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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 Conditioned disjunction ： ウィキペディア英語版 Conditioned disjunction In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church. Given operands ''p'', ''q'', and ''r'', which represent truth-valued propositions, the meaning of the conditioned disjunction is given by: :$(q,\; r)\; ~\backslash leftrightarrow~(q\; \backslash rightarrow\; p)\; \backslash and\; (\backslash neg\; q\; \backslash rightarrow\; r)$ In words, is equivalent to: "if ''q'' then ''p'', else ''r''", or "''p'' or ''r'', according as ''q'' or not ''q''". This may also be stated as "''q'' implies ''p'', and not ''q'' implies ''r''". So, for any values of ''p'', ''q'', and ''r'', the value of is the value of ''p'' when ''q'' is true, and is the value of ''r'' otherwise. The conditioned disjunction is also equivalent to: :$(q\; \backslash and\; p)\; \backslash or\; (\backslash neg\; q\; \backslash and\; r)$ and has the same truth table as the "ternary" (?:) operator in many programming languages. In conjunction with truth constants denoting each truth-value, conditioned disjunction is truth-functionally complete for classical logic.〔Wesselkamper, T., "A sole sufficient operator", ''Notre Dame Journal of Formal Logic'', Vol. XVI, No. 1 (1975), pp. 86-88.〕 Its truth table is the following: There are other truth-functionally complete ternary connectives. ==References== 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「Conditioned disjunction」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.