From word embedding to ontology embeddings - preserving meaning in space

Uli Sattler presents an introduction to ontology embeddings, contrasting them with word embeddings and knowledge graph embeddings. She begins by defining ontologies in computer science as knowledge bases capturing domain knowledge, and explains the distinction between terminological (TBox) and assertional (ABox) components. She emphasizes the importance of logic-based semantics for precise entailments and automated reasoning, using examples like classification and query answering. She then introduces OWL as a standardized ontology language, highlighting its features beyond logic, such as annotations and datatypes. The talk clarifies the difference between ontologies and knowledge graphs, noting that knowledge graphs focus on factual data and often require link prediction, while ontologies provide conceptual structure enabling logical inference. Transitioning to embeddings, she explains word embeddings as vector representations capturing meaning via proximity, and knowledge graph embeddings as vector representations of nodes and relations using score functions like TransE and DistMult, but notes their limitations in handling logical properties like symmetry and transitivity. The core of the talk is ontology embeddings, where concept names are mapped to regions in vector space, and subsumption and instance relationships are captured via geometric containment. She outlines criteria for faithful embeddings that preserve entailments, and raises the question of which geometric regions to use, setting the stage for further discussion.