Reasoning with preconditions such as “glass can be used for drinking water unless the glass is shattered” remains an open problem for language models. The main challenge lies in the scarcity of preconditions data and the model’s lack of support for such reasoning. We present PInKS , Preconditioned Commonsense Inference with WeaK Supervision, an improved model for reasoning with preconditions through minimum supervision. We show, empirically and theoretically, that PInKS improves the results on benchmarks focused on reasoning with the preconditions of commonsense knowledge (up to 40% Macro-F1 scores). We further investigate PInKS through PAC-Bayesian informativeness analysis, precision measures, and ablation study.