Monotonic Distributive Semilattices
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 CelaniImplicative 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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