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.

这项调查探讨了学习和推理在人工智能两个不同领域的整合：神经符号人工智能和统计关系人工智能。神经符号人工智能（NeSy）研究符号推理和神经网络的集成，而统计关系人工智能（StarAI）则专注于逻辑与概率图形模型的集成。这项调查确定了人工智能这两个子领域之间的七个共同维度。这些维度可用于表征不同的 NeSy 和 StarAI 系统。他们关注的是（1）逻辑推理的方法，无论是基于模型还是基于证明；(2)所使用的逻辑理论的句法；(3)系统的逻辑语义及其扩展，以方便学习；(4) 学习的范围，包括参数学习或结构学习；(5) 符号和子符号表示的存在；(6) 系统捕捉原始逻辑、概率和神经范式的程度；(7) 系统适用的学习任务类别。通过沿着这些维度定位各种 NeSy 和 StarAI 系统并指出它们之间的异同，本次调查为理解学习和推理的整合提供了基本概念。