Neural-Symbolic Entangled Framework for Complex Query Answering

Answering complex queries over knowledge graphs (KG) is an important yet challenging task because of the KG incompleteness issue and cascading errors during reasoning. Recent query embedding (QE) approaches embed the entities and relations in a KG and the first-order logic (FOL) queries into a low dimensional space, making the query can be answered by dense similarity searching. However, previous works mainly concentrate on the target answers, ignoring intermediate entities' usefulness, which is essential for relieving the cascading error problem in logical query answering. In addition, these methods are usually designed with their own geometric or distributional embeddings to handle logical operators like union, intersection, and negation, with the sacrifice of the accuracy of the basic operator -- projection, and they could not absorb other embedding methods to their models. In this work, we propose a Neural and Symbolic Entangled framework (ENeSy) for complex query answering, which enables the neural and symbolic reasoning to enhance each other to alleviate the cascading error and KG incompleteness. The projection operator in ENeSy could be any embedding method with the capability of link prediction, and the other FOL operators are handled without parameters. With both neural and symbolic reasoning results contained, ENeSy answers queries in ensembles. We evaluate ENeSy on complex query answering benchmarks, and ENeSy achieves the state-of-the-art, especially in the setting of training model only with the link prediction task.