# EL Embeddings: Geometric construction of models for the Description Logic EL ++

arXiv: https://arxiv.org/abs/1902.10499 · HTML: https://mlsanity.com/paper/1902.10499/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 30 of 48)

- [Knowledge-aware Zero-Shot Learning: Survey and Perspective](https://mlsanity.com/paper/2103.00070/) (2021)
- [Contextual Semantic Embeddings for Ontology Subsumption Prediction](https://mlsanity.com/paper/2202.09791/) (2022)
- [A Unified Review of Deep Learning for Automated Medical Coding](https://mlsanity.com/paper/2201.02797/) (2022)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Zero-shot and Few-shot Learning with Knowledge Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2112.10006/) (2021)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [DeepOnto: A Python Package for Ontology Engineering with Deep Learning](https://mlsanity.com/paper/2307.03067/) (2023)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [Shrinking Embeddings for Hyper-Relational Knowledge Graphs](https://mlsanity.com/paper/2306.02199/) (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)
- [Start from Zero: Triple Set Prediction for Automatic Knowledge Graph Completion](https://mlsanity.com/paper/2406.18166/) (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)
- [Ontology-based n-ball Concept Embeddings Informing Few-shot Image Classification](https://mlsanity.com/paper/2109.09063/) (2021)
- [Ontology Completion with Natural Language Inference and Concept Embeddings: An Analysis](https://mlsanity.com/paper/2403.17216/) (2024)
- [Towards Semantically Enriched Embeddings for Knowledge Graph Completion](https://mlsanity.com/paper/2308.00081/) (2023)
- [ProtSAE: Disentangling and Interpreting Protein Language Models via Semantically-Guided Sparse Autoencoders](https://mlsanity.com/paper/2509.05309/) (2025)
- [To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits](https://mlsanity.com/paper/2601.14894/) (2026)
- [Prediction of Adverse Biological Effects of Chemicals Using Knowledge Graph Embeddings](https://mlsanity.com/paper/2112.04605/) (2021)
- [TAR: Neural Logical Reasoning across TBox and ABox](https://mlsanity.com/paper/2205.14591/) (2022)
- [FALCON: Scalable Reasoning over Inconsistent ALC Ontologies](https://mlsanity.com/paper/2208.07628/) (2022)
- [Embedding Ontologies via Incorporating Extensional and Intensional Knowledge](https://mlsanity.com/paper/2402.01677/) (2024)
- [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)
- [Why Settle for Just One? Extending EL++ Ontology Embeddings with Many-to-Many Relationships](https://mlsanity.com/paper/2110.10555/) (2021)
- [Link Analysis meets Ontologies: Are Embeddings the Answer?](https://mlsanity.com/paper/2111.11710/) (2021)
- [Differentiable Fuzzy ALC: A Neural-Symbolic Representation Language for Symbol Grounding](https://mlsanity.com/paper/2211.12006/) (2022)
- [Biomedical Knowledge Graph Embeddings with Negative Statements](https://mlsanity.com/paper/2308.03447/) (2023)

## Abstract (arXiv)

An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can be used for machine learning, similarity search, or similar tasks. We address the problem of finding vector space embeddings for theories in the Description Logic EL++ that are also models of the TBox. To find such embeddings, we define an optimization problem that characterizes the model-theoretic semantics of the operators in EL++ within Ren, thereby solving the problem of finding an interpretation function for an EL++ theory given a particular domain Delta. Our approach is mainly relevant to large EL++ theories and knowledge bases such as the ontologies and knowledge graphs used in the life sciences. We demonstrate that our method can be used for improved prediction of protein--protein interactions when compared to semantic similarity measures or knowledge graph embedding