A Duality for Involutive Bisemilattices

Bonzio, Stefano
;Loi, Andrea;Peruzzi, Luisa
2019-01-01

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.
2019
Duality; Involutive bisemilattice; Paraconsistent weak Kleene; Płonka sum; Stone space; Logic; History and Philosophy of Science
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