Talk:Logical graph - Revision history

Jon Awbrey: /* Tables */ back to ordinary parentheses for function notation

2008-12-14T12:46:22Z

Tables: back to ordinary parentheses for function notation

Jon Awbrey: /* Functional Quantifiers */ sub concrete domain X for abstract domain B^2 to prevent possible confusion

2008-12-14T12:32:43Z

Functional Quantifiers: sub concrete domain X for abstract domain B^2 to prevent possible confusion

Jon Awbrey: /* Table 5 */ typo

2008-12-13T21:03:56Z

Table 5: typo

Jon Awbrey: /* Table 2 */ typo

2008-12-13T21:00:42Z

Table 2: typo

Jon Awbrey: /* Tables */ sub [0/1]

2008-12-13T04:06:00Z

Tables: sub [0/1]

Jon Awbrey: /* Tables */ tables a la escher

2008-12-13T03:28:19Z

Tables: tables a la escher

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Jon Awbrey: /* Tables */ redo beta table

2008-12-12T22:18:15Z

Tables: redo beta table

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Jon Awbrey: /* Tables */ redo alpha table as fractal checkerboard

2008-12-12T21:40:15Z

Tables: redo alpha table as fractal checkerboard

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Jon Awbrey: /* Functional Quantifiers */ + table of simple qualifiers with props arranged by group orbits

2008-12-12T19:24:55Z

Functional Quantifiers: + table of simple qualifiers with props arranged by group orbits

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Jon Awbrey: /* Functional Quantifiers */ blanks for zeroes

2008-12-12T18:56:18Z

Functional Quantifiers: blanks for zeroes

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@@ Line 452: / Line 452: @@
 {| align="center" cellpadding="8"
-| <math>\alpha_i f = \Upsilon \langle f_i, f \rangle = \Upsilon \langle f_i \Rightarrow f \rangle,</math>
+| <math>\alpha_i f = \Upsilon (f_i, f) = \Upsilon (f_i \Rightarrow f),</math>
 |-
-| <math>\beta_i f = \Upsilon \langle f, f_i \rangle = \Upsilon \langle f \Rightarrow f_i \rangle.</math>
+| <math>\beta_i f = \Upsilon (f, f_i) = \Upsilon (f \Rightarrow f_i).</math>
 |}
@@ Line 462: / Line 462: @@
 {| align="center" border="1" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
-|+ '''Table 1.  Qualifiers of Implication Ordering:&nbsp; <math>\alpha_i f = \Upsilon \langle f_i, f \rangle = \Upsilon \langle f_i \Rightarrow f \rangle</math>'''
+|+ '''Table 1.  Qualifiers of Implication Ordering:&nbsp; <math>\alpha_i f = \Upsilon (f_i, f) = \Upsilon (f_i \Rightarrow f)</math>'''
 |- style="background:ghostwhite"
 | align="right" | <math>u:</math><br><math>v:</math>
@@ Line 810: / Line 810: @@
 {| align="center" border="1" cellpadding="1" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
-|+ '''Table 2.  Qualifiers of Implication Ordering:&nbsp; <math>\beta_i f = \Upsilon \langle f, f_i \rangle = \Upsilon \langle f \Rightarrow f_i \rangle</math>'''
+|+ '''Table 2.  Qualifiers of Implication Ordering:&nbsp; <math>\beta_i f = \Upsilon (f, f_i) = \Upsilon (f \Rightarrow f_i)</math>'''
 |- style="background:ghostwhite"
 | align="right" | <math>u:</math><br><math>v:</math>

@@ Line 429: / Line 429: @@
 ==Functional Quantifiers==
-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:
 {| 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>
 |}
-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:
 {| 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>
 |}

@@ Line 1,638: / Line 1,638: @@
 | <math>\text{Some}\ u\ \text{is}\ v</math>
 | &nbsp;
-| <math>\text{Some}\ u\ \text{is}\ y</math>
+| <math>\text{Some}\ u\ \text{is}\ v</math>
 | <math>\ell_{11}\!</math>
 |}<br>

@@ Line 1,114: / Line 1,114: @@
 | <math>f_{14}</math>
 | 1110
-| <math>((u)(y))\!</math>
+| <math>((u)(v))\!</math>
 | style="background:white; color:black" | 0
 | style="background:white; color:black" | 0

@@ Line 446: / Line 446: @@
 {| align="center" cellpadding="8"
-| <math>\alpha_i, \beta_i : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}, i = 1 \ldots 15,</math>
+| <math>\alpha_i, \beta_i : (\mathbb{B}^2 \to \mathbb{B}) \to \mathbb{B}, i = 0 \ldots 15,</math>
 |}