Current best performing models for knowledge graph reasoning (KGR) introduce geometry objects or probabilistic distributions to embed entities and first-order logical (FOL) queries into low-dimensional vector spaces. They can be summarized as a center-size framework (point/box/cone, Beta/Gaussian distribution, etc.). However, they have limited logical reasoning ability. And it is difficult to generalize to various features, because the center and size are one-to-one constrained, unable to have multiple centers or sizes. To address these challenges, we instead propose a novel KGR framework named Feature-Logic Embedding framework, FLEX, which is the first KGR framework that can not only TRULY handle all FOL operations including conjunction, disjunction, negation and so on, but also support various feature spaces. Specifically, the logic part of feature-logic framework is based on vector logic, which naturally models all FOL operations. Experiments demonstrate that FLEX significantly outperforms existing state-of-the-art methods on benchmark datasets.

翻译：当前知识图谱推理（KGR）领域性能最优的模型通过引入几何对象或概率分布，将实体与一阶逻辑（FOL）查询嵌入低维向量空间。这些模型可归纳为中心-尺寸框架（点/盒/锥、Beta/高斯分布等）。然而，其逻辑推理能力有限，且难以泛化至多种特征空间——由于中心与尺寸存在一对一约束，无法支持多中心或多尺寸。为应对这些挑战，我们提出名为特征-逻辑嵌入框架（FLEX）的新型KGR框架。这是首个既能真正处理所有FOL运算（包括合取、析取、否定等），又支持多种特征空间的KGR框架。具体而言，特征-逻辑框架中的逻辑部分基于向量逻辑，可自然建模所有FOL运算。实验表明，FLEX在基准数据集上显著优于现有最先进方法。