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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク disjunctive syllogism ： ウィキペディア英語版 disjunctive syllogism In classical logic disjunctive syllogism (historically known as modus tollendo ponens) is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.〔Hurley〕〔Copi and Cohen〕 :Either the breach is a safety violation, or it is not subject to fines. :The breach is not a safety violation. :Therefore, it is not subject to fines. In propositional logic, disjunctive syllogism (also known as disjunction elimination and or elimination, or abbreviated ∨E),〔Sanford, David Hawley. 2003. ''If P, Then Q: Conditionals and the Foundations of Reasoning''. London, UK: Routledge: 39〕〔Hurley〕〔Copi and Cohen〕〔Moore and Parker〕 is a valid rule of inference. If we are told that at least one of two statements is true; and also told that it is not the former that is true; we can infer that it has to be the latter that is true. If either ''P'' or ''Q'' is true and ''P'' is false, then ''Q'' is true. The reason this is called "disjunctive syllogism" is that, first, it is a syllogism, a three-step argument, and second, it contains a logical disjunction, which simply means an "or" statement. "Either P or Q" is a disjunction; P and Q are called the statement's ''disjuncts''. The rule makes it possible to eliminate a disjunction from a logical proof. It is the rule that: :$\backslash frac$ where the rule is that whenever instances of "$P\; \backslash or\; Q$", and "$\backslash neg\; P$" appear on lines of a proof, "$Q$" can be placed on a subsequent line. Disjunctive syllogism is closely related and similar to hypothetical syllogism, in that it is also type of syllogism, and also the name of a rule of inference. It is also related to the Law of noncontradiction and the Law of excluded middle, two of the three traditional laws of thought. == Formal notation == The ''disjunctive syllogism'' rule may be written in sequent notation: : $P\; \backslash lor\; Q,\; \backslash lnot\; P\; \backslash vdash\; Q$ where $\backslash vdash$ is a metalogical symbol meaning that $Q$ is a syntactic consequence of $P\; \backslash lor\; Q$, and $\backslash lnot\; P$ in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :$((P\; \backslash or\; Q)\; \backslash and\; \backslash neg\; P)\; \backslash to\; Q$ where $P$, and $Q$ are propositions expressed in some formal system. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「disjunctive syllogism」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.