Abstract: Many natural language questions require qualitative, quantitative or logical comparisons between two entities or events. This paper addresses the problem of improving the accuracy and consistency of responses to comparison questions by integrating logic rules and neural models. Our method leverages logical and linguistic knowledge to augment labeled training data and then uses a consistency-based regularizer to train the model. Improving the global consistency of predictions, our approach achieves large improvements over previous methods in a variety of question answering (QA) tasks, including multiple-choice qualitative reasoning, cause-effect reasoning, and extractive machine reading comprehension. In particular, our method significantly improves the performance of RoBERTa-based models by 1-5% across datasets. We advance state of the art by around 5-8% on WIQA and QuaRel and reduce consistency violations by 58% on HotpotQA. We further demonstrate that our approach can learn effectively from limited data.