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Studia Logica

, Volume 107, Issue 2, pp 423–444 | Cite as

A Duality for Involutive Bisemilattices

  • Stefano BonzioEmail author
  • Andrea Loi
  • Luisa Peruzzi
Article

Abstract

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation.

Keywords

Duality Involutive bisemilattice Stone space Płonka sum Paraconsistent weak Kleene 

Mathematics Subject Classification

Primary 08C20 Secondary 06E15 18A99 22A30 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università Politecnica delle MarcheAnconaItaly
  2. 2.Università di CagliariCagliariItaly

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