From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules

TL;DR

This paper analyzes how well different vector space embeddings can represent ontological rules, revealing limitations of popular methods and proposing a convex region model that accurately captures certain ontologies.

Contribution

It introduces a framework to evaluate the compatibility of vector space embeddings with ontological rules and proposes a convex region model for exact representation of specific ontologies.

Findings

Popular embedding methods cannot model simple rules.

Convex region embeddings can represent quasi-chained existential rules.

Embeddings can ensure logical consistency with ontologies.

Abstract

Recent years have witnessed the successful application of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. However, it is not yet well-understood to what extent ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a general framework based on a view of relations as regions, which allows us to study the compatibility between ontological knowledge and different types of vector space embeddings. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding methods are not capable of modelling even very simple types of rules, which in particular also means that they are not able to learn the type of dependencies captured by such rules. Second, we study a model in which relations are modelled as convex regions. We show particular that ontologies which are expressed using so-called quasi-chained existential rules can be exactly represented using convex regions, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.