Collaborative Filtering (CF) is an important approach to recommendation. However, existing CF methods are mostly designed based on the idea of matching, i.e., by learning user and item embeddings from data using shallow or deep models, they try to capture the relevance patterns in data, so that a user embedding can be matched with appropriate item embeddings using designed or learned similarity functions. However, as a cognition rather than a perception intelligent task, recommendation requires not only the ability of pattern recognition and matching from data, but also the ability of cognitive logical reasoning in data. In this work, we propose to advance Collaborative Filtering (CF) to Collaborative Reasoning (CR), which means that each user knows part of the logical space, and they collaborate to conduct logical reasoning in the space to estimate the preferences for each other. Inspired by recent progress on neural- symbolic learning, we propose a Neural Collaborative Reasoning (NCR) framework to integrate the power of embedding learning and logical reasoning, where the embeddings capture similarity patterns in data from perceptual perspectives, and the logic facilitates cognitive reasoning for informed decision making. An important challenge, however, is to bridge differentiable neural networks and symbolic reasoning in a shared architecture for optimization and inference. To solve the problem, we propose a neural logic reasoning architecture, which learns logical operations such as AND (∧), OR (∨) and NOT (¬) as neural modules for implication reasoning (→) in the form of Horn clause. In this way, each Horn clause can be equivalently organized as a neural network, so that logic reasoning and prediction can be conducted in a continuous space. Experiments on several real-world datasets verified the advantages of our framework compared with both shallow and deep recommendation models as well as state-of-the-art logical reasoning models.