Box Embeddings for the Description Logic EL++

Recently, various methods for representation learning on Knowledge Bases (KBs) have been developed. However, these approaches either only focus on learning the embeddings of the data-level knowledge (ABox) or exhibit inherent limitations when dealing with the concept-level knowledge (TBox), e.g., not properly modelling the structure of the logical knowledge. We present BoxEL, a geometric KB embedding approach that allows for better capturing logical structure expressed in the theories of Description Logic EL++. BoxEL models concepts in a KB as axis-parallel boxes exhibiting the advantage of intersectional closure, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the trained model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on subsumption reasoning and a real-world application--protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.