Exploring the integration of if-then logic rules within neural network architectures presents an intriguing area. This integration seamlessly transforms the rule learning task into neural network training using backpropagation and stochastic gradient descent. From a well-trained sparse and shallow neural network, one can interpret each layer and neuron through the language of logic rules, and a global explanatory rule set can be directly extracted. However, ensuring interpretability may impose constraints on the flexibility, depth, and width of neural networks. In this paper, we propose HyperLogic: a novel framework leveraging hypernetworks to generate weights of the main network. HyperLogic can unveil multiple diverse rule sets, each capable of capturing heterogeneous patterns in data. This provides a simple yet effective method to increase model flexibility and preserve interpretability. We theoretically analyzed the benefits of the HyperLogic by examining the approximation error and generalization capabilities under two types of regularization terms: sparsity and diversity regularizations. Experiments on real data demonstrate that our method can learn more diverse, accurate, and concise rules.