Faithiful Embeddings for EL++ Knowledge Bases

TL;DR

BoxEL is a novel geometric embedding method for EL++ knowledge bases that effectively models both concept and data-level knowledge, preserving logical structure and improving reasoning and prediction tasks.

Contribution

It introduces BoxEL, a geometric embedding approach that models concepts as boxes and relations as transformations, with theoretical guarantees for logical structure preservation.

Findings

Outperforms traditional KG embedding methods in reasoning tasks

Achieves better modeling of concept intersections and logical axioms

Demonstrates effectiveness in protein-protein interaction prediction

Abstract

Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application for protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.