Cosine-Based Embedding for Completing Schematic Knowledge

Schematic knowledge, as a critical ingredient of knowledge graphs, defines logical axioms based on concepts to support for eliminating heterogeneity, integration, and reasoning over knowledge graphs (KGs). Although some well-known KGs contain large scale schematic knowledge, they are far from complete, especially schematic knowledge stating that two concepts have subclassOf relations (also called subclassOf axioms) and schematic knowledge stating that two concepts are logically disjoint (also called disjointWith axioms). One of the most important characters of these axioms is their logical properties such as transitivity and symmetry. Current KG embedding models focus on encoding factual knowledge (i.e., triples) in a KG and cannot directly be applied to further schematic knowledge (i.e., axioms) completion. The main reason is that they ignore these logical properties. To solve this issue, we propose a novel model named CosE for schematic knowledge. More precisely, CosE projects each concept into two semantic spaces. One is an angle-based semantic space that is utilized to preserve transitivity or symmetry of an axiom. The other is a translation-based semantic space utilized to measure the confidence score of an axiom. Moreover, two score functions tailored for subclassOf and disjointWith are designed to learn the representation of concepts with these two relations sufficiently. We conduct extensive experiments on link prediction on benchmark datasets like YAGO and FMA ontologies. The results indicate that CosE outperforms state-of-the-art methods and successfully preserve the transitivity and symmetry of axioms.