Neurosymbolic AI is an increasingly active area of research which aims to combine symbolic reasoning methods with deep learning to generate models with both high predictive performance and some degree of human-level comprehensibility. As knowledge graphs are becoming a popular way to represent heterogeneous and multi-relational data, methods for reasoning on graph structures have attempted to follow this neurosymbolic paradigm. Traditionally, such approaches have utilized either rule-based inference or generated representative numerical embeddings from which patterns could be extracted. However, several recent studies have attempted to bridge this dichotomy in ways that facilitate interpretability, maintain performance, and integrate expert knowledge. Within this article, we survey a breadth of methods that perform neurosymbolic reasoning tasks on graph structures. To better compare the various methods, we propose a novel taxonomy by which we can classify them. Specifically, we propose three major categories: (1) logically-informed embedding approaches, (2) embedding approaches with logical constraints, and (3) rule-learning approaches. Alongside the taxonomy, we provide a tabular overview of the approaches and links to their source code, if available, for more direct comparison. Finally, we discuss the applications on which these methods were primarily used and propose several prospective directions toward which this new field of research could evolve.

翻译：神经符号AI是一个日益活跃的研究领域，旨在结合符号推理方法与深度学习，以生成既具有高预测性能又具备一定程度人类可理解性的模型。随着知识图谱成为表示异构和多关系数据的流行方式，图结构上的推理方法也试图遵循这一神经符号范式。传统上，这类方法要么利用基于规则的推理，要么生成代表性数值嵌入以从中提取模式。然而，近期多项研究试图弥合这一二分法，以促进可解释性、保持性能并整合专家知识。本文中，我们综述了在图结构上执行神经符号推理任务的广泛方法。为更好地比较各种方法，我们提出了一种新颖的分类法来对它们进行归类。具体而言，我们提出三大类别：（1）逻辑引导的嵌入方法，（2）带逻辑约束的嵌入方法，（3）规则学习方法。伴随该分类法，我们提供了方法的表格概览及其源代码链接（如可用），以便更直接地进行比较。最后，我们讨论了这些方法主要应用场景，并提出了这一新兴研究领域可能发展的几个前瞻性方向。