Description logic (DL) ontologies extend knowledge graphs (KGs) with
conceptual information and logical background knowledge. In recent years, there
has been growing interest in inductive reasoning techniques for such
ontologies, which promise to complement classical deductive reasoning
algorithms. Similar to KG completion, several existing approaches learn
ontology embeddings in a latent space, while additionally ensuring that they
faithfully capture the logical semantics of the underlying DL. However, they
suffer from several shortcomings, mainly due to a limiting role representation.
We propose Box2EL, which represents both concepts and roles as boxes (i.e.,
axis-aligned hyperrectangles) and demonstrate how it overcomes the limitations
of previous methods. We theoretically prove the soundness of our model and
conduct an extensive experimental evaluation, achieving state-of-the-art
results across a variety of datasets. As part of our evaluation, we introduce a
novel benchmark for subsumption prediction involving both atomic and complex
concepts