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Recent years have witnessed the successful application of low-dimensionalvector space representations of knowledge graphs to predict missing facts orfind erroneous ones. However, it is not yet well-understood to what extentontological knowledge, e.g. given as a set of (existential) rules, can beembedded in a principled way. To address this shortcoming, in this paper weintroduce a general framework based on a view of relations as regions, whichallows us to study the compatibility between ontological knowledge anddifferent types of vector space embeddings. Our technical contribution istwo-fold. First, we show that some of the most popular existing embeddingmethods are not capable of modelling even very simple types of rules, which inparticular also means that they are not able to learn the type of dependenciescaptured by such rules. Second, we study a model in which relations aremodelled as convex regions. We show particular that ontologies which areexpressed using so-called quasi-chained existential rules can be exactlyrepresented using convex regions, such that any set of facts which is inducedusing that vector space embedding is logically consistent and deductivelyclosed with respect to the input ontology.

From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules