# From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings

arXiv: https://arxiv.org/abs/2303.16519 · HTML: https://mlsanity.com/paper/2303.16519/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 39 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [Contextual Semantic Embeddings for Ontology Subsumption Prediction](https://mlsanity.com/paper/2202.09791/) (2022)
- [GammaE: Gamma Embeddings for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2210.15578/) (2022)
- [FALCON: Scalable Reasoning over Inconsistent ALC Ontologies](https://mlsanity.com/paper/2208.07628/) (2022)

## Built on by (most cited first, 3 of 3)

- [Enhancing Geometric Ontology Embeddings for EL++ with Negative Sampling and Deductive Closure Filtering](https://mlsanity.com/paper/2405.04868/) (2024)
- [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)

## Abstract (arXiv)

Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in ℝn. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms.