# Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning

arXiv: https://arxiv.org/abs/1905.06088 · HTML: https://mlsanity.com/paper/1905.06088/

## Key facts

- Cited by 151 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 30 of 151)

- [LlamaV-o1: Rethinking Step-by-step Visual Reasoning in LLMs](https://mlsanity.com/paper/2501.06186/) (2025)
- [Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Models](https://mlsanity.com/paper/2503.20752/) (2025)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [Look-Back: Implicit Visual Re-focusing in MLLM Reasoning](https://mlsanity.com/paper/2507.03019/) (2025)
- [Leveraging Explanations in Interactive Machine Learning: An Overview](https://mlsanity.com/paper/2207.14526/) (2022)
- [Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Text](https://mlsanity.com/paper/2105.03659/) (2021)
- [Deep Learning with Logical Constraints](https://mlsanity.com/paper/2205.00523/) (2022)
- [Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systems](https://mlsanity.com/paper/2205.01128/) (2022)
- [From LSAT: The Progress and Challenges of Complex Reasoning](https://mlsanity.com/paper/2108.00648/) (2021)
- [Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use cases](https://mlsanity.com/paper/2102.11965/) (2021)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review](https://mlsanity.com/paper/2202.12205/) (2022)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Symbols as a Lingua Franca for Bridging Human-AI Chasm for Explainable and Advisable AI Systems](https://mlsanity.com/paper/2109.09904/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case](https://mlsanity.com/paper/2104.11914/) (2021)
- [Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2308.12595/) (2023)
- [HAKE: A Knowledge Engine Foundation for Human Activity Understanding](https://mlsanity.com/paper/2202.06851/) (2022)
- [Differentiable Inductive Logic Programming for Structured Examples](https://mlsanity.com/paper/2103.01719/) (2021)
- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AI](https://mlsanity.com/paper/2401.01040/) (2024)
- [ProTo: Program-Guided Transformer for Program-Guided Tasks](https://mlsanity.com/paper/2110.00804/) (2021)
- [Neuro-Symbolic Verification of Deep Neural Networks](https://mlsanity.com/paper/2203.00938/) (2022)
- [Differentiable Logic Machines](https://mlsanity.com/paper/2102.11529/) (2021)
- [Injecting Knowledge in Data-driven Vehicle Trajectory Predictors](https://mlsanity.com/paper/2103.04854/) (2021)
- [Grounded Object Centric Learning](https://mlsanity.com/paper/2307.09437/) (2023)
- [LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning](https://mlsanity.com/paper/2309.13556/) (2023)
- [Neuro-Symbolic Forward Reasoning](https://mlsanity.com/paper/2110.09383/) (2021)

## Abstract (arXiv)

Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns about interpretability and accountability of AI have been raised by influential thinkers. In spite of the recent impact of AI, several works have identified the need for principled knowledge representation and reasoning mechanisms integrated with deep learning-based systems to provide sound and explainable models for such systems. Neural-symbolic computing aims at integrating, as foreseen by Valiant, two most fundamental cognitive abilities: the ability to learn from the environment, and the ability to reason from what has been learned. Neural-symbolic computing has been an active topic of research for many years, reconciling the advantages of robust learning in neural networks and reasoning and interpretability of symbolic representation. In this paper, we survey recent accomplishments of neural-symbolic computing as a principled methodology for integrated machine learning and reasoning. We illustrate the effectiveness of the approach by outlining the main characteristics of the methodology: principled integration of neural learning with symbolic knowledge representation and reasoning allowing for the construction of explainable AI systems. The insights provided by neural-symbolic computing shed new light on the increasingly prominent need for interpretable and accountable AI systems.