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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 Hypothetical syllogism ： ウィキペディア英語版 Hypothetical syllogism In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises.〔Hurley〕〔Copi and Cohen〕 :If I do not wake up, then I cannot go to work. :If I cannot go to work, then I will not get paid. :Therefore, if I do not wake up, then I will not get paid. In propositional logic, hypothetical syllogism is the name of a valid rule of inference〔Hurley〕〔Copi and Cohen〕 (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). Hypothetical syllogism is one of the rules in classical logic that is not always accepted in certain systems of non-classical logic. The rule may be stated: :$\backslash frac$ where the rule is that whenever instances of "$P\; \backslash to\; Q$", and "$Q\; \backslash to\; R$" appear on lines of a proof, "$P\; \backslash to\; R$" can be placed on a subsequent line. Hypothetical syllogism is closely related and similar to disjunctive syllogism, in that it is also type of syllogism, and also the name of a rule of inference. == Formal notation == The ''hypothetical syllogism'' rule may be written in sequent notation: : $(P\; \backslash to\; Q),\; (Q\; \backslash to\; R)\; \backslash vdash\; (P\; \backslash to\; R)$ where $\backslash vdash$ is a metalogical symbol meaning that $P\; \backslash to\; R$ is a syntactic consequence of $P\; \backslash to\; Q$, and $Q\; \backslash to\; R$ in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: :$((P\; \backslash to\; Q)\; \backslash and\; (Q\; \backslash to\; R))\; \backslash to\; (P\; \backslash to\; R)$ where $P$, $Q$, and $R$ 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「Hypothetical 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.