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

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

About This Book#

Yushu Liu | yushuliu@outlook.com | GitHub | Open-source Book

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.

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.

How the Book Is Organized#

The book follows a deliberately layered architecture:

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

Quick Start Guide#

If you want to…	Start here
Read the full introduction	Introduction
Browse the chapter map	Neuro-Symbolic Reasoning: Fundamentals, Models, Certification, and Systems
Get the fastest unique contribution overview	Ch. 7, 10, 15, 21, 22, 25
Run hands-on Python experiments	Appendix C — Experiment Code
Understand the knowledge graph structure	Book Relationship Map (Knowledge Graph View)

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

Citation#

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

@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}
}

License#

Book text, figures, diagrams: CC BY-NC-SA 4.0
Example code: MIT

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