LNN: Logical Neural Networks

Logical Neural Networks (LNN) is a framework that assumes knowledge of a logic program a-priori and uses gradient descent to fit the logic program to training data via parameterized logical operators, resulting in fuzzy logic semantics. The framework has several desirable properties, namely the ability to support open world reasoning, omnidirectional inference, and explainability. While consistency cannot be guaranteed, LNN’s use an additional term in the loss function to minimize inconsistencies in their approach. In this chapter, we review the foundations of LNN’s and discuss the architectural decisions that make LNN’s comparable and different from other neuro symbolic approaches.