## Course: Exercises in Information Sciences II (Theorem Proving)

Every Wednesday from 10:40 to 12:10

Rooms: 理学部3号館504室 or 共通講義棟3号館408室

**[Theme]** In a course of mathematical logic, a student performs pen-and-paper formal proofs by means of logical derivations. How does a student know that her formal proof is correct? complete? Alternatively, she can use a software/tool such as a proof assistant. The advantage of using a proof assistant in the class is to, first, check the correctness of a proof, and, second, assist the student in writing a formal proof where no step is omitted, the logic is explicit and the proof method is clearly stated.

**[Objective]** In this class, we:

- learn how to write formal proofs using the proof assistant Isabelle/HOL (https://isabelle.in.tum.de/).
- study and practice various proving techniques (e.g. natural deduction, induction, etc.).

#### Course materials

- 2017.10.04, room 504: Course overview: Why theorem proving is vital? slides
- 2017.10.11, room 504: Natural deduction in propositional logic (I). slides, examples,quiz.
- 2017.10.18, room 504: Natural deduction in propositional logic (II). slides, examples, mt rule, quiz
- 2017.10.25, room 504: Natural deduction in propositional logic (III). slides
- 2017.11.01, room 504: First assignement: exercises
- 2017.11.08, room 504: Predicate logic (I). slides, quiz
- 2017.11.15, room 504: Predicate logic (II). slides, quiz
- 2017.11.22, room 504:Second assignement: exercises
- 2017.11.29, room 504: Second assignement (continuation)
- 2017.12.06, room 504: Inductive reasoning: introductive example
- 2017.12.13, room 504: Types and functions (I). slides, quiz
- 2017.12.20, room 504: Types and functions (II). slides, quiz
- 2017.12.27, room 504: Types and functions (III). slides
- 2018.01.17, room 504: Elementary set theory. class notes (updated on Jan. 30, 2018), examples

#### Other documents

List of natural deduction rules for the propositional logic: rules1

List of natural deduction rules for the predicate logic: rules2

Difference between erule and rule: examples

#### Evaluation

Quiz during the class: 50%

Assignements: 50%

#### Lecturer

Fadoua Ghourabi

Contact: ghourabi "dot" fadoua "at" ocha "dot" ac "dot" jp

Office: 人間文化創成科学研究科・全学共用研究棟 603室

For questions, students can visit my office on Friday from 14:00 to 16:00

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.