Skip to main content

Ctrl+K

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

Introduction

Introduction

Part I · Foundations

1.1 The rise and fall of symbolic AI: from expert systems to the knowledge-engineering bottleneck
2.1 Propositional logic and first-order predicate logic
3.1 Basic concepts of knowledge graphs: entities, relations, attributes, events
4.1 Basic ideas of deep representation learning

Part II · Domain Knowledge Modeling

5.1 Object system for low-altitude traffic / UAM: aircraft, airspace, missions, infrastructure, stakeholders
6.1 Ontology layering: concept layer, instance layer, rule layer

Part III · Hybrid Reasoning

7.1 Classical taxonomies: Henry Kautz’s neuro-symbolic spectrum
8.1 Logic rules as loss functions
9.1 SPARQL queries and deterministic evidence extraction
10.1 Defining static risk reasoning
11.1 From static KG to temporal KG
12.1 Formalizing multi-UAV dynamic coordination
13.1 Conflict detection vs. conflict resolution

Part IV · Trustworthy Certification

14.1 Why Neuro-Symbolic Systems Are Still Not Inherently Trustworthy
15.1 Types of Uncertainty: Epistemic vs. Aleatoric
16.1 Failure Modes in Online Inference
17.1 Layers of Explainability: Local, Rule-Based, Causal

Part V · System Deployment

18.1 Complexity in Symbolic, Graph, and LLM Reasoning
19.1 Roles of Edge vs. Cloud Inference
20.1 Spatiotemporal-Aware Graph Partitioning
21.1 Integrating Knowledge Substrate, Reasoning Models, Certification, and Deployment

Part VI · Frontier

22.1 The LLM as System 1: Strengths, Hallucinations, and Structural Limitations
23.1 Intelligent Transportation and Scene-Graph Understanding for Autonomous Driving
24.1 Molecular Graphs, Scientific Knowledge, and Interpretable Discovery
25.1 Book Arc: Knowledge Substrate, Reasoning, Certification, Systems

Appendices

Appendix A — Mathematical, Logical and Graph Learning Notation
Appendix B — Open-Source Libraries and Engineering Tools
Appendix C — Course Labs and Practice Projects

Experiments

Appendix C — Experiment Code

Repository
Open issue

Index

By Yushu Liu

© Copyright 2025.

Yushu Liu · yushuliu@outlook.com · GitHub
Text licensed under CC BY-NC-SA 4.0 · Code licensed under MIT