This survey explores the integration of learning and reasoning in two different fields of artificial intelligence: neurosymbolic and statistical relational artificial intelligence. Neurosymbolic artificial intelligence (NeSy) studies the integration of symbolic reasoning and neural networks, while statistical relational artificial intelligence (StarAI) focuses on integrating logic with probabilistic graphical models. This survey identifies seven shared dimensions between these two subfields of AI. These dimensions can be used to characterize different NeSy and StarAI systems. They are concerned with (1) the approach to logical inference, whether model or proof-based; (2) the syntax of the used logical theories; (3) the logical semantics of the systems and their extensions to facilitate learning; (4) the scope of learning, encompassing either parameter or structure learning; (5) the presence of symbolic and subsymbolic representations; (6) the degree to which systems capture the original logic, probabilistic, and neural paradigms; and (7) the classes of learning tasks the systems are applied to. By positioning various NeSy and StarAI systems along these dimensions and pointing out similarities and differences between them, this survey contributes fundamental concepts for understanding the integration of learning and reasoning.

翻译：本综述探讨了人工智能两个不同领域中学习与推理的整合：神经符号人工智能与统计关系人工智能。神经符号人工智能（NeSy）研究符号推理与神经网络的整合，而统计关系人工智能（StarAI）则聚焦于逻辑与概率图模型的融合。本文识别了这两个人工智能子领域间的七个共同维度。这些维度可用于描述不同的NeSy与StarAI系统，涉及：（1）逻辑推理方法——基于模型还是基于证明；（2）所用逻辑理论的语法；（3）系统的逻辑语义及其为促进学习所做的扩展；（4）学习范围，涵盖参数学习或结构学习；（5）符号表示与亚符号表示的存在性；（6）系统对原始逻辑、概率与神经范式的保留程度；以及（7）系统所应用的学习任务类别。通过沿这些维度定位各类NeSy与StarAI系统并指出其异同，本综述为理解学习与推理的整合贡献了基础概念。