Enhancing Geometric Ontology Embeddings for $\mathcal{EL}^{++}$ with Negative Sampling and Deductive Closure Filtering

TL;DR

This paper improves geometric ontology embeddings for $ ext{EL}^{++}$ by introducing negative sampling and deductive closure filtering, leading to better ontology completion results.

Contribution

It proposes novel negative loss functions and methods to incorporate deductive closure, enhancing the accuracy of $ ext{EL}^{++}$ ontology embeddings.

Findings

Improved ontology completion performance

Effective use of deductive closure in embeddings

Novel negative sampling techniques

Abstract

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.