LTNtorch: PyTorch Implementation of Logic Tensor Networks

TL;DR

LTNtorch is a PyTorch implementation of Logic Tensor Networks, enabling neural-symbolic learning by integrating logical reasoning with deep learning through gradient-based optimization.

Contribution

This work provides a fully documented, tested PyTorch framework for Logic Tensor Networks, facilitating neuro-symbolic learning and reasoning tasks.

Findings

Successful implementation of LTN in PyTorch

Demonstration with a binary classification example

Framework enables logical reasoning in neural models

Abstract

Logic Tensor Networks (LTN) is a Neuro-Symbolic framework that effectively incorporates deep learning and logical reasoning. In particular, LTN allows defining a logical knowledge base and using it as the objective of a neural model. This makes learning by logical reasoning possible as the parameters of the model are optimized by minimizing a loss function composed of a set of logical formulas expressing facts about the learning task. The framework learns via gradient-descent optimization. Fuzzy logic, a relaxation of classical logic permitting continuous truth values in the interval [0,1], makes this learning possible. Specifically, the training of an LTN consists of three steps. Firstly, (1) the training data is used to ground the formulas. Then, (2) the formulas are evaluated, and the loss function is computed. Lastly, (3) the gradients are back-propagated through the logical computational graph, and the weights of the neural model are changed so the knowledge base is maximally satisfied. LTNtorch is the fully documented and tested PyTorch implementation of Logic Tensor Networks. This paper presents the formalization of LTN and how LTNtorch implements it. Moreover, it provides a basic binary classification example.