Abstract: Document-level event argument extraction aims to identify event arguments beyond sentence level, where a significant challenge is to model long-range dependencies. Focusing on this challenge, we present a new chain reasoning paradigm for the task, which can generate decomposable first-order logic rules for reasoning. This paradigm naturally captures long-range interdependence due to the chains' compositional nature, which also improves interpretability by explicitly modeling the reasoning process. We introduce T-norm fuzzy logic for optimization, which permits end-to-end learning and shows promise for integrating the expressiveness of logical reasoning with the generalization of neural networks. In experiments, we show that our approach outperforms previous methods by a significant margin on two standard benchmarks (over 6 points in F1). Moreover, it is data-efficient in low-resource scenarios and robust enough to defend against adversarial attacks.