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In logic, ''inference'' is the process of deriving logical conclusions from premises known or assumed to be true. In checking a logical inference for ''formal'' and material validity, the meaning of only its logical vocabulary and of both its logical and extra-logical vocabulary is considered, respectively. ==Examples== For example, the inference "''Socrates is a human, and each human must eventually die, therefore Socrates must eventually die''" is a formally valid inference; it remains valid if the nonlogical vocabulary "''Socrates''", "''is human''", and "''must eventually die''" is arbitrarily, but consistently replaced. 〔A completely fictitious, but formally valid inference obtained by consistent replacement is e.g. "''Buckbeak is a unicorn, and each unicorn has gills, therefore Buckbeak has gills''".〕 In contrast, the inference "''Montreal is north of New York, therefore New York is south of Montreal''" is materially valid only; its validity relies on the extra-logical relations "''is north of''" and "''is south of''" being converse to each other. 〔A completely fictitious, but materially (and formally) invalid inference obtained by consistent replacement is e.g. "''Hagrid is younger than Albus, therefore Albus is larger than Hagrid''". Consistent replacement doesn't respect conversity.〕 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「Material inference」の詳細全文を読む スポンサード リンク
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