MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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, 13:32, 12 December 2008
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| ==Functional Quantifiers== | | ==Functional Quantifiers== |
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− | The '''umpire measure''' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}</math> takes a proposition of type <math>\mathbb{B}^2 \to \mathbb{B}</math> as argument, giving the constant proposition <math>1 : \mathbb{B}^2 \to \mathbb{B}</math> a value of 1 and every other proposition a value of 0. Expressed in symbolic form: | + | The '''umpire measure''' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}</math> links the constant proposition <math>1 : \mathbb{B}^2 \to \mathbb{B}</math> to a value of 1 and every other proposition to a value of 0. Expressed in symbolic form: |
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| {| align="center" cellpadding="8" | | {| align="center" cellpadding="8" |
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− | The '''umpire operator''' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B})^2 \to \mathbb{B}</math> takes two propositions of type <math>\mathbb{B}^2 \to \mathbb{B}</math> as arguments, giving pairs of propositions in which the first implies the second a value of 1 and every other pair a value of 0. Expressed in symbolic form: | + | The '''umpire operator''' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B})^2 \to \mathbb{B}</math> links pairs of propositions in which the first implies the second to a value of 1 and every other pair to a value of 0. Expressed in symbolic form: |
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| {| align="center" cellpadding="8" | | {| align="center" cellpadding="8" |