### 2021　Logic and Computation

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Graduate major in Mathematical and Computing Science
Instructor(s)
Kashima Ryo
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Mon3-4()  Thr3-4()
Group
-
Course number
MCS.T416
Credits
2
2021
Offered quarter
4Q
Syllabus updated
2021/9/30
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

This course covers the intersection of programming language theory and mathematical logic.
The key notion is "Curry-Howard correspondence", which shows the direct relationship between computer programs and mathematical proofs.
Topics include syntax and semantics of various logics (classical, intuitionistic, modal, etc.), various proof systems (natural deduction, sequent calculus, etc.) , and lambda calculus.

### Student learning outcomes

Students will acquire an insight into the logical foundations of computation.

### Keywords

Curry-Howard correspondence, lambda calculus, classical logic, intuitionistic logic, modal logic, natural deduction, sequent calculus, Kripke model

### Competencies that will be developed

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

### Class flow

The course consists of lectures.
Students will have exercise assignments several times.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction: intuitionistic and classical logics. Instructed in the class.
Class 2 Natural deduction (1): syntax. Instructed in the class.
Class 3 Natural deduction (2): normalization of proofs. Instructed in the class.
Class 4 Sequent calculus (1): syntax. Instructed in the class.
Class 5 Sequent calculus (1): cut-elimination. Instructed in the class.
Class 6 Hilbert-style system. Instructed in the class.
Class 7 Kripke model. Instructed in the class.
Class 8 ILambda calculus (1): syntax, Curry-Howard correspondence. Instructed in the class.
Class 9 Lambda calculus (2): Church‒Rosser theorem. Instructed in the class.
Class 10 Lambda calculus (3): type inference. Instructed in the class.
Class 11 Lambda calculus (4): strong normalization theorem. Instructed in the class.
Class 12 Combinatory logic. Instructed in the class.
Class 13 Various systems (1): higher order logics. Instructed in the class.
Class 14 Various systems (2): modal logics. Instructed in the class.

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

### Textbook(s)

Dirk van Dalen: Logic and Structure, Fourth Edition (Corrected 2nd printing 2008).
Henk Barendregt, Erik Barendsen: Introduction to Lambda Calculus (Revised edition December 1998, March 2000).

### Reference books, course materials, etc.

Instructed in the class.

### Assessment criteria and methods

Based on exercise assignments.

### Related courses

• MCS.T313 ： Mathematical Logic

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

Students who had completed MCS.T404 "Logical Foundations of Computing" cannot take this course.