Varieties of interlaced bilattices

Algebra Universalis 66 (1-2):115-141 (2011)
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Abstract

The paper contains some algebraic results on several varieties of algebras having an (interlaced) bilattice reduct. Some of these algebras have already been studied in the literature (for instance bilattices with conflation, introduced by M. Fit- ting), while others arose from the algebraic study of O. Arieli and A. Avron’s bilattice logics developed in the third author’s PhD dissertation. We extend the representation theorem for bounded interlaced bilattices (proved, among others, by A. Avron) to un- bounded bilattices and prove analogous representation theorems for the other classes of bilattices considered. We use these results to establish categorical equivalences between these structures and well-known varieties of lattices.

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Author Profiles

Felix Bou moliner
University of Valencia
Umberto Rivieccio
Universidad Nacional de Educación a Distancia
Ramon Jansana Ferrer
Universitat de Barcelona

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References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
The logic of distributive bilattices.Félix Bou & Umberto Rivieccio - 2011 - Logic Journal of the IGPL 19 (1):183-216.

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