逻辑

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逻辑(logic)

关於推论与论证之研究。在逻辑中，一个论证的组成是，一组为真的陈述（前提）是使得进一步陈述（论证的结论）为真的充分条件。逻辑可分为演绎逻辑、归纳逻辑以及所谓非形式谬误的研究（参阅deduction、induction、fallacy, formal and informal）。现代形式逻辑以命题与演绎论证为主题，并从这些命题与演绎论证的内容抽离出它们所包含的逻辑形式。逻辑学家使用符号来表示那些逻辑形式，便於推论，也便於验证有效性。逻辑常项包括（一）命题连结词，如「非」（@8(logicNon.jpg），「且」（@8(logicAnd.jpg），「或」（@8(logicOr.jpg），「若－则」（(），（二）存在量词与全称量词「(@8(logicSome.jpgx)」（可读作「对於至少有一个体，称为x，……为真」）以及「(@8(logicAll.jpgx)」（「对於每一个体，称为x，……为真」）。再加上（三）等同概念（以=表示）与（四）一些属於逻辑的谓词。单单上述（一）的逻辑常项之研究，称作命题演算（propositional calculus）。涉及上述（一）、（二）与（四）者，属一阶谓词演算（first-order predicate calculus）领域。若强调上述（三），则加入「不等同」之词。逻辑是哲学与数学领域的重要基础。亦请参阅deontic logic、modal logic。

English version：

logic

Study of inference and argument. In logic, an argument consists of a set of statements (the premises) whose truth is claimed to be sufficient for the truth of a further statement (the conclusion of the argument). Logic may be divided into deductive logic, inductive logic, and the study of what are often called informal fallacies (see deduction, induction, fallacy). Modern formal logic takes as its main subject matter propositions and deductive arguments, and it abstracts from their content the logical forms they embody. The logician uses a symbolic notation to express these logical forms and to facilitate inference and tests of validity. The logical constants include (1) such propositional connectives as "not" (symbolized as ¬), "and" (symbolized as ∧), "or" (symbolized as ∨), and "if-then" (symbolized as ⊃), and (2) the existential and universal quantifiers "(∃x)" (which may be read: "For at least one individual, call it x, it is true that") and "(∀x)" ("For each individual, call it x, it is true that"). Furthermore, (3) the concept of identity (expressed by =) and (4) some notion of predication belong to logic. When the logical constants in (1) alone are studied, the field is called propositional calculus. When (1), (2), and (4) are considered, the field is first-order predicate calculus. If the absence of (3) is stressed, the epithet "without identity" is added. Logic is fundamental to the fields of philosophy and mathematics. See also deontic logic, modal logic.

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