# Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture

arXiv: https://arxiv.org/abs/2302.12195 · HTML: https://mlsanity.com/paper/2302.12195/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [Ontology Reasoning with Deep Neural Networks](https://mlsanity.com/paper/1808.07980/) (2018)
- [Differentiable Inductive Logic Programming for Structured Examples](https://mlsanity.com/paper/2103.01719/) (2021)
- [MANCaLog: A Logic for Multi-Attribute Network Cascades (Technical Report)](https://mlsanity.com/paper/1301.0302/) (2013)
- [Reasoning about Complex Networks: A Logic Programming Approach](https://mlsanity.com/paper/2209.15067/) (2022)

## Built on by (most cited first, 6 of 6)

- [PyReason: Software for Open World Temporal Logic](https://mlsanity.com/paper/2302.13482/) (2023)
- [Scalable Semantic Non-Markovian Simulation Proxy for Reinforcement Learning](https://mlsanity.com/paper/2310.06835/) (2023)
- [Sea-cret Agents: Maritime Abduction for Region Generation to Expose Dark Vessel Trajectories](https://mlsanity.com/paper/2502.01503/) (2025)
- [Geospatial Trajectory Generation via Efficient Abduction: Deployment for Independent Testing](https://mlsanity.com/paper/2407.06447/) (2024)
- [EntailLLM: Verifying LLM-Generated Vulnerability Discovery Paths with Domain Knowledge via Logic Programming](https://mlsanity.com/paper/2608.01763/) (2026)
- [Lattice Annotated Temporal (LAT) Logic for Non-Markovian Reasoning](https://mlsanity.com/paper/2509.02958/) (2025)

## Abstract (arXiv)

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.