Query embedding approaches answer complex logical queries over incomplete knowledge graphs (KGs) by computing and operating on low-dimensional vector representations of entities, relations, and queries. However, current query embedding models heavily rely on excessively parameterized neural networks and cannot explain the knowledge learned from the graph. We propose a novel query embedding method, AConE, which explains the knowledge learned from the graph in the form of SROI^{-} description logic axioms while being more parameter-efficient than most existing approaches. AConE associates queries to a SROI^{-} description logic concept. Every SROI^{-} concept is embedded as a cone in complex vector space, and each SROI^{-} relation is embedded as a transformation that rotates and scales cones. We show theoretically that AConE can learn SROI^{-} axioms, and defines an algebra whose operations correspond one to one to SROI^{-} description logic concept constructs. Our empirical study on multiple query datasets shows that AConE achieves superior results over previous baselines with fewer parameters. Notably on the WN18RR dataset, AConE achieves significant improvement over baseline models. We provide comprehensive analyses showing that the capability to represent axioms positively impacts the results of query answering.

翻译：查询嵌入方法通过计算和操作实体、关系及查询的低维向量表示，在不完整知识图谱上回答复杂逻辑查询。然而，当前查询嵌入模型严重依赖过度参数化的神经网络，且无法解释从图谱中习得的知识。我们提出一种新型查询嵌入方法AConE，该方法能以SROI^{-}描述逻辑公理的形式解释从图谱习得的知识，同时比现有大多数方法更具参数效率。AConE将查询关联至SROI^{-}描述逻辑概念。每个SROI^{-}概念被嵌入为复数向量空间中的锥体，每个SROI^{-}关系则被嵌入为旋转和缩放锥体的变换。我们从理论上证明AConE能够学习SROI^{-}公理，并定义了一个代数结构，其运算与SROI^{-}描述逻辑概念构造一一对应。在多个查询数据集上的实证研究表明，AConE以更少的参数取得了优于先前基线模型的结果。特别是在WN18RR数据集上，AConE较基线模型实现了显著提升。我们通过全面分析表明，表征公理的能力对查询回答结果具有积极影响。