Modules with fusion and implication based over distributive lattices: Representation and Duality

2020/07/28 by Ismael Calomino, Calomino, Ismael, W. J. Zuluaga Botero +1
Computer Science · Decision Sciences · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2007.14500

Abstract

In this paper we study the class of modules with fusion and implication based over distributive lattices, or FIDL-modules, for short. We introduce the concepts of FIDL-subalgebra and FIDL-congruence as well as the notions of simple and subdirectly irreducible FIDL-modules. We give a bi-sorted Priestley-like duality for FIDL-modules and moreover, as an application of such a duality, we provide a topological bi-spaced description of the FIDL-congruences. This result will allows us to characterize the simple and subdirectly irreducible FIDL-modules.

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