Enhancing Geometric Ontology Embeddings for $\mathcal{EL}^{++}$ with Negative Sampling and Deductive Closure Filtering
This work addresses the problem of improving ontology embeddings for knowledge base completion, which is significant for applications relying on Description Logic $mathcal{EL}^{++}$, such as semantic web and artificial intelligence.
The authors tackled the problem of enhancing geometric ontology embeddings for $mathcal{EL}^{++}$ and achieved improved results in knowledge base completion tasks by incorporating deductive closure filtering and negative sampling. Their method outperformed the baseline ontology embedding.
Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $\mathcal{EL}^{++}$, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $\mathcal{EL}^{++}$ ontologies based on high-dimensional ball representation of concept descriptions, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.