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Duality Theory for Sequent Algebras
Sergio A. Celani, William Zuluaga
Sequent algebras were introduced by D. Vakarelov \cite{VakarelovSequentALg} as a generalization of contact algebras, replacing the binary contact relation with a relation between f…
From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions
William Zuluaga, Belén Gimenez
We develop a relational duality for semilattices with adjunctions (SLatas) based on binary meet-relations. First, we introduce the category of MoS-spaces and establish a dual equiv…
Extended Contact Algebras: Algebraic analysis and duality theory
Rafał Gruszczyński, Paula Menchón, William Zuluaga
The ternary extended contact relation was introduced in (Ivanova, 2020) as a more expressive counterpart of the standard binary contact relation. The class of Boolean algebras expa…
A Stone-type duality for semilattices with adjunctions
B. Gimenez, G. Pelaitay, W. Zuluaga
This paper focuses on semilattices with adjunctions (SLatas), which are semilattices with a greatest element enriched with a pair of adjoint maps. We develop a spectral-style duali…
On Heyting algebras with negative tense operators
F. Almiñana, G. Pelaitay, W. Zuluaga
In this paper, we will study Heyting algebras endowed with tense negative operators, which we call tense H-algebras and we proof that these algebras are the algebraic semantics of…
Tense operators on distributive lattices with implication
Gustavo Pelaitay, William Zuluaga
Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study the variety of tense distributi…