MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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, 12:32, 14 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> 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: | + | The '''umpire measure''' of type <math>\Upsilon : (X \to \mathbb{B}) \to \mathbb{B}</math> links the constant proposition <math>1 : X \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" |
− | | <math>\Upsilon \langle u \rangle = 1_\mathbb{B} \quad \Leftrightarrow \quad u = 1_{\mathbb{B}^2 \to \mathbb{B}}.</math> | + | | <math>\Upsilon (u) = 1_\mathbb{B} \quad \Leftrightarrow \quad u = 1_{X \to \mathbb{B}}.</math> |
| |} | | |} |
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− | 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: | + | The '''umpire operator''' of type <math>\Upsilon : (X \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" |
− | | <math>\Upsilon \langle u, v \rangle = 1 \quad \Leftrightarrow \quad u \Rightarrow v.</math> | + | | <math>\Upsilon (u, v) = 1 \quad \Leftrightarrow \quad u \Rightarrow v.</math> |
| |} | | |} |
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