课程详述

COURSE SPECIFICATION

以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请

联系授课教师。

The course information as follows may be subject to change, either during the session because of unforeseen

circumstances, or following review of the course at the end of the session. Queries about the course should be

directed to the course instructor.

课程名称 Course Title

数理逻辑导论 (H) Introduction to Mathematical Logic (H)

授课院系

Originating Department

计算机科学与工程系 Department of Computer Science and Engineering

课程编号

Course Code

CS108

课程学分 Credit Value

课程类别

Course Type

专业基础课 Major Foundational Courses

授课学期

Semester

春季 Spring

授课语言

Teaching Language

双语 Bilingual

授课教师、所属学系、联系方

式（如属团队授课，请列明其

他授课教师）

Instructor(s), Affiliation&

Contact

（For team teaching, please list

all instructors）

程京德，教学教授，计算机科学与工程系，chengjd@sustech.edu.cn

Jingde Cheng, Teaching Professor, Department of Computer Science and Engineering,

chengjd@sustech.edu.cn

实验员/助教、所属学系、联系

方式

Tutor/TA(s), Contact

待公布 To be announced

10.

选课人数限额(可不填)

Maximum Enrolment

（Optional）

11.

授课方式

Delivery Method

讲授

Lectures

习题/辅导/讨论

Tutorials

实验/实习

Lab/Practical

其它(请具体注明)

Other（Please specify）

总学时

Total

学时数

Credit Hours

12.

先修课程、其它学习要求

Pre-requisites or Other

Academic Requirements

None

13.

后续课程、其它学习规划

Courses for which this course

is a pre-requisite

计算机科学，智能科学，及人工智能的全部理论课程 All theoretical courses for

Computer Science, Intelligent Sciences, and Artificial Intelligence

14.

其它要求修读本课程的学系

Cross-listing Dept.

数学系 Dept. of Mathematics

教学大纲及教学日历 SYLLABUS

15.

教学目标 Course Objectives

作为 UNESCO 推荐科学技术领域分类中基础学科之首的逻辑学，是包括数学、计算机科学、智能科学在内的诸多学科之最

重要的必要理论基础。“数理逻辑导论(H)”课程对于经典数理逻辑的历史背景、基本概念和原理、主要方法论以及重要

理论结果给予学生一个入门性介绍，为今后深入学习研究现代逻辑学及其应用的学生提供研究逻辑学课题的良好基础，为

今后深入学习研究各学科理论课题的学生提供使用逻辑学方法论的基本素养。但是，因为这是一门基础性理论性极强的课

程，所以数学基础较差的学生以及今后有志于从事工程技术工作的学生不必选修此课。

“数理逻辑导论(H)”课程的教学目标为：（1）让学生知道逻辑学的历史背景、本质、目的、基本假设、范围、主要方法

论。（2）让学生知道经典数理逻辑的本质、目的、基本假设、范围、应用领域。（3）让学生熟知经典数理逻辑中的命题

演算部分。（4）让学生熟知经典数理逻辑中的一阶谓词演算部分。（5）让学生知道经典数理逻辑的局限性。（6）让学

生知道各种模态逻辑（规范模态逻辑、时态逻辑、空间逻辑、时空逻辑、规范（道义）逻辑、认知逻辑）以及相关逻辑及

其它们的应用领域。

Logic, as the first fundamental discipline in the fields of science and technology recommended by UNESCO, is the most

important and indispensable theoretical foundation for many disciplines, including mathematics, computer science,

intelligent science, and so on. The course "Introduction to Mathematical Logic (H)" gives students an elementary

introduction to the historical background, the basic concepts and principles, the major methodology, and important

theoretical results of classical mathematical logic. It provides a good foundation for students to study modern logic and

its application in depth, and also provides students with basic qualities of using logic methodology for further study and

research of theoretical subjects in various disciplines. However, students with poor mathematical foundation and those

who are interested in engineering and technical jobs in the future need not take this course, because this course is a

quite fundamental and theoretical one.

The teaching objectives of the course "Introduction to Mathematical Logic (H)" are: (1) Let students know the historical

background, essence/nature, purpose, basic assumptions, scope, and major methodology of logic. (2) Let students

know the essence, purpose, basic assumptions, scope, and application fields of classical mathematical logic. (3) Let

students be familiar with the propositional calculus in classical mathematical logic. (4) Let students be familiar with the

first-order predicate calculus in classical mathematical logic. (5) Let students know the limitations of classical

mathematical logic. (6) Let students know various modal logics (including normal modal logics, temporal logics, spatial

logics, spatio-temporal logics, deontic logics, and epistemic logics) and relevant logics and their application fields.

16.

预达学习成果 Learning Outcomes

“数理逻辑导论(H)”课程的预达学习效果为：（1）学生能够在遇到任何问题时凭借在本课程学习到的逻辑知识辨别出问

题中的逻辑要素从而依据在本课程学习到的逻辑知识不犯或少犯逻辑错误。（2）学生能够使用经典数理逻辑来形式化地

表达经验领域知识以及构造经验领域形式理论。（3）学生能够使用经典数理逻辑（以及自动推理/证明工具，如果可能）

解决经验领域中的推理/证明问题。（4）学生能够清楚地识别出由于经典数理逻辑的局限性所导致的经验领域应用困难课

题。（5）学生能够基于本课程学习到的知识进一步学习研究现代逻辑学各个分支及其应用。

The learning outcomes of the course "Introduction to Mathematical Logic (H)" is as follows: (1) When students

encounter any problem, they can identify those logic-related elements in the problem by applying the logic knowledge

learned in this course, and therefore, they can avoid or minimize logical mistakes based on the logic knowledge learned

in this course. (2) Students can use classical mathematical logic to formally represent knowledge in empirical fields and

construct formal theories for the empirical fields. (3) Students can use classical mathematical logic (and automatic

reasoning/proof tools, if possible) to solve reasoning/proof problems in empirical fields. (4) Students can clearly identify

those difficult issues in empirical field applications that are due to the limitations of classical mathematical logic. (5)

Students can further study various branches of modern logic and their applications based on the knowledge acquired in

this course.

