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Generating vector representations (embeddings) of OWL ontologies is a growingtask due to its applications in predicting missing facts and knowledge-enhancedlearning in fields such as bioinformatics. The underlying semantics of OWLontologies are expressed using Description Logics (DLs). Initial approaches togenerate embeddings relied on constructing a graph out of ontologies,neglecting the semantics of the logic therein. Recent semantic-preservingembedding methods often target lightweight DL languages like$\mathcal{EL}^{++}$, ignoring more expressive information in ontologies.Although some approaches aim to embed more descriptive DLs like$\mathcal{ALC}$, those methods require the existence of individuals, while manyreal-world ontologies are devoid of them. We propose an ontology embeddingmethod for the $\mathcal{ALC}$ DL language that considers the lattice structureof concept descriptions. We use connections between DL and Category Theory tomaterialize the lattice structure and embed it using an order-preservingembedding method. We show that our method outperforms state-of-the-art methodsin several knowledge base completion tasks. Furthermore, we incoporatesaturation procedures that increase the information within the constructedlattices. We make our code and data available at\url{https://github.com/bio-ontology-research-group/catE}.

Lattice-preserving $\mathcal{ALC}$ ontology embeddings with saturation