Spherical Embeddings for Atomic Relation Projection Reaching Complex Logical Query Answering

Projecting knowledge graph queries into an embedding space using geometric models (points, boxes and spheres) can help to answer queries for large incomplete knowledge graphs. In this work, we propose a symbolic learning-free approach using fuzzy logic to address the shape-closure problem that restricted geometric-based embedding models to only a few shapes (e.g. ConE) for answering complex logical queries. The use of symbolic approach facilitates non-closure geometric models (e.g. point, box) to handle logical operators (including negation). This enabled our newly proposed spherical embeddings (SpherE) in this work to use a polar coordinate system to effectively represent hierarchical relation. Results show that the SpherE model can answer existential positive first-order logic and negation queries. We show that SpherE significantly outperforms the point and box embeddings approaches while generating semantically meaningful hierarchy-aware embeddings.