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Many ontologies, in particular in the biomedical domain, are based on theDescription Logic EL++. Several efforts have been made to interpret and exploitEL++ ontologies by distributed representation learning. Specifically, conceptswithin EL++ theories have been represented as n-balls within an n-dimensionalembedding space. However, the intersectional closure is not satisfied whenusing n-balls to represent concepts because the intersection of two n-balls isnot an n-ball. This leads to challenges when measuring the distance betweenconcepts and inferring equivalence between concepts. To this end, we developedEL Box Embedding (ELBE) to learn Description Logic EL++ embeddings usingaxis-parallel boxes. We generate specially designed box-based geometricconstraints from EL++ axioms for model training. Since the intersection ofboxes remains as a box, the intersectional closure is satisfied. We reportextensive experimental results on three datasets and present a case study todemonstrate the effectiveness of the proposed method.

Description Logic EL++ Embeddings with Intersectional Closure