Cosine-Based Embedding for Completing Lightweight Schematic Knowledge in DL-Litecore

Schematic knowledge, an important component of knowledge graphs (KGs), defines a rich set of logical axioms based on concepts and relations to support knowledge integration, reasoning, and heterogeneity elimination over KGs. Although several KGs consist of lots of factual knowledge, their schematic knowledge (e.g., subclassOf axioms, disjointWith axioms) is far from complete. Currently, existing KG embedding methods for completing schematic knowledge still suffer from two limitations. Firstly, existing embedding methods designed to encode factual knowledge pay little attention to the completion of schematic knowledge (e.g., axioms). Secondly, several methods try to preserve logical properties of relations for completing schematic knowledge, but they cannot simultaneously preserve the transitivity (e.g., subclassOf) and symmetry (e.g., disjointWith) of axioms well. To solve these issues, we propose a cosine-based embedding method named CosE tailored for completing lightweight schematic knowledge in DL-Litecore. Precisely, the concepts in axioms will be encoded into two semantic spaces defined in CosE. One is called angle-based semantic space, which is employed to preserve the transitivity or symmetry of relations in axioms. The other one is defined as translation-based semantic space that is used to measure the confidence of each axiom. We design two types of score functions for these two semantic spaces, so as to sufficiently learn the vector representations of concepts. Moreover, we propose a novel negative sampling strategy based on the mutual exclusion between subclassOf and disjointWith. In this way, concepts can obtain better vector representations for schematic knowledge completion. We implement our method and verify it on four standard datasets generated by real ontologies. Experiments show that CosE can obtain better results than existing models and keep the logical properties of relations for transitivity and symmetry simultaneously.