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arXiv · 1810.08585

Monotonic Distributive Semilattices

Sergio A. Celani·Ma. Paula Menchón
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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 $\{\rightarrow,\wedge,\top\}$-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 $m$. 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.

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BibTeXRIS

Sergio A. Celani, Ma. Paula Menchón. 2018-10-19. Monotonic Distributive Semilattices. https://arxiv.org/abs/1810.08585

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