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.

通过逻辑推理，将感知模型与由符号知识库推断出的信息相结合的神经符号混合系统在整合机器学习和符号推理方面具有很大潜力。虽然经验证据显示了混合系统学习准确感知模型的能力，但对于可学性的理论理解仍然缺乏。本文通过研究知识库来解决这个问题，并提出了一个判定知识在促进成功学习方面的有效性的标准。综合实验确认了我们的标准在基准任务上的实用性。