Abstract
One way of enhancing link prediction in knowledge graphs in an interpretable and trustworthy way is to use ontology embeddings. These embeddings translate a knowledge graph together with its background ontology into a vector space by representing concepts as convex sets and logical operators between these concepts as geometric operations between the resp. sets. This allows for using both geometric regularities and background knowledge for learning. Some fragments of the description logic ℰℒ++ such as ℰℒℋO(o) are particularly well-suited as a basis for an embedding, as they offer a good trade-off between expressiveness and complexity. One popular approach for embedding these ontologies is to interpret concepts as boxes in some Rn. Although box embeddings proved to be particularly useful in this context, they are not able to represent every ontology correctly. In this work, we open the door to a new geometric framework by introducing prism embeddings. Firstly, we show that prisms do not suffer from the same restrictions as boxes. To illustrate this advantage, we present concrete ontology examples that are problematic for box embeddings but can be represented using prisms. Secondly, we show that prism embeddings extend box embeddings in the sense that each box interpretation of an ℰℒℋO(o) ontology induces a prism interpretation, though possibly at the cost of an increase in dimensionality of at most two. Finally, we discuss the usage of prism embeddings in practice by sketching adaptations of implementations of box-based embedding approaches to the prism case.