Recently, increasing efforts are put into learning continual representations
for symbolic knowledge bases (KBs). However, these approaches either only embed
the data-level knowledge (ABox) or suffer from inherent limitations when
dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model
the logical structure present in the KBs. We present BoxEL, a geometric KB
embedding approach that allows for better capturing the logical structure
(i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models
concepts in a KB as axis-parallel boxes that are suitable for modeling concept
intersection, 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 learned
model of BoxEL embedding with loss 0 is a (logical) model of the KB.
Experimental results on (plausible) subsumption reasonings and a real-world
application for protein-protein prediction show that BoxEL outperforms
traditional knowledge graph embedding methods as well as state-of-the-art EL++
embedding approaches.Comment: Published in ISWC'2