Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to reason abilities for generalization and composition. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations and has shown great empirical success. Though there has been much research following the same formulation, many of its claims lack a formal and systematic inspection. In this paper, we rethink this formulation and justify many of the previous claims by characterizing the scope of queries investigated previously and precisely identifying the gap between its formulation and its goal, as well as providing complexity analysis for the currently investigated queries. Moreover, we develop a new dataset containing ten new types of queries with features that have never been considered and therefore can provide a thorough investigation of complex queries. Finally, we propose a new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where we equip the neural link predictors with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability. Empirical results show that our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.

翻译：知识图谱推理是一项具有挑战性的任务，因为它利用已观测信息来预测缺失信息。特别地，基于一阶逻辑回答复杂查询是验证学习推理能力以实现泛化与组合的关键任务之一。当前主流方法是查询嵌入，该方法学习实体集合的嵌入表示，将逻辑操作视为集合操作，并在实证中取得了显著成功。尽管已有大量研究遵循相同框架，但许多相关论断缺乏系统性的形式化检验。本文重新审视这一框架，通过刻画此前研究中的查询范围、精确识别该框架与其目标之间的差距，以及对当前研究查询提供复杂性分析，论证了诸多先前论断。此外，我们构建了一个包含十种全新查询类型的新数据集，这些查询具备从未被考虑的特征，因此能够对复杂查询进行深入分析。最后，我们提出一种新的神经符号方法——真值模糊推理（FIT），该方法将神经链接预测器与模糊逻辑理论相结合，支持通过复杂查询进行端到端学习，并具备可证明的推理能力。实验结果表明，我们的方法在新数据集上显著优于此前方法，同时在现有数据集上也超越了以往方法。