  Can we train a system that, on any new input, either says "don't know" or
makes a prediction that is guaranteed to be correct? We answer the question in
the affirmative provided our model family is well-specified. Specifically, we
introduce the unanimity principle: only predict when all models consistent with
the training data predict the same output. We operationalize this principle for
semantic parsing, the task of mapping utterances to logical forms. We develop a
simple, efficient method that reasons over the infinite set of all consistent
models by only checking two of the models. We prove that our method obtains
100% precision even with a modest amount of training data from a possibly
adversarial distribution. Empirically, we demonstrate the effectiveness of our
approach on the standard GeoQuery dataset.
