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2024　Logic and Computation

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Kashima Ryo 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
-
Group
-
Course number
MCS.T416
Credits
2
Academic year
2024
Offered quarter
4Q
Syllabus updated
2024/3/14
Lecture notes updated
-
Language used
English
Access Index

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 classical and intuitionistic logics, various proof systems (natural deduction, sequent calculus, etc.), and lambda calculus (Church–Rosser theorem, type-free and typed lambda calculus, strong normalization theorem, etc.).

Student learning outcomes

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

Keywords

classical logic, intuitionistic logic, natural deduction, sequent calculus, Kripke model, Curry-Howard correspondence, type-free and typed lambda calculus, Church–Rosser theorem, strong normalization theorem, combinatory logic.

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 Truth, validity, and satisfiability of logical formulas. Instructed in the class.
Class 2 Natural deduction. Instructed in the class.
Class 3 Sequent calculus. Instructed in the class.
Class 4 Cut-elimination theorem and completeness theorem. Instructed in the class.
Class 5 Intuitionistic logic (1). Instructed in the class.
Class 6 Intuitionistic logic (2). Instructed in the class.
Class 7 Normalization of proofs in natural deduction. Combinatory logic (1). Instructed in the class.
Class 8 Introduction to lambda calculus. Instructed in the class.
Class 9 Combinatory logic (2). Arithmetic by lambda calculus. Instructed in the class.
Class 10 Church–Rosser theorem. Instructed in the class.
Class 11 Left-most reduction theorem. Simply typed lambda calculus. Instructed in the class.
Class 12 Curry-Howard correspondence. Instructed in the class.
Class 13 Strong normalization theorem. Instructed in the class.
Class 14 Second-order typed lambda calculus. 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.

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