We propose a novel paradigm for solving Inductive Logic Programming (ILP) problems via deep recurrent neural networks. This proposed ILP solver is designed based on differentiable implementation of the deduction via forward chaining. In contrast to the majority of past methods, instead of searching through the space of possible first-order logic rules by using some restrictive rule templates, we directly learn the symbolic logical predicate rules by introducing a novel differentiable Neural Logic (dNL) network. The proposed dNL network is able to learn and represent Boolean functions efficiently and in an explicit manner. We show that the proposed dNL-ILP solver supports desirable features such as recursion and predicate invention. Further, we investigate the performance of the proposed ILP solver in classification tasks involving benchmark relational datasets. In particular, we show that our proposed method outperforms the state of the art ILP solvers in classification tasks for Mutagenesis, Cora and IMDB datasets.