課程資訊
 課程名稱 演繹邏輯之形式化Formalization of Deductive Systems 開課學期 101-1 授課對象 文學院  哲學研究所 授課教師 楊金穆 課號 Phl7714 課程識別碼 124EM3000 班次 學分 3 全/半年 半年 必/選修 選修 上課時間 星期五6,7,8(13:20~16:20) 上課地點 哲研討室二 備註 本課程以英語授課。總人數上限：15人 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 This course is in essence an intermediate-level course for formal logic. I shall hence assume that the student has a nodding acquaintance with topics in Elementary Logic. Some basic knowledge of Elementary Set Theory is extremely helpful though not essential. I shall confine this course to the four main styles of formal systems for propositional logic (i.e.CPC) and predicate logic(i.e., CQC): (a) Hilbert-Frege style (axiom) systems, (b) Systems of natural deduction, (c) (Formal) tableaux systems, and (d) Sequent calculi. The syllabus is to be described as below: The construction of a formal language suitable for propositional logic, and the standard semantics Application of arguments by cases, and proofs by induction Formal proofs of general properties of semantic entailments, and some important results in propositional logic, including functional completeness, expressive adequacy, disjunctive normal form (DNF) and conjunctive normal form (CNF), the interpolation theorem, compactness, and decidability The construction of formal systems Formal proofs of the soundness theorem and completeness theorem for propositional logic. The construction of axiomatic systems, systems of natural deduction, formal tableaux systems, and sequent calculi for propositional logic The construction of a first-order language suitable for predicate logic and the standard semantics Substitutional interpretation of quantification and objectual interpretation of quantification: true-in-i-interpretation in a structure and i-equivalence interpretation; true-in-M (a structure) and true-in-M+ (an expansion of M); a Tarskian style semantics The congruence theorem, prenex normal form (PNF) and compactness of first-order language, Skolemization: Skolem functions, Skolemized form and Skolem axioms The construction of axiomatic systems for predicate logic, the independence of axioms and the nature of axioms. The construction of systems of natural deduction for predicate logic, and normalization of natural deduction The construction of systems of formal tableaux for predicate logic. The construction of sequent calculi for predicate logic and its normalization Formal proofs of the soundness and completeness theorem for predicate logic, the decidability/ undecidability of first-order languages The equivalence of systems of distinct styles 課程目標 課程要求 預期每週課後學習時數 Office Hours 參考書目 指定閱讀 評量方式(僅供參考)
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