2020 Logic and Computation

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Academic unit or major
Graduate major in Mathematical and Computing Science
Kashima Ryo  Nishizaki Shin-Ya 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue1-2(W833)  Fri1-2(W833)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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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 natural deduction, sequent calculus, classical and intuitionistic logics, and lambda calculus.

Student learning outcomes

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


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

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 about three times.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction to logic. Logical formulas. Instructed in the class.
Class 2 Truth values of formulas. Instructed in the class.
Class 3 Natural deduction. Instructed in the class.
Class 4 Sequent calculus. Instructed in the class.
Class 5 Completeness of classical logic. Instructed in the class.
Class 6 Completeness of intuitionistic logic. Instructed in the class.
Class 7 Properties of intuitionistic logic. Instructed in the class.
Class 8 Introduction to lambda calculus. Instructed in the class.
Class 9 Power of lambda calculus. Instructed in the class.
Class 10 Church-Rosser property. Instructed in the class.
Class 11 Introduction to the combinatory logic. Instructed in the class.
Class 12 Properties of the combinatory logic. Instructed in the class.
Class 13 Curry-Howard correspondence. Instructed in the class.
Class 14 Properties of type systems. 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.


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).
(Both are downloadable from the internet.)

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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