A Neural-symbolic Approach for Ontology-mediated Query Answering

Recently, low-dimensional vector space representations of knowledge graphs (KGs) have been applied to find answers to conjunctive queries (CQs) over incomplete KGs. However, the current methods only focus on inductive reasoning, i.e. answering CQs by predicting facts based on patterns learned from the data, and lack the ability of deductive reasoning by applying external domain knowledge. Such (expert or commonsense) domain knowledge is an invaluable resource which can be used to advance machine intelligence. To address this shortcoming, we introduce a neural-symbolic method for ontology-mediated CQ answering over incomplete KGs that operates in the embedding space. More specifically, we propose various data augmentation strategies to generate training queries using query-rewriting based methods and then exploit a novel loss function for training the model. The experimental results demonstrate the effectiveness of our training strategies and the new loss function, i.e., our method significantly outperforms the baseline in the settings that require both inductive and deductive reasoning.