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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)

Revision as of 02:05, 29 May 2008

2,722 bytes added ,  02:05, 29 May 2008
→‎Work Area 3: add orbit-partitioned table
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| true
 
| true
 
| <math>1\!</math>
 
| <math>1\!</math>
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|}<br>
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{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
 +
|+ '''Table 1.  Propositional Forms on Two Variables'''
 +
|- style="background:paleturquoise"
 +
| &nbsp;
 +
| align="right" | <math>x\!</math> :
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| 1 1 0 0
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| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
|- style="background:paleturquoise"
 +
| &nbsp;
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| align="right" | <math>y\!</math> :
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| 1 0 1 0
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
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|-
 +
| f<sub>0</sub>
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| g<sub>0</sub>
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| 0 0 0 0
 +
| (&nbsp;)
 +
| False
 +
| 0
 +
|-
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
&nbsp;<br>
 +
&nbsp;<br>
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&nbsp;<br>
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&nbsp;
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
g<sub>1</sub><br>
 +
g<sub>2</sub><br>
 +
g<sub>4</sub><br>
 +
g<sub>8</sub>
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
0 0 0 1<br>
 +
0 0 1 0<br>
 +
0 1 0 0<br>
 +
1 0 0 0
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
(x)(y)<br>
 +
(x) y <br>
 +
x (y)<br>
 +
x y
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
Neither x nor y<br>
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Not x but y<br>
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x but not y<br>
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x and y
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|}
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|
 +
{| style="background:lightcyan"
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|
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&not;x &and; &not;y<br>
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&not;x &and; y<br>
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x &and; &not;y<br>
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x &and; y
 +
|}
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|-
 +
|
 +
{| style="background:lightcyan"
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|
 +
f<sub>1</sub><br>
 +
f<sub>2</sub>
 +
|}
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|
 +
{| style="background:lightcyan"
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|
 +
g<sub>3</sub><br>
 +
g<sub>12</sub>
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|}
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|
 +
{| style="background:lightcyan"
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|
 +
0 0 1 1<br>
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1 1 0 0
 +
|}
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|
 +
{| style="background:lightcyan"
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|
 +
(x)<br>
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x
 +
|}
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|
 +
{| style="background:lightcyan"
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|
 +
Not x<br>
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x
 +
|}
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|
 +
{| style="background:lightcyan"
 +
|
 +
&not;x<br>
 +
x
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|}
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|-
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|
 +
{| style="background:lightcyan"
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|
 +
&nbsp;<br>
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&nbsp;
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|}
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|
 +
{| style="background:lightcyan"
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|
 +
g<sub>6</sub><br>
 +
g<sub>9</sub>
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|}
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|
 +
{| style="background:lightcyan"
 +
|
 +
0 1 1 0<br>
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1 0 0 1
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
(x, y)<br>
 +
((x, y))
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|}
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|
 +
{| style="background:lightcyan"
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|
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x not equal to y<br>
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x equal to y
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|}
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|
 +
{| style="background:lightcyan"
 +
|
 +
x &ne; y<br>
 +
x = y
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|}
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|-
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
&nbsp;<br>
 +
&nbsp;
 +
|}
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|
 +
{| style="background:lightcyan"
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|
 +
g<sub>5</sub><br>
 +
g<sub>10</sub>
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
0 1 0 1<br>
 +
1 0 1 0
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
(y)<br>
 +
y
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
Not y<br>
 +
y
 +
|}
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|
 +
{| style="background:lightcyan"
 +
|
 +
&not;y<br>
 +
y
 +
|}
 +
|-
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
&nbsp;<br>
 +
&nbsp;<br>
 +
&nbsp;<br>
 +
&nbsp;
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
g<sub>7</sub><br>
 +
g<sub>11</sub><br>
 +
g<sub>13</sub><br>
 +
g<sub>14</sub>
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
0 1 1 1<br>
 +
1 0 1 1<br>
 +
1 1 0 1<br>
 +
1 1 1 0
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
(x y)<br>
 +
(x (y))<br>
 +
((x) y)<br>
 +
((x)(y))
 +
|}
 +
|
 +
{| style="background:lightcyan"
 +
|
 +
Not both x and y<br>
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Not x without y<br>
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Not y without x<br>
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x or y
 +
|}
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|
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{| style="background:lightcyan"
 +
|
 +
&not;x &or; &not;y<br>
 +
x &rarr; y<br>
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x &larr; y<br>
 +
x &or; y
 +
|}
 +
|-
 +
| f<sub>3</sub>
 +
| g<sub>15</sub>
 +
| 1 1 1 1
 +
| ((&nbsp;))
 +
| True
 +
| 1
 
|}<br>
 
|}<br>
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o------o------------o------------o------------o------------o------------o
 
o------o------------o------------o------------o------------o------------o
 
</pre>
 
</pre>
−
  −
If the medium truly is the message, the blank slate is the innate idea.
      
==Table 14.  Differential Propositions==
 
==Table 14.  Differential Propositions==
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|- style="background:paleturquoise"
 
|- style="background:paleturquoise"
 
| &nbsp;
 
| &nbsp;
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| align="right" | A :
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| align="right" | <math>x\!</math> :
 
| 1 1 0 0  
 
| 1 1 0 0  
 
| &nbsp;
 
| &nbsp;
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| True
 
| True
 
| 1
 
| 1
−
|}
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|}<br>
−
<br>
 
Jon Awbrey
12,154

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