Monotonic Distributive Semilattices
Logic
2018-10-22 v1
Abstract
In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the -fragment of intuitionistic logic is the variety of implicative meet-semilattices \cite{CelaniImplicative} \cite{ChajdaHalasKuhr}. In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator . We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.
Cite
@article{arxiv.1810.08585,
title = {Monotonic Distributive Semilattices},
author = {Sergio A. Celani and Ma. Paula Menchón},
journal= {arXiv preprint arXiv:1810.08585},
year = {2018}
}