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Résumé : Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce unpredictability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop an iterative distillation method that transfers the structured information of logic rules into the weights of neural networks. We deploy the framework on a CNN for sentiment analysis, and an RNN for named entity recognition. With a few highly intuitive rules, we obtain substantial improvements and achieve state-of-the-art or comparable results to previous best-performing systems.