17.

课程内容及教学日历（如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明

主讲人）

Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if

this is a team teaching or module course.)

1. 导引

2. 什么是逻辑学？为什么要学习和研究逻辑学？

3. 逻辑学的基本概念：推理、证明、发现、预测、各种论证、演绎、归纳和假说生成

4. 逻辑学的基本概念：真理和有效性以及各种逻辑谬误

5. 逻辑学的基本概念：逻辑学的核心概念条件句、逻辑学的范围、数理逻辑与各种哲学逻辑

6. 形式逻辑系统与形式理论：模型（语义）理论与证明（语法）理论

7. 经典命题演算 CPC的形式（对象）语言与模型理论

8. 经典命题演算 CPC的希尔伯特形式系统及其健全性和完全性

9. 经典一阶谓词演算 CFOPC的形式（对象）语言

10. 经典一阶谓词演算 CFOPC的模型理论

11. 经典一阶谓词演算 CFOPC的希尔伯特形式系统及其健全性和完全性

12. 经典命题演算 CPC的其他形式系统

13. 经典一阶谓词演算 CFOPC的其他形式系统

14. 经典形式系统的局限性：哥德尔不完全性定理

15. 各种模态逻辑：规范模态逻辑、时态逻辑、空间逻辑、时空逻辑、规范逻辑、认知逻辑

16. 相关逻辑

1. Guidance

2. Logic: What Is It and Why Study It?

3. Basic Concepts of Logic: Reasoning, Proving, Discovery, Prediction, Various Arguments, Deduction,

Induction, and Abduction

4. Basic Concepts of Logic: Truth and Validity, and Various Logical Fallacies

5. Basic Concepts of Logic: The Notion of a Conditional as the Heart of Logic, the Scope of Logic, Mathematical

Logic and Various Philosophical Logics

6. Formal Logic Systems and Formal Theories: Model (Semantic) Theory and Proof (Syntactic) Theory

7. Formal (Object) Language of Classical Propositional Calculus (CPC) and Model Theory for CPC

8. Hilbert Style Formal System for CPC and Its Soundness and Completeness

9. Formal (Object) Language of Classical First Order Predicate Calculus (CFOPC)

10. Model Theory for CFOPC

11. Hilbert Style Formal System for CFOPC and Its Soundness and Completeness

12. Other Formal Systems for CPC

13. Other Formal Systems for CFOPC

14. Limitations of the Classical Formal Systems: Gödel’s Incompleteness Theorems

15. Various Modal Logics: Normal Modal Logics, Temporal Logics, Spatial Logics, Spatio-Temporal Logics,

Deontic Logics, and Epistemic Logics

16. Relevant Logics

18.

教材及其它参考资料 Textbook and Supplementary Readings

I. M. Copi and C. Cohen, “Introduction to Logic,”Routledge, 2019 (with V. Rodych) (15th Edition).

P. J. Hurley, “A Concise Introduction to Logic,” Wadsworth, 2016 (with L. Watson) (13th Edition).

D. Kelley, “The Art of Reasoning: An Introduction to Logic and Critical Thinking,” W. W. Norton & Company,

2014 (4th Edition).

E. Mendelson, “Introduction to Mathematical Logic,” Chapman & Hall, 2015 (6th Edition).

R. M. Smullyan, “A Beginner’s Guide to Mathematical Logic,” Dover Publications, 2014.

M. Ben-Ari, “Mathematical Logic for Computer Science,” Springer, 2012 (3rd Edition).

W. Routenberg, “A Concise Introduction to Mathematical Logic,” Springer, 2010 (3rd Edition).

S. Reeves and M. Clarke, “Logic for Computer Science,” Addison-Wesly, 1990-2003.

G. Priest, “An Introduction to Non-Classical Logic: From If to Is,” Cambridge University Press, 2001, 2008 (2nd

Edition).

E. D. Mares, “Relevant Logic: A Philosophical Interpretation,” Cambridge University Press, Cambridge, 2004.

课程评估 ASSESSMENT

19.

评估形式

Type of

Assessment

评估时间

Time

占总成绩百分比

% of final

score

违纪处罚

Penalty

备注

Notes

出勤 Attendance

课堂表现

Class

Performance

小测验

Quiz

课程项目 Projects

平时作业

Assignments

50 %

期中考试

Mid-Term Test

期末考试

Final Exam

50 %

期末报告

Final

Presentation

其它（可根据需要

改写以上评估方

式）

Others (The

above may be

modified as

necessary)

20.

记分方式 GRADING SYSTEM

 A. 十三级等级制 Letter Grading

 B. 二级记分制（通过/不通过） Pass/Fail Grading

课程审批 REVIEW AND APPROVAL

21.

本课程设置已经过以下责任人/委员会审议通过

This Course has been approved by the following person or committee of authority