Logical Neural Networks
Abstract
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.
Cite
@article{arxiv.2006.13155,
title = {Logical Neural Networks},
author = {Ryan Riegel and Alexander Gray and Francois Luus and Naweed Khan and Ndivhuwo Makondo and Ismail Yunus Akhalwaya and Haifeng Qian and Ronald Fagin and Francisco Barahona and Udit Sharma and Shajith Ikbal and Hima Karanam and Sumit Neelam and Ankita Likhyani and Santosh Srivastava},
journal= {arXiv preprint arXiv:2006.13155},
year = {2020}
}
Comments
10 pages (incl. references), 38 pages supplementary, 7 figures, 9 tables, 6 algorithms. In submission to NeurIPS 2020