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''Modus ponendo tollens'' (Latin: "mode that by affirming, denies")〔Stone, Jon R. 1996. ''Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language''. London, UK: Routledge:60.〕 is a valid rule of inference for propositional logic, sometimes abbreviated MPT.〔Politzer, Guy & Carles, Laure. 2001. 'Belief Revision and Uncertain Reasoning'. ''Thinking and Reasoning''. 7:217-234.〕 It is closely related to ''modus ponens'' and ''modus tollens''. It is usually described as having the form: #Not both A and B #A #Therefore, not B For example: # Ann and Bill cannot both win the race. # Ann won the race. # Therefore, Bill cannot have won the race. As E.J. Lemmon describes it:"''Modus ponendo tollens'' is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds."〔Lemmon, Edward John. 2001. ''Beginning Logic''. Taylor and Francis/CRC Press: 61.〕 In logic notation this can be represented as: # # # Based on the Sheffer Stroke (alternative denial), "|", the inference can also be formalized in this way: # # # ==References== nl:Modus tollens#Modus ponendo tollens 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「Modus ponendo tollens」の詳細全文を読む スポンサード リンク
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