# Dual Box Embeddings for the Description Logic EL++

arXiv: https://arxiv.org/abs/2301.11118 · HTML: https://mlsanity.com/paper/2301.11118/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Universal Representation Learning of Knowledge Bases by Jointly Embedding Instances and Ontological Concepts](https://mlsanity.com/paper/2103.08115/) (2021)
- [Contextual Semantic Embeddings for Ontology Subsumption Prediction](https://mlsanity.com/paper/2202.09791/) (2022)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [OntoEA: Ontology-guided Entity Alignment via Joint Knowledge Graph Embedding](https://mlsanity.com/paper/2105.07688/) (2021)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [LogicENN: A Neural Based Knowledge Graphs Embedding Model with Logical Rules](https://mlsanity.com/paper/1908.07141/) (2019)

## Built on by (most cited first, 21 of 21)

- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Approximating Probabilistic Inference in Statistical EL with Knowledge Graph Embeddings](https://mlsanity.com/paper/2407.11821/) (2024)
- [TransBox: EL++-closed Ontology Embedding](https://mlsanity.com/paper/2410.14571/) (2024)
- [Language Models as Ontology Encoders](https://mlsanity.com/paper/2507.14334/) (2025)
- [DAGE: DAG Query Answering via Relational Combinator with Logical Constraints](https://mlsanity.com/paper/2410.22105/) (2024)
- [Towards Semantically Enriched Embeddings for Knowledge Graph Completion](https://mlsanity.com/paper/2308.00081/) (2023)
- [To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits](https://mlsanity.com/paper/2601.14894/) (2026)
- [A Self-matching Training Method with Annotation Embedding Models for Ontology Subsumption Prediction](https://mlsanity.com/paper/2402.16278/) (2024)
- [Knowledge Base Embeddings: Semantics and Theoretical Properties](https://mlsanity.com/paper/2408.04913/) (2024)
- [Towards Consistent Language Models Using Declarative Constraints](https://mlsanity.com/paper/2312.15472/) (2023)
- [Enhancing Geometric Ontology Embeddings for EL++ with Negative Sampling and Deductive Closure Filtering](https://mlsanity.com/paper/2405.04868/) (2024)
- [RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions](https://mlsanity.com/paper/2501.17518/) (2025)
- [Graph Neural Network based Hierarchy-Aware Embeddings of Knowledge Graphs: Applications to Yeast Phenotype Prediction](https://mlsanity.com/paper/2605.03690/) (2026)
- [Lattice-preserving ALC ontology embeddings with saturation](https://mlsanity.com/paper/2305.07163/) (2023)
- [DELE: Deductive EL++ Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/2411.01574/) (2024)
- [PROMPT2BOX:Improving LLM Weakness Discovery and Specificity Estimation by Uncovering Entailment Structure among Prompts](https://mlsanity.com/paper/2603.21438/) (2026)
- [BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization](https://mlsanity.com/paper/2605.23937/) (2026)
- [NeurOWL: An LLM-Based Neural-symbolic Framework for Incomplete OWL Ontology Reasoning](https://mlsanity.com/paper/2607.15776/) (2026)
- [Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits](https://mlsanity.com/paper/2608.17741/) (2026)
- [Hierarchy-Aware Semantic Losses for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2608.22981/) (2026)
- [A hierarchy of faithfulness criteria for knowledge base completion](https://mlsanity.com/paper/2609.27863/) (2026)

## Abstract (arXiv)

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.