# Description Logic EL++ Embeddings with Intersectional Closure

arXiv: https://arxiv.org/abs/2202.14018 · HTML: https://mlsanity.com/paper/2202.14018/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [KBGAN: Adversarial Learning for Knowledge Graph Embeddings](https://mlsanity.com/paper/1711.04071/) (2017)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [Semantic Similarity from Natural Language and Ontology Analysis](https://mlsanity.com/paper/1704.05295/) (2017)

## Built on by (most cited first, 16 of 16)

- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [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)
- [Ontology Completion with Natural Language Inference and Concept Embeddings: An Analysis](https://mlsanity.com/paper/2403.17216/) (2024)
- [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)
- [Knowledge Base Embeddings: Semantics and Theoretical Properties](https://mlsanity.com/paper/2408.04913/) (2024)
- [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)
- [Lattice-preserving ALC ontology embeddings with saturation](https://mlsanity.com/paper/2305.07163/) (2023)
- [BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization](https://mlsanity.com/paper/2605.23937/) (2026)
- [A hierarchy of faithfulness criteria for knowledge base completion](https://mlsanity.com/paper/2609.27863/) (2026)
- [Uncertainty in Representation Learning on Knowledge Graphs](https://mlsanity.com/paper/2610.06974/) (2026)

## Abstract (arXiv)

Many ontologies, in particular in the biomedical domain, are based on the Description Logic EL++. Several efforts have been made to interpret and exploit EL++ ontologies by distributed representation learning. Specifically, concepts within EL++ theories have been represented as n-balls within an n-dimensional embedding space. However, the intersectional closure is not satisfied when using n-balls to represent concepts because the intersection of two n-balls is not an n-ball. This leads to challenges when measuring the distance between concepts and inferring equivalence between concepts. To this end, we developed EL Box Embedding (ELBE) to learn Description Logic EL++ embeddings using axis-parallel boxes. We generate specially designed box-based geometric constraints from EL++ axioms for model training. Since the intersection of boxes remains as a box, the intersectional closure is satisfied. We report extensive experimental results on three datasets and present a case study to demonstrate the effectiveness of the proposed method.