Abstract: Reasoning has been a central topic in artificial intelligence from the beginning. The recent progress made on distributed representation and neural networks continues to improve the state-of-the-art performance of natural language inference. However, it remains an open question whether the models perform real reasoning to reach their conclusions or rely on spurious correlations. Adversarial attacks have proven to be an important tool to help evaluate the Achilles' heel of the victim models. In this study, we explore the fundamental problem of developing attack models based on logic formalism. We propose NatLogAttack to perform systematic attacks centring around natural logic, a classical logic formalism that is traceable back to Aristotle's syllogism and has been closely developed for natural language inference. The proposed framework renders both label-preserving and label-flipping attacks. We show that compared to the existing attack models, NatLogAttack generates better adversarial examples with fewer visits to the victim models. The victim models are found to be more vulnerable under the label-flipping setting. NatLogAttack provides a tool to probe the existing and future NLI models' capacity from a key viewpoint and we hope more logic-based attacks will be further explored for understanding the desired property of reasoning.