Logical Neural Networks
This work addresses the problem of combining learning and reasoning for AI researchers, offering a novel framework that bridges neural and symbolic approaches.
The authors tackled the challenge of integrating neural networks' learning capabilities with symbolic logic's interpretability and reasoning, resulting in a differentiable model that supports logical inference and is resilient to inconsistent and incomplete knowledge.
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.