Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the ability of logical reasoning. However, the concrete ability of logical reasoning is critical to many theoretical and practical problems. In this paper, we propose Neural Logic Network (NLN), which is a dynamic neural architecture that builds the computational graph according to input logical expressions. It learns basic logical operations as neural modules, and conducts propositional logical reasoning through the network for inference. Experiments on simulated data show that NLN achieves significant performance on solving logical equations. Further experiments on real-world data show that NLN significantly outperforms state-of-the-art models on collaborative filtering and personalized recommendation tasks.