Changes

==Functional Quantifiers==

==Functional Quantifiers==

The ''umpire measure'' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}</math> evaluates propositions of type <math>\mathbb{B}^2 \to \mathbb{B},</math> assigning the constant proposition <math>1 : \mathbb{B}^2 \to \mathbb{B}</math> a value of 1 and everything else 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> 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 everything else a value of 0.  Expressed in symbolic form:

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The ''umpire operator'' of type <math>\Upsilon : (\mathbb{B}^2 \to \mathbb{B})^2 \to \mathbb{B}</math> evaluates ordered pairs of propositions of type <math>\mathbb{B}^2 \to \mathbb{B},</math> assigning pairs of propositions in which the first implies the second a value of 1 and everything else 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> takes two propositions of type <math>\mathbb{B}^2 \to \mathbb{B}</math> as arguments, giving pairs in which the first implies the second a value of 1 and everything else a value of 0.  Expressed in symbolic form:

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