  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.
