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

• URL: http://arxiv.org/abs/2305.07163v3
• Date: Wed, 06 Nov 2024 07:01:54 GMT
• Title: Lattice-preserving $\mathcal{ALC}$ ontology embeddings with saturation
• Authors: Fernando Zhapa-Camacho, Robert Hoehndorf,
• Abstract summary: An order-preserving embedding method is proposed to generate embeddings of OWL representations. We show that our method outperforms state-the-art theory-of-the-art embedding methods in several knowledge base completion tasks.
• Score: 50.05281461410368
• License:
• Abstract: 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 are 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 $\mathcal{EL}^{++}$, 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 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. Furthermore, we incoporate saturation procedures that increase the information within the constructed lattices. We make our code and data available at \url{https://github.com/bio-ontology-research-group/catE}.

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