Distributive nearlattices with a necessity modal operator

Abstract

The aim of this paper is to study the class of distributive nearlattices with a necessity modal operator. We develop a full duality to the category of distributive nearlattices whose morphisms are applications that preserving the infimum when exists and, as special case, we obtain a representation and duality for distributive nearlattices with a necessity modal operator. We study certain particular subclasses and give some applications.