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.
In this work, we present a novel approach to ontology reasoning that is based on deep learning rather than logic-based formal reasoning. To this end, we introduce a new model for statistical relational learning that is built upon deep recursive neural networks, and give experimental evidence that it can easily compete with, or even outperform, existing logic-based reasoners on the task of ontology reasoning. More precisely, we compared our implemented system with one of the best logic-based ontology reasoners at present, RDFox, on a number of large standard benchmark datasets, and found that our system attained high reasoning quality, while being up to two orders of magnitude faster. The ever increasing prevalence of publicly available structured data on the World Wide Web enables new applications in a variety of domains. In this paper, we provide a conceptual approach that leverages such data in order to explain the input-output behavior of trained artificial neural networks. We apply existing Semantic Web technologies in order to provide an experimental proof of concept. We present RDFox—a main-memory, scalable, centralised RDF store that supports materialisation-based parallel datalog reasoning and SPARQL query answering. RDFox uses novel and highly-efficient parallel reasoning algorithms for the computation and incremental update of datalog materialisations with efficient handling of owl:sameAs. In this system description paper, we present an overview of the system architecture and highlight the main ideas behind our indexing data structures and our novel reasoning algorithms. In addition, we evaluate RDFox on a high-end SPARC T5-8 server with 128 physical cores and 4TB of RAM. Our results show that RDFox can effectively exploit such a machine, achieving speedups of up to 87 times, storage of up to 9.2 billion triples, memory usage as low as 36.9 bytes per triple, importation rates of up to 1 million triples per second, and reasoning rates of up to 6.1 million triples per second.