  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, both 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.
