MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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, 19:52, 11 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> is a higher order proposition that holds for the constant proposition <math>1 : \mathbb{B}^2 \to \mathbb{B}</math> and fails for the rest. | + | The ''umpire measure'' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}</math> assigns the constant proposition <math>1 : \mathbb{B}^2 \to \mathbb{B}</math> a value of 1 and everything else of that type a value of 0. Expressed in symbolic form: |
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− | : <math>\Upsilon p = 1 \quad \Leftrightarrow \quad p = 1.</math>
| + | {| align="center" cellpadding="8" |
| + | | <math>\Upsilon p = 1 \quad \Leftrightarrow \quad p = 1.</math> |
| + | |} |
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− | The '''umpire operator''' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B})^2 \to \mathbb{B}</math> is a higher order proposition that holds for ordered pairs of propositions in which the first implies the second and fails for the rest. | + | The ''umpire operator'' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B})^2 \to \mathbb{B}</math> assigns ordered pairs of propositions in which the first implies the second a value of 1 and everything else of that type a value of 0. Expressed in symbolic form: |
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− | : <math>\Upsilon \langle p, q \rangle = 1 \quad \Leftrightarrow \quad p \Rightarrow q.</math>
| + | {| align="center" cellpadding="8" |
| + | | <math>\Upsilon \langle p, q \rangle = 1 \quad \Leftrightarrow \quad p \Rightarrow q.</math> |
| + | |} |
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| ===Tables=== | | ===Tables=== |