# Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture

## TL;DR

This paper introduces an extension to generalized annotated logic enabling a binarized neural network framework that integrates symbolic reasoning with discrete optimization, aiming to improve explainability and modularity in neural systems.

## Contribution

It proposes a novel extension to generalized annotated logic for neuro symbolic systems, creating an equivalent neural architecture trained via discrete optimization.

## Key findings

- Proofs of correctness for the proposed framework
- Discussion of challenges for implementation
- Extension to logic enabling neural-symbolic hybridization

## Abstract

While deep neural networks have led to major advances in image recognition, language translation, data mining, and game playing, there are well-known limits to the paradigm such as lack of explainability, difficulty of incorporating prior knowledge, and modularity. Neuro symbolic hybrid systems have recently emerged as a straightforward way to extend deep neural networks by incorporating ideas from symbolic reasoning such as computational logic. In this paper, we propose a list desirable criteria for neuro symbolic systems and examine how some of the existing approaches address these criteria. We then propose an extension to generalized annotated logic that allows for the creation of an equivalent neural architecture comprising an alternate neuro symbolic hybrid. However, unlike previous approaches that rely on continuous optimization for the training process, our framework is designed as a binarized neural network that uses discrete optimization. We provide proofs of correctness and discuss several of the challenges that must be overcome to realize this framework in an implemented system.