Answering complex First-Order Logical (FOL) queries on large-scale incomplete knowledge graphs (KGs) is an important yet challenging task. Recent advances embed logical queries and KG entities in the vector space and conduct query answering via dense similarity search. However, most of the designed logical operators in existing works do not satisfy the axiomatic system of classical logic. Moreover, these logical operators are parameterized so that they require a large number of complex FOL queries as training data, which are often arduous or even inaccessible to collect in most real-world KGs. In this paper, we present FuzzQE, a fuzzy logic based query embedding framework for answering FOL queries over KGs. FuzzQE follows fuzzy logic to define logical operators in a principled and learning free manner. Extensive experiments on two benchmark datasets demonstrate that FuzzQE achieves significantly better performance in answering FOL queries compared to the state-of-the-art methods. In addition, FuzzQE trained with only KG link prediction without any complex queries can achieve comparable performance with the systems trained with all FOL queries.
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