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Several approaches have been developed that generate embeddings forDescription Logic ontologies and use these embeddings in machine learning. Oneapproach of generating ontologies embeddings is by first embedding theontologies into a graph structure, i.e., introducing a set of nodes and edgesfor named entities and logical axioms, and then applying a graph embedding toembed the graph in $\mathbb{R}^n$. Methods that embed ontologies in graphs(graph projections) have different formal properties related to the type ofaxioms they can utilize, whether the projections are invertible or not, andwhether they can be applied to asserted axioms or their deductive closure. Weanalyze, qualitatively and quantitatively, several graph projection methodsthat have been used to embed ontologies, and we demonstrate the effect of theproperties of graph projections on the performance of predicting axioms fromontology embeddings. We find that there are substantial differences betweendifferent projection methods, and both the projection of axioms into nodes andedges as well ontological choices in representing knowledge will impact thesuccess of using ontology embeddings to predict axioms.

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