ndiv / lnn

A `Neural = Symbolic` framework for sound and complete weighted real-value logic

Logical Neural Networks

LNNs are a novel Neuro = symbolic framework designed to seamlessly provide 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 interpretable disentangled representation.
• Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic (FOL) 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.

Quickstart

To install the LNN:

1. Run:

   pip install git+https://github.com/IBM/LNN.git
   

To install the LNN with graph plot support:

1. Install GraphViz
2. Run:

   pip install git+https://github.com/IBM/LNN.git#egg=lnn"[plot]"
   

Documentation

Read the Docs	Academic Papers	Educational Resources	Neuro-Symbolic AI	API Overview	Python Module

Citation

If you use Logical Neural Networks for research, please consider citing the reference paper:

@article{riegel2020logical,
  title={Logical neural networks},
  author={Riegel, Ryan and Gray, Alexander and Luus, Francois and Khan, Naweed and Makondo, Ndivhuwo and Akhalwaya, Ismail Yunus and Qian, Haifeng and Fagin, Ronald and Barahona, Francisco and Sharma, Udit and others},
  journal={arXiv preprint arXiv:2006.13155},
  year={2020}
}