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.
2015
73
103
141
Leonardo Manuel Cabrer; Hilary Priestley
File in questo prodotto:
File Dimensione Formato  
dbilat-AUsubmittedWebVersion.pdf

Accesso chiuso

Tipologia: Altro
Licenza: Tutti i diritti riservati
Dimensione 458.38 kB
Formato Adobe PDF
458.38 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/975606
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 8
social impact