Machine learning models can make basic errors that are easily hidden within vast amounts of data. Such errors often run counter to human intuition referred to as "common sense". We thereby seek to characterize common sense for data-driven models, and quantify the extent to which a model has learned common sense. We propose a framework that integrates logic-based methods with statistical inference to derive common sense rules from a model's training data without supervision. We further show how to adapt models at test-time to reduce common sense rule violations and produce more coherent predictions. We evaluate our framework on datasets and models for three different domains. It generates around 250 to 300k rules over these datasets, and uncovers 1.5k to 26k violations of those rules by state-of-the-art models for the respective datasets. Test-time adaptation reduces these violations by up to 38% without impacting overall model accuracy.