Logical Neural Networks: Towards Unifying Statistical and Symbolic AI

Abstract

Recently there has been renewed interest in the long-standing goal of somehow unifying the capabilities of both statistical AI (learning and prediction) and symbolic AI (knowledge representation and reasoning). We introduce Logical Neural Networks, a new neuro-symbolic framework which identifies and leverages a 1-to-1 correspondence between an artificial neuron and a logic gate in a weighted form of real-valued logic. With a few key modifications of the standard modern neural network, we construct a model which performs the equivalent of logical inference rules such as modus ponens within the message-passing paradigm of neural networks, and utilizes a new form of loss, contradiction loss, which maximizes logical consistency in the face of imperfect and inconsistent knowledge. The result differs significantly from other neuro-symbolic ideas in that 1) the model is fully disentangled and understandable since every neuron has a meaning, 2) the model can perform both classical logical deduction and its real-valued generalization (which allows for the representation and propagation of uncertainty) exactly, as special cases, as opposed to approximately as in nearly all other approaches, and 3) the model is compositional and modular, allowing for fully reusable knowledge across talks. The framework has already enabled state-of-the-art results in several problems, including question answering.