  Recent years have witnessed the 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 cognitive reasoning. However, the concrete ability of
reasoning is critical to many theoretical and practical problems. On the other
hand, traditional symbolic reasoning methods do well in making logical
inference, but they are mostly hard rule-based reasoning, which limits their
generalization ability to different tasks since difference tasks may require
different rules. Both reasoning and generalization ability are important for
prediction tasks such as recommender systems, where reasoning provides strong
connection between user history and target items for accurate prediction, and
generalization helps the model to draw a robust user portrait over noisy
inputs.
  In this paper, we propose Logic-Integrated Neural Network (LINN) to integrate
the power of deep learning and logic reasoning. LINN is a dynamic neural
architecture that builds the computational graph according to input logical
expressions. It learns basic logical operations such as AND, OR, NOT as neural
modules, and conducts propositional logical reasoning through the network for
inference. Experiments on theoretical task show that LINN achieves significant
performance on solving logical equations and variables. Furthermore, we test
our approach on the practical task of recommendation by formulating the task
into a logical inference problem. Experiments show that LINN significantly
outperforms state-of-the-art recommendation models in Top-K recommendation,
which verifies the potential of LINN in practice.
