Neuro-symbolic hybrid systems are promising for integrating machine learning and symbolic reasoning, where perception models are facilitated with information inferred from a symbolic knowledge base through logical reasoning. Despite empirical evidence showing the ability of hybrid systems to learn accurate perception models, the theoretical understanding of learnability is still lacking. Hence, it remains unclear why a hybrid system succeeds for a specific task and when it may fail given a different knowledge base. In this paper, we introduce a novel way of characterising supervision signals from a knowledge base, and establish a criterion for determining the knowledge's efficacy in facilitating successful learning. This, for the first time, allows us to address the two questions above by inspecting the knowledge base under investigation. Our analysis suggests that many knowledge bases satisfy the criterion, thus enabling effective learning, while some fail to satisfy it, indicating potential failures. Comprehensive experiments confirm the utility of our criterion on benchmark tasks.

翻译：神经符号混合系统有望融合机器学习和符号推理，其中感知模型通过逻辑推理从符号知识库中推断出的信息得到增强。尽管实证证据表明混合系统能够学习准确的感知模型，但其可学习性的理论理解仍然缺乏。因此，尚不清楚混合系统为何在特定任务上成功，以及在面对不同知识库时何时可能失败。本文提出了一种从知识库中表征监督信号的新方法，并建立了确定知识促进成功学习效能的标准。这首次使我们能够通过检查待研究的知识库来回答上述两个问题。我们的分析表明，许多知识库满足该标准，从而能够实现有效学习，而有些知识库未能满足该标准，表明潜在失败风险。综合实验证实了该标准在基准任务中的实用性。