# From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules

arXiv: https://arxiv.org/abs/1805.10461 · HTML: https://mlsanity.com/paper/1805.10461/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2018.

## Built on by (most cited first, 19 of 19)

- [OntoZSL: Ontology-enhanced Zero-shot Learning](https://mlsanity.com/paper/2102.07339/) (2021)
- [Universal Representation Learning of Knowledge Bases by Jointly Embedding Instances and Ontological Concepts](https://mlsanity.com/paper/2103.08115/) (2021)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?](https://mlsanity.com/paper/2409.13456/) (2024)
- [Learning Description Logic Ontologies. Five Approaches. Where Do They Stand?](https://mlsanity.com/paper/2104.01193/) (2021)
- [Poisoning Knowledge Graph Embeddings via Relation Inference Patterns](https://mlsanity.com/paper/2111.06345/) (2021)
- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Capturing Knowledge Graphs and Rules with Octagon Embeddings](https://mlsanity.com/paper/2401.16270/) (2024)
- [Geometric Models for (Temporally) Attributed Description Logics](https://mlsanity.com/paper/2108.12239/) (2021)
- [Towards Loosely-Coupling Knowledge Graph Embeddings and Ontology-based Reasoning](https://mlsanity.com/paper/2202.03173/) (2022)
- [To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuits](https://mlsanity.com/paper/2601.14894/) (2026)
- [Knowledge Base Embeddings: Semantics and Theoretical Properties](https://mlsanity.com/paper/2408.04913/) (2024)
- [Modelling Monotonic and Non-Monotonic Attribute Dependencies with Embeddings: A Theoretical Analysis](https://mlsanity.com/paper/2106.14431/) (2021)
- [Embeddings as Epistemic States: Limitations on the Use of Pooling Operators for Accumulating Knowledge](https://mlsanity.com/paper/2210.05723/) (2022)
- [Faithful Differentiable Reasoning with Reshuffled Region-based Embeddings](https://mlsanity.com/paper/2406.09529/) (2024)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [Graph Neural Network based Hierarchy-Aware Embeddings of Knowledge Graphs: Applications to Yeast Phenotype Prediction](https://mlsanity.com/paper/2605.03690/) (2026)
- [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)

## Abstract (arXiv)

Recent years have witnessed the successful application of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. However, it is not yet well-understood to what extent ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a general framework based on a view of relations as regions, which allows us to study the compatibility between ontological knowledge and different types of vector space embeddings. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding methods are not capable of modelling even very simple types of rules, which in particular also means that they are not able to learn the type of dependencies captured by such rules. Second, we study a model in which relations are modelled as convex regions. We show particular that ontologies which are expressed using so-called quasi-chained existential rules can be exactly represented using convex regions, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.