Neural axiom network for knowledge graph reasoning

Knowledge graph reasoning (KGR) aims to infer new knowledge or detect noises, which is essential for improving the quality of knowledge graphs. Recently, various KGR techniques, such as symbolic- and embedding-based methods, have been proposed and shown strong reasoning ability. Symbolic-based reasoning methods infer missing triples according to predefined rules or ontologies. Although rules and axioms have proven effective, it is difficult to obtain them. Embedding-based reasoning methods represent entities and relations as vectors, and complete KGs via vector computation. However, they mainly rely on structural information and ignore implicit axiom information not predefined in KGs but can be reflected in data. That is, each correct triple is also a logically consistent triple and satisfies all axioms. In this paper, we propose a novel NeuRal Axiom Network (NeuRAN) framework that combines explicit structural and implicit axiom information without introducing additional ontologies. Specifically, the framework consists of a KG embedding module that preserves the semantics of triples and five axiom modules that encode five kinds of implicit axioms. These axioms correspond to five typical object property expression axioms defined in OWL2, including ObjectPropertyDomain, ObjectPropertyRange, DisjointObjectProperties, IrreflexiveObjectProperty and AsymmetricObjectProperty. The KG embedding module and axiom modules compute the scores that the triple conforms to the semantics and the corresponding axioms, respectively. Compared with KG embedding models and CKRL, our method achieves comparable performance on noise detection and triple classification and achieves significant performance on link prediction. Compared with TransE and TransH, our method improves the link prediction performance on the Hits@1 metric by 22.0% and 20.8% on WN18RR-10% dataset, respectively.