findings

Dualities relate to product representations for bilattices

Descriptions of algebraic and categorical properties are obtained

'Truth' and 'knowledge' are interpreted as dual notions

Abstract

This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures 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.