Lattice-Preserving \(\mathcal {ALC}\) Ontology Embeddings

Generating vector representations (embeddings) of OWL ontologies is a growing task due to its applications in predicting missing facts and knowledge-enhanced learning in fields such as bioinformatics. The underlying semantics of OWL ontologies is expressed using Description Logics (DLs). Initial approaches to generate embeddings relied on constructing a graph out of ontologies, neglecting the semantics of the logic therein. Recent semantic-preserving embedding methods often target lightweight DL languages like \(\mathcal{E}\mathcal{L}^{++}\) , 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 many real-world ontologies are devoid of them. We propose an ontology embedding method for the \(\mathcal {ALC}\) DL language that considers the lattice structure of concept descriptions. We use connections between DL and Category Theory to materialize the lattice structure and embed it using an order-preserving embedding method. We show that our method outperforms state-of-the-art methods in several knowledge base completion tasks. We make our code and data available at https://github.com/bio-ontology-research-group/catE .