In logic, predicate abstraction is the result of creating a predicate from an open sentence. If Q(x) is any formula with x free then the predicate formed from that sentence is (λx. Q), where λ is an abstraction operator. The resultant predicate (λx. Q) is a monadic predicate capable of taking a term t as argument as in (λx. Q)(t), which says that the object denoted by 't' has the property of being such that Q. The law of abstraction states (λy.

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  • In logic, predicate abstraction is the result of creating a predicate from an open sentence. If Q(x) is any formula with x free then the predicate formed from that sentence is (λx. Q), where λ is an abstraction operator. The resultant predicate (λx. Q) is a monadic predicate capable of taking a term t as argument as in (λx. Q)(t), which says that the object denoted by 't' has the property of being such that Q. The law of abstraction states (λy. Q)(t) ≡ Q(t/x) where Q(t/x) is the result of replacing all free occurrences of t in Q by x. 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): <math>\Box A(t)</math> 2. (DE RE): <math>(\lambda x. \Box A)(t)</math>. 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.
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  • In logic, predicate abstraction is the result of creating a predicate from an open sentence. If Q(x) is any formula with x free then the predicate formed from that sentence is (λx. Q), where λ is an abstraction operator. The resultant predicate (λx. Q) is a monadic predicate capable of taking a term t as argument as in (λx. Q)(t), which says that the object denoted by 't' has the property of being such that Q. The law of abstraction states (λy.
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  • Predicate abstraction
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