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TransBox: EL++-closed Ontology Embedding

Hui Yang, Jiaoyan Chen, Uli Sattler

TL;DR

This paper tackles the challenge of embedding OWL ontologies with DL semantics by introducing EL^{++}-closed ontology embeddings and the TransBox method. TransBox represents concepts as boxes and roles as box-based translations, enabling closure under conjunction, existential quantification, and role composition, and extends box intersections to a space that includes the empty set to preserve meaningful overlaps. The authors also propose semantic and intersection enhancements, along with training objectives (distance, inclusion, negative sampling, regularization) to learn robust embeddings. Empirical results on GALEN, GO, and Anatomy show TransBox often achieves state-of-the-art performance for predicting complex axioms, with theoretical soundness proofs and a detailed ablation study. The work advances ontology learning and reasoning by enabling accurate inference over complex EL^{++} constructs and provides a foundation for future extensions to more expressive DLs and hybrid language-geometry approaches.

Abstract

OWL (Web Ontology Language) ontologies, which are able to represent both relational and type facts as standard knowledge graphs and complex domain knowledge in Description Logic (DL) axioms, are widely adopted in domains such as healthcare and bioinformatics. Inspired by the success of knowledge graph embeddings, embedding OWL ontologies has gained significant attention in recent years. Current methods primarily focus on learning embeddings for atomic concepts and roles, enabling the evaluation based on normalized axioms through specially designed score functions. However, they often neglect the embedding of complex concepts, making it difficult to infer with more intricate axioms. This limitation reduces their effectiveness in advanced reasoning tasks, such as Ontology Learning and ontology-mediated Query Answering. In this paper, we propose EL++-closed ontology embeddings which are able to represent any logical expressions in DL via composition. Furthermore, we develop TransBox, an effective EL++-closed ontology embedding method that can handle many-to-one, one-to-many and many-to-many relations. Our extensive experiments demonstrate that TransBox often achieves state-of-the-art performance across various real-world datasets for predicting complex axioms.

TransBox: EL++-closed Ontology Embedding

TL;DR

This paper tackles the challenge of embedding OWL ontologies with DL semantics by introducing EL^{++}-closed ontology embeddings and the TransBox method. TransBox represents concepts as boxes and roles as box-based translations, enabling closure under conjunction, existential quantification, and role composition, and extends box intersections to a space that includes the empty set to preserve meaningful overlaps. The authors also propose semantic and intersection enhancements, along with training objectives (distance, inclusion, negative sampling, regularization) to learn robust embeddings. Empirical results on GALEN, GO, and Anatomy show TransBox often achieves state-of-the-art performance for predicting complex axioms, with theoretical soundness proofs and a detailed ablation study. The work advances ontology learning and reasoning by enabling accurate inference over complex EL^{++} constructs and provides a foundation for future extensions to more expressive DLs and hybrid language-geometry approaches.

Abstract

OWL (Web Ontology Language) ontologies, which are able to represent both relational and type facts as standard knowledge graphs and complex domain knowledge in Description Logic (DL) axioms, are widely adopted in domains such as healthcare and bioinformatics. Inspired by the success of knowledge graph embeddings, embedding OWL ontologies has gained significant attention in recent years. Current methods primarily focus on learning embeddings for atomic concepts and roles, enabling the evaluation based on normalized axioms through specially designed score functions. However, they often neglect the embedding of complex concepts, making it difficult to infer with more intricate axioms. This limitation reduces their effectiveness in advanced reasoning tasks, such as Ontology Learning and ontology-mediated Query Answering. In this paper, we propose EL++-closed ontology embeddings which are able to represent any logical expressions in DL via composition. Furthermore, we develop TransBox, an effective EL++-closed ontology embedding method that can handle many-to-one, one-to-many and many-to-many relations. Our extensive experiments demonstrate that TransBox often achieves state-of-the-art performance across various real-world datasets for predicting complex axioms.

Paper Structure

This paper contains 50 sections, 5 theorems, 23 equations, 4 figures, 15 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Related Work
  3. Ontologies
  4. Ontology Embeddings
  5. EL++-Closed Embeddings
  6. Method: TransBox
  7. Geometric Construction
  8. Concept and individual
  9. Role
  10. Expressiveness
  11. Model Complexity
  12. EL++-closeness
  13. Semantic Enhancement
  14. Enhancing Box Intersections
  15. Extended Box intersections over $(\mathbb{R}\xspace\cup\{\emptyset\})^n$
  16. ...and 35 more sections

Key Result

proposition 2

Let $Box(r \circ t)$ be the box with center $\mathbf{c}\xspace(r) + \mathbf{c}\xspace(t)$ and offset $\mathbf{o}\xspace(r) + \mathbf{o}\xspace(t)$. Then, we have $E_{Box(r \circ t)} = E_{Box(r)} \circ E_{Box(t)}$, where the composition is defined as $E_{Box(r)} \circ E_{Box(t)} =$$\{(\mathbf{x}, \ma

Figures (4)

  • Figure 1: Illustration of embedding roles as boxes
  • Figure 2: Illustration of $Box(\exists r. B)$
  • Figure 3: Illustration of $Box(\exists^{\text{all}}_r B)$
  • Figure 4: Embedding visualization of ELBE and TransBox for the family ontology in the 2-dimensional case. The box embeddings for roles in TransBox are highlighted in blue. 'w/o Enhancement' refers to training TransBox without the semantic and intersection enhancements.

Theorems & Definitions (11)

  • Example 1
  • Example 2
  • definition 1: $\mathcal{EL}^{++}$-Closed Embeddings
  • Example 3
  • proposition 2
  • proposition 3
  • proposition 4
  • theorem 1
  • theorem 2: Soundness
  • Example 4
  • ...and 1 more