Answering first-order logical (FOL) queries over knowledge graphs (KG) remains a challenging task mainly due to KG incompleteness. Query embedding approaches this problem by computing the low-dimensional vector representations of entities, relations, and logical queries. KGs exhibit relational patterns such as symmetry and composition and modeling the patterns can further enhance the performance of query embedding models. However, the role of such patterns in answering FOL queries by query embedding models has not been yet studied in the literature. In this paper, we fill in this research gap and empower FOL queries reasoning with pattern inference by introducing an inductive bias that allows for learning relation patterns. To this end, we develop a novel query embedding method, RoConE, that defines query regions as geometric cones and algebraic query operators by rotations in complex space. RoConE combines the advantages of Cone as a well-specified geometric representation for query embedding, and also the rotation operator as a powerful algebraic operation for pattern inference. Our experimental results on several benchmark datasets confirm the advantage of relational patterns for enhancing logical query answering task.

翻译：在知识图谱（KG）上回答一阶逻辑（FOL）查询仍然是一项具有挑战性的任务，这主要源于知识图谱的不完备性。查询嵌入方法通过计算实体、关系和逻辑查询的低维向量表示来应对这一问题。知识图谱展现出诸如对称性和复合性等关系模式，对这些模式进行建模可以进一步提升查询嵌入模型的性能。然而，此类模式在查询嵌入模型回答一阶逻辑查询中的作用，在现有文献中尚未得到研究。本文填补了这一研究空白，通过引入一种能够学习关系模式的归纳偏置，赋予一阶逻辑查询推理以模式推断的能力。为此，我们提出了一种新颖的查询嵌入方法 RoConE，该方法将查询区域定义为几何锥体，并通过复数空间中的旋转来定义代数查询运算符。RoConE 结合了锥体作为查询嵌入的明确几何表示的优势，以及旋转运算符作为模式推断的强大代数运算的优势。我们在多个基准数据集上的实验结果证实了关系模式在增强逻辑查询应答任务中的优势。