本課程介紹當代的符號邏輯系統，研究推論的邏輯結構與特徵，主要以形式邏輯為主。形式邏輯這門學科，旨在研究推論的抽象結構與邏輯性質，而基礎符號邏輯系統，可分為命題邏輯(propositional logic)和述詞邏輯(predicate logic)兩大部分。在命題邏輯部份，我們將介紹邏輯的基本概念，包括命題(proposition)與論證(argument)，以及有效性(validity)與真確性(soundness)，說明如何以邏輯語言將自然語言符號化，並介紹命題邏輯的語法(syntax)及語意(semantics)。此外，我們也將說明命題邏輯的分類，以及命題的邏輯關係，介紹命題邏輯有效性判定的一些方法，如歸謬真值表法、樹枝法、直接證法、條件證法與反證法。在述詞邏輯部分，我們將進一步討論述詞邏輯的符號系統，介紹述詞邏輯的語法及語意，並解說述詞邏輯論證有效性的判定方法，以及推論規則與證明(proof)。

This course introduces contemporary systems of symbolic logic and examines the logical structure and characteristics of inference, with a primary focus on formal logic. Formal logic is a discipline devoted to the study of the abstract structure and logical properties of inference. Basic systems of symbolic logic can be divided into two main parts: propositional logic and predicate logic.

In the section on propositional logic, we will introduce fundamental logical concepts, including propositions and arguments, as well as validity and soundness. We will explain how natural language can be symbolized using logical notation, and we will introduce the syntax and semantics of propositional logic. In addition, we will discuss classifications of propositional logic and the logical relations among propositions, and present several methods for determining validity in propositional logic, such as reductio ad absurdum via truth tables, the semantic tree (tableau) method, direct proof, conditional proof, and proof by contradiction.

In the section on predicate logic, we will further examine the symbolic system of predicate logic, introduce its syntax and semantics, and explain methods for determining the validity of arguments in predicate logic, as well as rules of inference and formal proof.

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