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In logic, predicate abstraction is the result of creating a predicate from a sentence. If Q is any formula then the predicate abstract formed from that sentence is (λy.Q), where λ is an abstraction operator and in which every occurrence of y occurs bound by λ in (λy.Q). The resultant predicate (λx.Q(x)) is a monadic predicate capable of taking a term t as argument as in (λx.Q(x))(t), which says that the object denoted by 't' has the property of being such that Q. The ''law of abstraction'' states ( λx.Q(x) )(t) ≡ Q(t/x) where Q(t/x) is the result of replacing all free occurrences of x in Q by t. This law is shown to fail in general in at least two cases: (i) when t is irreferential and (ii) when Q contains modal operators. In modal logic the "''de re'' / ''de dicto'' distinction" is stated as 1. (DE DICTO): 2. (DE RE): . In (1) the modal operator applies to the formula A(t) and the term t is within the scope of the modal operator. In (2) t is ''not'' within the scope of the modal operator. ==References== For the semantics and further philosophical developments of predicate abstraction see Fitting and Mendelsohn, ''First-order Modal Logic'', Springer, 1999. 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「Predicate abstraction」の詳細全文を読む スポンサード リンク
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