Description Logic EL++ Embeddings with Intersectional Closure
This work addresses a specific challenge in embedding EL++ ontologies, particularly relevant for biomedical applications, by introducing a novel geometric representation to improve accuracy in concept inference.
The paper tackled the problem of representing Description Logic EL++ concepts using n-balls, which fails to satisfy intersectional closure, leading to issues in distance measurement and equivalence inference. They proposed EL Box Embedding (ELBE) using axis-parallel boxes to ensure intersectional closure, reporting extensive experimental results on three datasets to demonstrate effectiveness.
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.