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）上进行一阶逻辑（FOL）查询仍是一项挑战性任务，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解决该问题。知识图谱展现出诸如对称性和组合性等关系模式，对此类模式进行建模可进一步提升查询嵌入模型的性能。然而，现有文献尚未研究这些模式在查询嵌入模型回答FOL查询时所起的作用。本文通过引入一种可学习关系模式的归纳偏置，填补了这一研究空白，并实现了具有模式推理能力的FOL查询推理。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操作定义代数查询算子。RoConE融合了锥体作为查询嵌入的明确几何表示的优势，以及旋转算子作为模式推理的强大代数运算能力。在多个基准数据集上的实验结果表明，关系模式在增强逻辑查询回答任务中具有显著优势。