Neurosymbolic Reasoning Shortcuts under the Independence Assumption

The ubiquitous independence assumption among symbolic concepts in neurosymbolic (NeSy) predictors is a convenient simplification: NeSy predictors use it to speed up probabilistic reasoning. Recent works like van Krieken et al. (2024) and Marconato et al. (2024) argued that the independence assumption can hinder learning of NeSy predictors and, more crucially, prevent them from correctly modelling uncertainty. There is, however, scepticism in the NeSy community around the scenarios in which the independence assumption actually limits NeSy systems (Faronius and Dos Martires, 2025). In this work, we settle this question by formally showing 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, i.e., the pathological behaviour of NeSy predictors that predict correct downstream tasks but for the wrong reasons.