The ubiquitous independence assumption among symbolic concepts in neurosymbolic (NeSy) predictors is a convenient simplification that speeds up probabilistic reasoning. Recent works argued that this assumption can hinder learning and prevent the correct modelling of uncertainty.
We formally show that assuming independence among symbolic concepts entails that a model can never represent uncertainty over certain concept combinations. Thus, the model fails to be aware of reasoning shortcuts, the pathological behaviour of NeSy predictors that predict correct downstream tasks but for the wrong reasons. This work settles the question of when the independence assumption actually limits NeSy systems.