Mathematical Logic

Course title

L0980800

Mathematical Logic

sugimoto tooru

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Course description

Basic definitions, properties and applications of propositional logic and first-order predicate logic are explained.

Purpose of class

Students can learn logical analysis method that is needed for designing software and hardware.

Goals and objectives

To express logical conditions and information contents using propositional logic and first-order logic
To understand relationship between syntax and semantics, and between proofs and models
To learn basic proof methods, e.g., mathematical induction and proof by contradiction

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Overview of mathematical logic	Read syllabus	90minutes
2.	Propositional logic (1) : formula, truth value table, validity	Textbook 1.1-1.3	90minutes
2.		Exercises	90minutes
3.	Propositional logic (2) : logical operations, duality, normal forms	Textbook 1.4-1.5	90minutes
3.		Exercises	90minutes
4.	Propositional logic (3) : formal system, natural deduction	Textbook 6.1-6.3	90minutes
4.	Propositional logic (3) : formal system, natural deduction	Exercises	90minutes
5.	Propositional logic (4) : natural deduction, completeness and soundness	Textbook 6.1-6.3	90minutes
5.		Exercises	90minutes
6.	Intermediate exam and comments	Review	180minutes
7.	Predicate logic (1) : formula, logical structure analysis	Textbook 2.1 and 2.2	90minutes
7.	Predicate logic (1) : formula, logical structure analysis	Exercises	90minutes
8.	Predicate logic (2) : term and substitution, free and bound variables	Textbook 2.1 and 2.2	90minutes
8.		Exercises	90minutes
9.	Predicate logic (3) : interpretation, structure, validity	Textbook 2.3 and 2.4	90minutes
9.	Predicate logic (3) : interpretation, structure, validity	Exercises	90minutes
10.	Predicate logic (4) : properties of formulas, examples	Textbook 2.4	90minutes
10.	Predicate logic (4) : properties of formulas, examples	Exercises	90minutes
11.	Predicate logic (5) : natural deduction, completeness and soundness	Review natural deduction	90minutes
11.		Exercises	90minutes
12.	Predicate logic (6) : theory, model, incompleteness theorem	Read printed materials	90minutes
12.	Predicate logic (6) : theory, model, incompleteness theorem	Exercises	90minutes
13.	Proof techniques : mathematical induction, proof by contradiction	Read printed materials	90minutes
13.		Exercises	90minutes
14.	Final exam and comments	Review all	180minutes
Total.	-	-	2430minutes

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Assignments	Intermediate exam	Final exam	Total.
1.	5%	25%	25%	55%
2.	5%	10%	15%	30%
3.		5%	10%	15%
Total.	10%	40%	50%	-

Evaluation method and criteria

Assignments (10%), intermediate exam (40%) and final exam (50%)

Textbooks and reference materials

H. Ono, "Logic in Information Science", Nihon Hyoronsha, 1994.

Prerequisites

Discrete Mathematics 1, Logic Circuits

Office hours and How to contact professors for questions

Monday, lunch break

Relation to the environment

Non-environment-related course

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge
Course that cultivates a basic problem-solving skills

Active-learning course

More than one class is interactive

Last modified : Wed Oct 17 06:49:02 JST 2018