Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Specifically, answering first-order logic formulas is of particular interest, because of its clear syntax and semantics. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations. Though there has been much research following the same methodology, it lacks a systematic inspection from the standpoint of logic. In this paper, we characterize the scope of queries investigated previously and precisely identify the gap between it and the whole family of existential formulas. Moreover, we develop a new dataset containing ten new formulas and discuss the new challenges arising concurrently. Finally, we propose a new inference algorithm from fuzzy logic theory with provable reasoning capability. Empirical results show that our method succeeds in outperforming the previous methods in both the new dataset and the existing dataset.

翻译：知识图谱上的推理是一项具有挑战性的任务，因为它利用已观察到的信息来预测缺失的信息。具体而言，回答一阶逻辑公式因其清晰的语法和语义而备受关注。近年来，主流方法是查询嵌入，它学习实体集合的嵌入，并将逻辑操作视为集合操作。尽管已有大量研究遵循相同的方法论，但从逻辑的角度来看，缺乏系统的审查。在本文中，我们刻画了先前研究中所探讨的查询范围，并精确识别了其与整个存在性公式族之间的差距。此外，我们开发了一个包含十个新公式的新数据集，并讨论了随之而来的新挑战。最后，我们提出了一种基于模糊逻辑理论的新推理算法，该算法具有可证明的推理能力。实验结果表明，我们的方法在新数据集和现有数据集上均成功超越了先前的方法。