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The aim of this course is to give a gentle introduction to mathematical logic.
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The goal of this course is to obtain the principle and practice of mathematical logic, including formal representations by using logical connectives, propositional logic, and predicate logic.
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The relationship of this course to our diploma policy is as follows:
A: Basic knowledge and understanding of various sciences ◎
B: Logical and creative thinking ability ◎
C: Communication ability ー
D: Social ethics and internationality ー
E: Understanding the issues of the information society and
utilization of informatics knowledge ー
F: Knowledge of social organizations and systems and ability to analyze
by a social scientific approach ー
G: Basic knowledge of data science and social implementation ability ー
H: Knowledge base for creating and utilizing information technology ○
I: Ability to formulate tasks based on humanistic and informatics knowledge
and search for practical philosophy ー
J: Ability to discover issues and propose social systems utilizing
social science knowledge ー
K: Ability to solve problem through data collection, analysis and
mathematical optimization ー
L: Knowledge of computations and information and ability to develop
technology related to computers ○
(◎：Especially important ○：Important △：Subject to evaluation ー：Not subject to evaluation)
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Mathematical logic is said to be the art of reasoning, and nowadays the applications of logic to AI, CS, etc. are numerous and well recognized. This course provides a gentle introduction to propositional and predicate logics, and, in particular, focuses on formal representations by using logical connectives, and the semantics and syntax of formal logic, together with logic puzzles.
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This is a lecture style class. Students are expected to bring their computer.
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01. Introduction
02. Logic and Formalization（1）
03. Logic and Formalization（2）
04. Logic and Formalization（3）
05. Propositional Logic and Its Semantics (1)
05. Propositional Logic and Its Semantics (2)
07. Boolean Algebra (1)
08. Boolean Algebra (2)
09. Formal System of Propositional Logic: (1)
10. Formal System of Propositional Logic: (2)
11. Formal System of Propositional Logic: (3)
12. Formal System of Propositional Logic: (4)
13. Predicate Logic (1)
14. Predicate Logic (2)
15. Predicate Logic (3)
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This is a normal 2-credit course, which basically means that in addition to the scheduled meeting times, students are expected to do at least 3 hours of course-related work outside of class each week during the session. This includes work done completing assigned readings, preparing written assignments, studying for tests and examinations, and other course-related tasks.
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During the term, small examinations and the final examination are held. There also will be hand-written reports. Assessment will be based on: small examinations and the final examination (total 60% [A, B, H, L]), and hand-written reports (total 40% [A, B, H, L]). (Full attendance is assumed in this calculation.)
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Propositional logic, predicate logic, semantics, inference rules, soundness and completeness theorem
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