DELE: Deductive $\mathcal{EL}^{++}$ Embeddings for Knowledge Base Completion

TL;DR

This paper introduces DELE, a novel ontology embedding method for $ ext{EL}^{++}$ that leverages deductive closure to improve knowledge base completion, addressing limitations of existing optimization-based approaches.

Contribution

The paper presents a new embedding approach that incorporates deductive closure and novel negative loss functions for better ontology and knowledge base completion.

Findings

Improved accuracy in knowledge base completion tasks.

Effective utilization of deductive closure in embeddings.

Outperforms baseline ontology embedding methods.

Abstract

Ontology embeddings map classes, roles, 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 optimization-based 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, 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 and formulated evaluation methods for knowledge base completion. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.