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.

这篇论文通过系统检视问题之前的范围并提出一个新的数据集，讨论了同时出现的新挑战，并提出了一种模糊逻辑理论的新搜索算法，以解决新的公式并在现有公式中胜过以前的方法。