Monotonic Distributive Semilattices

2018/10/19 by Celani, Sergio A., Menchón, Ma. Paula
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1810.08585

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 \→,\wedge,\top\-fragment of intuitionistic logic is the variety of implicative meet-semilattices \citeCelaniImplicative \citeChajdaHalasKuhr. 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.

Related

• The Distributive Full Lambek Calculus with Modal Operators
• On distributive join-semilattices
• Join-semilattices whose principal filters are pseudocomplemented lattices
• A topological duality for monotone expansions of semilattices
• Duality for distributive and implicative semi-lattices