Description Logic EL++ Embeddings with Intersectional Closure

TL;DR

This paper introduces EL Box Embedding (ELBE), a novel method for representing EL++ ontologies using axis-aligned boxes, ensuring intersectional closure and improving the modeling of concept intersections.

Contribution

The paper proposes ELBE, a new embedding approach that uses boxes instead of n-balls, satisfying intersectional closure for EL++ ontologies, with extensive experiments validating its effectiveness.

Findings

ELBE effectively models concept intersections in EL++ ontologies.

ELBE outperforms previous n-ball based methods in experimental evaluations.

The case study demonstrates practical advantages of ELBE in biomedical ontologies.

Abstract

Many ontologies, in particular in the biomedical domain, are based on the Description Logic EL++. Several efforts have been made to interpret and exploit EL++ ontologies by distributed representation learning. Specifically, concepts within EL++ theories have been represented as n-balls within an n-dimensional embedding space. However, the intersectional closure is not satisfied when using n-balls to represent concepts because the intersection of two n-balls is not an n-ball. This leads to challenges when measuring the distance between concepts and inferring equivalence between concepts. To this end, we developed EL Box Embedding (ELBE) to learn Description Logic EL++ embeddings using axis-parallel boxes. We generate specially designed box-based geometric constraints from EL++ axioms for model training. Since the intersection of boxes remains as a box, the intersectional closure is satisfied. We report extensive experimental results on three datasets and present a case study to demonstrate the effectiveness of the proposed method.