# Neuro-Symbolic Reasoning: Fundamentals, Models, Certification, and Systems

**V1.0 — Open English Manuscript**

*A Knowledge-Graph-Driven Framework for Trustworthy Governance in Urban Air Mobility and Safety-Critical AI*

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## About This Book

<b>Yushu Liu</b> &nbsp;|&nbsp;
<a href="mailto:yushuliu@outlook.com">yushuliu@outlook.com</a> &nbsp;|&nbsp;
<a href="https://github.com/liuyushugreat/Neuro-Symbolic-Reasoning-Fundamentals-Models-Certification-and-Systems">GitHub</a> &nbsp;|&nbsp;
<a href="https://liuyushugreat.github.io/Neuro-Symbolic-Reasoning-Fundamentals-Models-Certification-and-Systems/intro.html">Open-source Book</a>

Modern AI excels at perception and generation but still struggles with **explicit reasoning, rule compliance, uncertainty calibration, and certifiable deployment** in safety-critical settings.

This book develops a **complete technical stack** for neuro-symbolic AI — not just one model trick, but a full pipeline:

> **Knowledge Base → Hybrid Reasoning → Trustworthy Certification → System Deployment → Governance Loop**

It covers **25 chapters** across six layers, from symbolic logic and knowledge graphs all the way to cloud-edge deployment and LLM-era agents. **Urban air mobility (UAM)** is the primary scenario, but the methodology applies broadly to autonomous driving, medical AI, industrial control, and AI for Science.

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## What Makes This Book Different?

| Dimension | Typical NeSy / Trustworthy AI Resources | This Book |
|-----------|----------------------------------------|-----------|
| **Scope** | Single technique (e.g., logic + NN) | Full stack: knowledge → reasoning → certification → deployment |
| **Trustworthiness** | Interpretability-focused | Goes beyond to **conformal prediction, online monitoring, certification wrapping, audit trails** |
| **System view** | Model-centric | Addresses **compute gaps, cloud-edge collaboration, spatiotemporal partitioning, governance loops** |
| **Application** | Abstract benchmarks | Grounded in a **real safety-critical domain** (UAM) with generalizable patterns |
| **Openness** | Closed textbook or scattered papers | **Full open manuscript** with runnable labs, knowledge graph, and structured reading paths |

**In one sentence:** This is the first open resource that traces the entire path from symbolic logic to certifiable, deployable neuro-symbolic systems, with a real safety-critical domain as its testbed.

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## How the Book Is Organized

The book follows a deliberately layered architecture:

1. **Foundations** (Ch. 1–4) — Symbolic logic, knowledge graphs, graph neural networks, and deep representation learning
2. **Domain Knowledge Base** (Ch. 5–6) — Ontology modeling, SkyKG construction, and unified knowledge representation
3. **Hybrid Reasoning** (Ch. 7–13) — Neuro-symbolic taxonomy, knowledge injection, KG-driven reasoning, temporal graphs, conflict detection, and multi-agent coordination
4. **Trustworthy Certification** (Ch. 14–17) — Conformal prediction, online monitoring, drift detection, audit trails, and regulatory interfaces
5. **System Deployment** (Ch. 18–21) — Computing gaps, cloud-edge collaboration, spatiotemporal partitioning, and platformized governance loops
6. **Frontier** (Ch. 22–25) — LLM-era neuro-symbolic AI, safety-critical applications, AI for Science, and the future roadmap

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## Quick Start Guide

| If you want to… | Start here |
|-----------------|------------|
| Read the full introduction | {doc}`INTRODUCTION_EN` |
| Browse the chapter map | {doc}`chapters/TABLE_OF_CONTENTS` |
| Get the fastest unique contribution overview | Ch. 7, 10, 15, 21, 22, 25 |
| Run hands-on Python experiments | {doc}`experiments/README` |
| Understand the knowledge graph structure | {doc}`knowledge_graph/Book_Knowledge_Graph` |

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## About the Author

**Yushu Liu (刘玉书)** is a researcher in artificial intelligence, decision intelligence, and digital governance. He is currently pursuing a Ph.D. in Electronic Information Engineering (Large Models) at **Tianjin University** and serves as Deputy Secretary-General of the Zhongguancun Software and Information Service Industry Innovation Alliance.

**Research directions:**
- Neuro-symbolic AI and hybrid reasoning
- Trustworthy, certifiable, and governable AI
- Knowledge-graph-driven decision intelligence
- Low-altitude traffic governance and safety-critical systems
- Deployable AI under real-world constraints

**Contact:** [yushuliu@outlook.com](mailto:yushuliu@outlook.com)

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## Citation

If this work is useful to your research or teaching, please cite:

```bibtex
@book{liu2025neurosymbolic,
  title     = {Neuro-Symbolic Reasoning: Fundamentals, Models, Certification, and Systems},
  author    = {Liu, Yushu},
  year      = {2025},
  publisher = {GitHub open manuscript},
  url       = {https://github.com/liuyushugreat/Neuro-Symbolic-Reasoning-Fundamentals-Models-Certification-and-Systems}
}
```

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## License

- **Book text, figures, diagrams:** [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/)
- **Example code:** [MIT](https://opensource.org/licenses/MIT)

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*Knowledge as the substrate · Reasoning as the core · Certification as the bridge · Deployment as the destination*