Changes

126 bytes added ,  19:52, 11 December 2008
→‎Functional Quantifiers: rephrase one more time for good measure
Line 429: Line 429:  
==Functional Quantifiers==
 
==Functional Quantifiers==
   −
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:
   −
: <math>\Upsilon p = 1 \quad \Leftrightarrow \quad p = 1.</math>
+
{| align="center" cellpadding="8"
 +
| <math>\Upsilon p = 1 \quad \Leftrightarrow \quad p = 1.</math>
 +
|}
   −
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:
   −
: <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>
 +
|}
    
===Tables===
 
===Tables===
12,080

edits