Ebook: Distributive bilattices from the perspective of natural duality theory

NY.: Ithaca, Cornell University Library, 2014. — 28 p. English.{Free Published: Cornell University Library (arXiv:1308.4495v2 [math.RA] 15 Jan 2014)}.

[Submitted on 21 Aug 2013 (v1), last revised 15 Jan 2014 (this version, v2)].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.Introduction.
Distributive pre-bilattices and bilattices.
The natural duality framework.
A natural duality for distributive bilattices.
A natural duality for unbounded distributive bilattices.
How to dismount from a piggyback ride.
From a natural duality to the product representation.
Applications of the natural dualities for DB and DBu:
Limits and colimits.
Free algebras.
Injective and projective objects.
Uni cation type.
Admissibility.
Multisorted natural dualities.
Dualities for distributive pre-bilattices.
Concluding remarks.
References (32 publ).