HyperQuaternionE: A hyperbolic embedding model for qualitative spatial and temporal reasoning

Qualitative spatial/temporal reasoning (QSR/QTR) plays a key role in research on human cognition, e.g., as it relates to navigation, as well as in work on robotics and artificial intelligence. Although previous work has mainly focused on various spatial and temporal calculi, more recently representation learning techniques such as embedding have been applied to reasoning and inference tasks such as query answering and knowledge base completion. These subsymbolic and learnable representations are well suited for handling noise and efficiency problems that plagued prior work. However, applying embedding techniques to spatial and temporal reasoning has received little attention to date. In this paper, we explore two research questions: (1) How do embedding-based methods perform empirically compared to traditional reasoning methods on QSR/QTR problems? (2) If the embedding-based methods are better, what causes this superiority? In order to answer these questions, we first propose a hyperbolic embedding model, called HyperQuaternionE, to capture varying properties of relations (such as symmetry and anti-symmetry), to learn inversion relations and relation compositions (i.e., composition tables), and to model hierarchical structures over entities induced by transitive relations. We conduct various experiments on two synthetic datasets to demonstrate the advantages of our proposed embedding-based method against existing embedding models as well as traditional reasoners with respect to entity inference and relation inference. Additionally, our qualitative analysis reveals that our method is able to learn conceptual neighborhoods implicitly. We conclude that the success of our method is attributed to its ability to model composition tables and learn conceptual neighbors, which are among the core building blocks of QSR/QTR.