### 2018　Logic and Computation

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Graduate major in Mathematical and Computing Science
Instructor(s)
Kashima Ryo  Nishizaki Shin-Ya
Course component(s)
Lecture
Mode of instruction

Day/Period(Room No.)
Tue1-2(W833)  Fri1-2(W833)
Group
-
Course number
MCS.T416
Credits
2
2018
Offered quarter
1Q
Syllabus updated
2018/4/6
Lecture notes updated
2018/6/5
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 lambda calculus, natural deduction, sequent calculus, classical logic, intuitionistic logic, and various logics in computer science.

### Student learning outcomes

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

### Keywords

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.
Homework assignments are given 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): sysntax. 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 (2): 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 Lambda 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): linear logic, modal logics. Instructed in the class.
Class 14 Various systems (2): higher order logic, polymorphism. Instructed in the class.
Class 15 Conclusion and supplementary explanations. Instructed in the class.

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### Reference books, course materials, etc.

J.-Y.Girard et.al.: Proofs and Types (Cambridge Univ.P.). D. van Dalen: Logic and Structure (Springer).
Hindley J.R. & Seldin J.P. : Introduction to Combinators and lambda-calculus (Cambridge Univ. P.).

### Assessment criteria and methods

final exams (60%), exercise problems (40%).

### Related courses

• MCS.T502 ： Functional Programming
• MCS.T411 ： Computational Complexity Theory
• CSC.T425 ： Concurrent System Theory

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

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