# Neural Logic Machines

arXiv: https://arxiv.org/abs/1904.11694 · HTML: https://mlsanity.com/paper/1904.11694/

## Key facts

- Cited by 145 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2019.

## Built on by (most cited first, 30 of 145)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [A Survey on Interpretable Reinforcement Learning](https://mlsanity.com/paper/2112.13112/) (2021)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [R2-Guard: Robust Reasoning Enabled LLM Guardrail via Knowledge-Enhanced Logical Reasoning](https://mlsanity.com/paper/2407.05557/) (2024)
- [Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Review](https://mlsanity.com/paper/2202.12205/) (2022)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [From Machine Learning to Robotics: Challenges and Opportunities for Embodied Intelligence](https://mlsanity.com/paper/2110.15245/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [A Review of Emerging Research Directions in Abstract Visual Reasoning](https://mlsanity.com/paper/2202.10284/) (2022)
- [Skills-in-Context Prompting: Unlocking Compositionality in Large Language Models](https://mlsanity.com/paper/2308.00304/) (2023)
- [What's Left? Concept Grounding with Logic-Enhanced Foundation Models](https://mlsanity.com/paper/2310.16035/) (2023)
- [Learning Domain-Independent Heuristics for Grounded and Lifted Planning](https://mlsanity.com/paper/2312.11143/) (2023)
- [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)
- [Neuro-Symbolic Reinforcement Learning with First-Order Logic](https://mlsanity.com/paper/2110.10963/) (2021)
- [HAKE: A Knowledge Engine Foundation for Human Activity Understanding](https://mlsanity.com/paper/2202.06851/) (2022)
- [Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning](https://mlsanity.com/paper/2111.12990/) (2021)
- [Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AI](https://mlsanity.com/paper/2401.01040/) (2024)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [Neuro-Symbolic AI: An Emerging Class of AI Workloads and their Characterization](https://mlsanity.com/paper/2109.06133/) (2021)
- [Reinforcement Learning for Classical Planning: Viewing Heuristics as Dense Reward Generators](https://mlsanity.com/paper/2109.14830/) (2021)
- [LLMs for Relational Reasoning: How Far are We?](https://mlsanity.com/paper/2401.09042/) (2024)
- [Hierarchical Programmatic Reinforcement Learning via Learning to Compose Programs](https://mlsanity.com/paper/2301.12950/) (2023)
- [Differentiable Logic Machines](https://mlsanity.com/paper/2102.11529/) (2021)
- [GALOIS: Boosting Deep Reinforcement Learning via Generalizable Logic Synthesis](https://mlsanity.com/paper/2205.13728/) (2022)

## Abstract (arXiv)

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.