### 2020　Mathematical Logic

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Undergraduate major in Mathematical and Computing Science
Instructor(s)
Kashima Ryo
Course component(s)
Lecture
Day/Period(Room No.)
Tue3-4(W834)  Fri3-4(W834)
Group
-
Course number
MCS.T313
Credits
2
2020
Offered quarter
2Q
Syllabus updated
2020/3/24
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

In mathematics class, we learn logic as the language of mathematics (for example, the usage of ∀ and ∃). In this course, we study logic itself mathematically, and we investigate the ability and limitation of logic. We also give an overview of non-classical logics (especially modal logics and intuitionistic logic) in computer science. In mathematics and computer science, logic is the foundation and an important tool. This course gives correct understanding of logic.

### Student learning outcomes

At the end of this course, students will be able to:
(1) Write a logical formula that represents intended meaning correctly.
(2) Have a correct understanding of the basic results of mathematical logic, as follows: propositional logic, predicate logic, syntax, semantics, Gentzen's natural deduction, Goedel's completeness theorem, Goedel's incompleteness theorem, compactness, decidability, undecidability, normal form of formulas, etc.
(3) Have basic knowledge about non-classical logics (especially modal logics and intuitionistic logic) in computer science.

### Keywords

propositional logic, predicate logic, Gentzen's natural deduction, Goedel's completeness theorem, Goedel's incompleteness theorem, modal logic, intuitionistic logic.

### Competencies that will be developed

 Intercultural skills Communication skills ✔ Specialist skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

The course consists of lectures.
Homework assignments are given several times for checking your understanding.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction. Problems in Chapter 1 of the textbook.
Class 2 Natural deduction. Problems in Chapter 2 of the textbook.
Class 3 Natural deduction (2). Problems in Chapter 2 of the textbook.
Class 4 Natural deduction (3). Problems in Chapter 2 of the textbook.
Class 5 Truth, validity, and satisfiability of logical formulas. Problems in Chapter 3 of the textbook.
Class 6 Soundness of natural deduction. Problems in Chapter 4 of the textbook.
Class 7 Completeness of natural deduction (1). Problems in Chapter 5 of the textbook.
Class 8 Completeness of natural deduction (2). Problems in Chapter 5 of the textbook.
Class 9 Incompleteness Theorem (1). Problems in Chapter 6 of the textbook.
Class 10 Incompleteness Theorem (2). Problems in Chapter 6 of the textbook.
Class 11 Propositional logic. Problems in Chapter 7 of the textbook.
Class 12 Modal logic (1). Instructed in the class.
Class 13 Modal logic (2). Instructed in the class.
Class 14 Intuitionistic logic. Instructed in the class.

### Textbook(s)

Materials for Classes 12, 13 and 14 can be found on OCW-i.

### Reference books, course materials, etc.

Instructed in the class.

### Assessment criteria and methods

Final exam (80%) and exercise problems (20%).

### Related courses

• MCS.T201 ： Set and Topology I
• MCS.T204 ： Introduction to Computer Science
• MCS.T214 ： Theory of Automata and Languages
• MCS.T323 ： Theory of Computation

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites. 