# Faithiful Embeddings for EL++ Knowledge Bases

arXiv: https://arxiv.org/abs/2201.09919 · HTML: https://mlsanity.com/paper/2201.09919/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 24 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Analogical Inference for Multi-Relational Embeddings](https://mlsanity.com/paper/1705.02426/) (2017)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [Onto2Vec: joint vector-based representation of biological entities and their ontology-based annotations](https://mlsanity.com/paper/1802.00864/) (2018)
- [From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules](https://mlsanity.com/paper/1805.10461/) (2018)
- [Towards Statistical Reasoning in Description Logics over Finite Domains (Full Version)](https://mlsanity.com/paper/1706.03207/) (2017)

## Built on by (most cited first, 25 of 25)

- [Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?](https://mlsanity.com/paper/2409.13456/) (2024)
- [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)
- [HiPrompt: Few-Shot Biomedical Knowledge Fusion via Hierarchy-Oriented Prompting](https://mlsanity.com/paper/2304.05973/) (2023)
- [Geometric Relational Embeddings: A Survey](https://mlsanity.com/paper/2304.11949/) (2023)
- [Capturing Knowledge Graphs and Rules with Octagon Embeddings](https://mlsanity.com/paper/2401.16270/) (2024)
- [Generating SROI^- Ontologies via Knowledge Graph Query Embedding Learning](https://mlsanity.com/paper/2407.09212/) (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)
- [A Self-matching Training Method with Annotation Embedding Models for Ontology Subsumption Prediction](https://mlsanity.com/paper/2402.16278/) (2024)
- [Biomedical Knowledge Graph Embeddings with Negative Statements](https://mlsanity.com/paper/2308.03447/) (2023)
- [Neuro-Symbolic RDF and Description Logic Reasoners: The State-Of-The-Art and Challenges](https://mlsanity.com/paper/2308.04814/) (2023)
- [Enhancing Geometric Ontology Embeddings for EL++ with Negative Sampling and Deductive Closure Filtering](https://mlsanity.com/paper/2405.04868/) (2024)
- [Building Trustworthy AI: Transparent AI Systems via Large Language Models, Ontologies, and Logical Reasoning (TranspNet)](https://mlsanity.com/paper/2411.08469/) (2024)
- [Graph Neural Network based Hierarchy-Aware Embeddings of Knowledge Graphs: Applications to Yeast Phenotype Prediction](https://mlsanity.com/paper/2605.03690/) (2026)
- [Scalable Uncertainty Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2605.16568/) (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)
- [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)

Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application for protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.