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《相关逻辑与人工智能》教学大纲

The Syllabus of “Relevant Logic and AI” 

程京德 

[这是本人为国内大学讲授“相关逻辑与人工智能”课程的教学大纲最新版。相应的中文科普文章发布在微信公众号“数理逻辑与哲学逻辑”及本人科学网博客上。]

课程简介：本课程向学生们系统地介绍相关逻辑及其在实现人工通用智能(AGI)中不可或缺的基础作用。在讲授逻辑学一系列重要概念、相关性逻辑谬误、作为逻辑学及数学之核心的条件句、相关逻辑的由来及其哲学背景、相关推理、相关逻辑的各个形式逻辑系统之后，我们将展示相关逻辑的各种应用（包括：强相关逻辑作为各种应用逻辑的统一核心基础，扩展推理，準一致推理，溯因推理，非单调推理，自动定理发现，推理规则自动生成，自动知识获取，自动知识扩展，认知过程模型化及认知程序设计，基于规范相关逻辑的法律信息系统，基于时态相关逻辑的先期推理，三维空间中物体运动的基于时空相关逻辑的推理，动态世界中对行为者意图的先期推理，等等），并且说明为什么相关逻辑，尤其是强相关逻辑，对于相关推理、发现和预测来说是不可或缺的逻辑基础。最后，我们将提出支撑人工通用智能(AGI)的基础逻辑系统所必须满足的基本要求，说明目前只有强相关逻辑能够满足这些要求。

Course Introduction: This course systematically introduces students to the relevant logic and its indispensable foundational role in achieving Artificial General Intelligence (AGI). After teaching a series of important concepts of logic, fallacies of relevance, the notion of conditional as the core of logic and mathematics, the origin and philosophical background of relevant logic, relevant reasoning, and various formal logic systems of relevant logic, we will show various applications of relevant logic (including: strong relevant logic as the universal core basis of various applied logics, ampliative reasoning, paraconsistent reasoning, abductive reasoning, non-monotonic reasoning, automated theorem finding, automatic generation of inference rules, automatic knowledge acquisition, automatic knowledge appreciation, modeling of epistemic processes and epistemic programming, legal information systems based on deontic relevant logic, anticipatory reasoning based on temporal relevant logic, reasoning about motion objects in three-dimensional space based on spatio-temporal relevant logic, anticipatory reasoning about agents' intentions in dynamic worlds, etc.), and explain why relevant logic, especially strong relevant logic, is an indispensable logical foundation for relevant reasoning, discovery, and prediction. Finally, we will present the basic requirements that the foundational logic system underlying Artificial General Intelligence (AGI) must satisfy, and explain that currently only strongly relevant logic can meet these requirements. 

Course Contents 

1. Logic: What Is It and Why Study It? -- An Elementary Introduction to Logic (From a Viewpoint of Relevant Logic) 

    1.1 Logic: What Is It and Why Study It? 
    1.2 Reasoning, Proving, Discovery, and Prediction 
    1.3 Arguments, Deduction, Induction, and Abduction 
    1.4 Truth, Validity, Soundness, and Argument Forms 
    1.5 Informal Fallacies 
    1.6 Logic: What Is It All About? 
    1.7 Formal Logic Systems and Formal Theories 

2. Fallacies of Relevance 

3. The Notion of a Conditional: The Heart of Logic and Mathematics 

    3.1 Object Logic/Language and Meta-logic/language
    3.2 The Notion of a Conditional as the Heart of Logic and Mathematics 
    3.3 The Truth of a Conditional 
    3.4 Empirical and Logical Conditionals 
    3.5 The Notion of Conditional in Classical Mathematical Logic 
    3.6 A Comparison of Conditional and Material Implication 
    3.7 Paradoxes of Material Implication in Classical Mathematical Logic 
    3.8 The Notion of Conditional in Lewis’s Modal Logics 
    3.9 Sugihara’s Characterization of Implicational Paradoxes 

4. Relevant Logic: What Is It and Why Study It? 

    4.1 Ackermann’s Strengen Implikation (Rigorous Implication) and the von-Wright-Geach-Smiley Criterion for Entailment 
    4.2 Traditional (Weak) Relevant (Relevance) Logics 
    4.3 The Notion of Conditional (Entailment) in Relevant Logics 
    4.4 Variable-Sharing and the Relevance Principle 
    4.5 The Relationship between Relevant Logics and Classical Mathematical Logic 
    4.6 Intrinsic Differences in Applications of Classical Mathematical Logic and Relevant Logics 

5. Relevant Reasoning Based on Strong Relevant Logic 

    5.1 Paradoxes of Relevant Implication 
    5.2 Relevant Reasoning 
    5.3 Strong Relevant Logics and the Strong Relevance Principle 
    5.4 Relevant Reasoning Based on Strong Relevant Logic 

6. Relevant Logics: Proof Theory 

    6.1 The Formal Language of Relevant Logics 
    6.2 Hilbert Style Axiomatic Systems of Relevant Logics 
    6.3 Various Proof-theoretical Properties of Relevant Logics 

7. Strong Relevant Logic as the Universal Core Basis of Various Applied Logics for Knowledge Representation and Reasoning

    7.1 Background, Motivation, and Goal 
    7.2 Essential Requirements for the Universal Core Basis of Various Applied Logics 
    7.3 Strong Relevant Logics 
    7.4 Temporal Relevant Logics 
    7.5 Spatial Relevant Logics 
    7.6 Spatio-temporal Relevant Logics 
    7.7 Deontic Relevant Logics 
    7.8 Epistmic Relevant Logics 

8. Various Applications of Relevant Reasoning Based on Strong Relevant Logic 

    8.1 Strong Relevant Logic as the Universal Core Basis of Various Applied Logics 
    8.2 Ampliative Reasoning 
    8.3 Paraconsistent Reasoning 
    8.4 Abductive Reasoning 
    8.5 Non-monotonic Reasoning 
    8.6 Automated Theorem Finding by Entailment Calculus 
    8.7 Automatic Generation of Inference Rules
    8.8 Automatic Knowledge Acquisition 
    8.9 Automatic Knowledge Appreciation 
    8.10 Modeling Epistemic Processes 
    8.11 Epistemic Programming 
    8.12 Legal Information Systems Based on Deontic Relevant Logic 
    8.13 Anticipatory Reasoning Based on Temporal Relevant Logic 
    8.14 Reasoning about Motion Objects in a Three-dimensional Space Based on Spatio-temporal Relevant Logic 
    8.15 Anticipatory Reasoning about Agents' Intentions in Dynamic Worlds 

9. Research Directions and Challenging Problems 

Bibliography 

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