Dual Box Embeddings for the Description Logic EL++

Mathias Jackermeier, Jiaoyan Chen, Ian Horrocks

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


OWL ontologies, whose formal semantics are rooted in Description Logic (DL), have been widely used for knowledge representation. Similar to Knowledge Graphs (KGs), ontologies are often incomplete, and maintaining and constructing them has proved challenging. While classical deductive reasoning algorithms use the precise formal semantics of an ontology to predict missing facts, recent years have witnessed growing interest in inductive reasoning techniques that can derive probable facts from an ontology. Similar to KGs, a promising approach is to learn ontology embeddings in a latent vector space, while additionally ensuring they adhere to the semantics of the underlying DL. While a variety of approaches have
been proposed, current ontology embedding methods suffer from several shortcomings, especially that they all fail to faithfully model one-to-many, many-to-one, and many-to-many relations and role inclusion axioms. To address this problem and improve ontology completion performance, we propose a novel ontology embedding method named Box2EL for the DL EL++, which represents both concepts and roles as boxes (i.e., axis-aligned hyperrectangles), and
models inter-concept relationships using a bumping mechanism. We theoretically prove the soundness of Box2EL and conduct an extensive experimental evaluation, achieving state-of-the-art results across a variety of datasets on the tasks of subsumption prediction, role assertion prediction, and approximating deductive reasoning.1
Original languageEnglish
Title of host publicationThe Web Conference 2024
Publication statusAccepted/In press - 23 Jan 2024


  • Ontology Embedding
  • Ontology Completion
  • Description Logic
  • Web Ontology Language
  • Link Prediction


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