Work

A Stone-type duality for semilattices with adjunctions

Year: 2025

Type: article

Abstract: 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 duality for SLatas, building on prior topological dualities for monotone semilattices. As an application of this duality, we characterize SLata congruences through an adaptation of lower-Vietoris-type families. Furthermore, we investigate tense operators on semilattices with a greatest element, deriving a duality for this case by extending the results obtained for SLatas.

Source: Journal of Logic and Computation

DOI: 10.1093/logcom/exaf014

Authors: Belén Gimenez, Gustavo Pelaitay, William Zuluaga

Institutions: Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, National University of San Juan

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4408376674

FWCI:

Cites: 22

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Related to: 10