From knowledge graph embedding to ontology embedding? An analysis of the compatibility between vector space representations and rules

Gutierrez Basulto, Victor ORCID: https://orcid.org/0000-0002-6117-5459 and Schockaert, Steven ORCID: https://orcid.org/0000-0002-9256-2881 2018. From knowledge graph embedding to ontology embedding? An analysis of the compatibility between vector space representations and rules. Presented at: 16th International Conference on Principles of Knowledge Representation and Reasoning, Tempe, Arizona, 27 Oct - 2 Nov 2018. Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning. Association for the Advancement of Artificial Intelligence, pp. 379-388.

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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.

Item Type:	Conference or Workshop Item - published (Paper)
Date Type:	Publication
Status:	Published
Schools:	Schools > Computer Science & Informatics
Publisher:	Association for the Advancement of Artificial Intelligence
ISBN:	9781577358039
ISSN:	2334-1025
Date of First Compliant Deposit:	7 November 2018
Last Modified:	06 Aug 2026 14:00
URI:	https://orca.cardiff.ac.uk/id/eprint/114789

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