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

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