The Distributive, Graded Lattice of EL Concept Descriptions and its Neighborhood Relation (Extended Version)

Abstract

For the description logic EL, we consider the neighborhood relation which is induced by the subsumption order, and we show that the corresponding lattice of EL concept descriptions is distributive, modular, graded, and metric. In particular, this implies the existence of a rank function as well as the existence of a distance function.