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 query embedding method has been proposed 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 coming simultaneously. Finally, we propose a new search algorithm from fuzzy logic theory which is capable of solving new formulas and outperforming the previous methods in existing formulas.

翻译：知识图谱推理是一项具有挑战性的任务，因为它利用已知信息来预测缺失信息。特别地，由于一阶逻辑公式具有明确的语法和语义，其回答尤为引人关注。近年来，查询嵌入方法被提出，该方法学习一组实体的嵌入，并将逻辑操作视为集合操作。尽管已有大量基于相同方法论的研究，但从逻辑的角度来看，这些研究缺乏系统性的审视。本文刻画了先前研究中所涉及查询的范围，并精确指出了其与所有存在性公式全集之间的差距。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搜索算法，该算法能够解决新的公式，并在现有公式上优于以往的方法。