Type of Credit: Elective
Credit(s)
Number of Students
邏輯(logic)又稱理則學，自公元前三世紀由亞里斯多德(Aristotle)發展成正式學科後，兩千多年來持續研究發展。在計算機科學上我們關注數理邏輯的發展與應用，這是在十九世紀由德國數學家與哲學家弗雷格(Gottlob Frege)及英格蘭數學家與哲學家布爾(George Boole)等前人共同奠定的基礎，透過數理邏輯建構起人類與計算機之間的共同思維架構。
本課程介紹了數理邏輯及其在計算機科學的基本應用，課程中將教授數理邏輯中基礎的命題邏輯(propositional logic)以及謂詞邏輯(predicate logic，如一階邏輯)。透過本課程的學習，修課同學除可獲得計算機科學中數理邏輯的相關知識，也可以獲取計算機科學相關理論主題及進階課程的預備知識。透過這些數理邏輯知識，將有助修課同學未來進一步學習進階計算理論相關課程，以及正規驗證、大數據與人工智慧等相關應用。
能力項目說明
獲得邏輯推理能力
了解數理邏輯的要素
了解數理邏輯在計算機科學中的基本應用
培植計算機科學理論基礎
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
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實際授課內容請參考Moodle課程網頁
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週次 Week |
課程主題 Topic |
課程內容與指定閱讀 Content and Reading Assignment |
教學活動與作業 Teaching Activities and Homework |
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1 |
Propositional Logic |
Syllabus |
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2 |
Propositional Logic |
Overview and Foundations of Propositional Logic |
V |
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3 |
Propositional Logic |
Equivalence and Normal Form |
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4 |
Propositional Logic |
CNF and DNF |
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5 |
Propositional Logic |
Horn Formulas |
V |
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6 |
Propositional Logic |
Compactness and Resolution |
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7 |
Predicate Logic |
Overview and Foundations of Predicate Logic |
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8 |
Midterm |
Midterm |
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9 |
Predicate Logic |
Problem Solving. Normal Forms |
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10 |
Predicate Logic |
Equivalences, Substitution, PNF and Skolem Form |
V |
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11 |
Predicate Logic |
Decidable & Undecidable. PCP, Church’s Theorem, and the Halting Problem |
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12 |
Predicate Logic |
Herbrand’s Theorem, Gödel-Herbrand-Skolem Theorem, and Semi-decision |
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13 |
Predicate Logic |
Gilmore's Algorithm, Clause Herbrand Expansion, and Ground Resolution |
V |
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14 |
Predicate Logic |
Unification Algorithm and Resolution Theorem |
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15 |
Predicate Logic |
Refinements of Resolution |
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16 |
Midterm |
Final Exam |
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Homework and Discussion: 40%
Midterm and Final Exam: 60%
教科書：
Logic for Computer Scientists
Author: Uwe Schöning
Publisher: Birkhäuser Boston, MA
eBook ISBN: 978-0-8176-4763-6
SpringerLink Online Access: https://link.springer.com/book/10.1007/978-0-8176-4763-6
參考書：
Introduction to Logic, Second Edition
Authors: Michael Genesereth , Eric Kao
Publisher: Springer Cham
eBook ISBN: 978-3-031-01799-5
SpringerLink Online Access: https://link.springer.com/book/10.1007/978-3-031-01799-5
Artificial Intelligence: A Modern Approach, 3rd Edition
Authors: Stuart Russell , Peter Norvig
Publisher: Prentice Hall
ISBN: 0132071487
中文版：
書名：人工智慧－現代方法, 3/e
譯者：歐崇明、時文中、陳龍
出版商：全華圖書
ISBN：9789862800249
| 書名 Book Title | 作者 Author | 出版年 Publish Year | 出版者 Publisher | ISBN | 館藏來源* | 備註 Note |
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