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

Revision as of 02:22, 30 May 2008

3,744 bytes added ,  02:22, 30 May 2008
→‎Work Area 1: add table variant
Line 2,724: Line 2,724:  
By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions in a number of different languages for zeroth order logic.
 
By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions in a number of different languages for zeroth order logic.
   −
===Table 1===
+
===Table 1 : Variant 1===
    
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
Line 2,861: Line 2,861:  
| <math>\operatorname{true}</math>
 
| <math>\operatorname{true}</math>
 
| <math>1\!</math>
 
| <math>1\!</math>
 +
|}
 +
<br>
 +
 +
===Table 1 : Variant 2===
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 +
|+ '''Table 2.  Propositional Forms on Two Variables'''
 +
|- style="background:ghostwhite"
 +
| <math>\mathcal{L}_1</math>
 +
| <math>\mathcal{L}_2</math>
 +
| <math>\mathcal{L}_3</math>
 +
| <math>\mathcal{L}_4</math>
 +
| <math>\mathcal{L}_5</math>
 +
| <math>\mathcal{L}_6</math>
 +
|-
 +
|
 +
{| align="center" style="background:ghostwhite"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|
 +
{| align="right" style="background:ghostwhite; text-align:right"
 +
| <math>x\!</math> :
 +
|-
 +
| <math>y\!</math> :
 +
|}
 +
|
 +
{| align="center" style="background:ghostwhite"
 +
| 1 1 0 0
 +
|-
 +
| 1 0 1 0
 +
|}
 +
|
 +
{| align="center" style="background:ghostwhite"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|
 +
{| align="center" style="background:ghostwhite"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|
 +
{| align="center" style="background:ghostwhite"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|-
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>f_{0}\!</math>
 +
|-
 +
| <math>f_{1}\!</math>
 +
|-
 +
| <math>f_{2}\!</math>
 +
|-
 +
| <math>f_{3}\!</math>
 +
|-
 +
| <math>f_{4}\!</math>
 +
|-
 +
| <math>f_{5}\!</math>
 +
|-
 +
| <math>f_{6}\!</math>
 +
|-
 +
| <math>f_{7}\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>f_{0000}\!</math>
 +
|-
 +
| <math>f_{0001}\!</math>
 +
|-
 +
| <math>f_{0010}\!</math>
 +
|-
 +
| <math>f_{0011}\!</math>
 +
|-
 +
| <math>f_{0100}\!</math>
 +
|-
 +
| <math>f_{0101}\!</math>
 +
|-
 +
| <math>f_{0110}\!</math>
 +
|-
 +
| <math>f_{0111}\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| 0 0 0 0
 +
|-
 +
| 0 0 0 1
 +
|-
 +
| 0 0 1 0
 +
|-
 +
| 0 0 1 1
 +
|-
 +
| 0 1 0 0
 +
|-
 +
| 0 1 0 1
 +
|-
 +
| 0 1 1 0
 +
|-
 +
| 0 1 1 1
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>(~)\!</math>
 +
|-
 +
| <math>(x)(y)\!</math>
 +
|-
 +
| <math>(x)\ y\!</math>
 +
|-
 +
| <math>(x)\!</math>
 +
|-
 +
| <math>x\ (y)\!</math>
 +
|-
 +
| <math>(y)\!</math>
 +
|-
 +
| <math>(x,\ y)\!</math>
 +
|-
 +
| <math>(x\ y)\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
|
 +
|-
 +
|
 +
|-
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|
 +
|-
 +
|
 +
|-
 +
|
 +
|-
 +
|
 +
|-
 +
|
 +
|-
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|
 +
|}
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|
 +
{| align="left" cellpadding="2" style="text-align:left"
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
 +
|-
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|
 +
|}
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|-
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|
 +
{| align="center" cellpadding="2"
 +
| <math>f_{8}\!</math>
 +
|-
 +
| <math>f_{9}\!</math>
 +
|-
 +
| <math>f_{10}\!</math>
 +
|-
 +
| <math>f_{11}\!</math>
 +
|-
 +
| <math>f_{12}\!</math>
 +
|-
 +
| <math>f_{13}\!</math>
 +
|-
 +
| <math>f_{14}\!</math>
 +
|-
 +
| <math>f_{15}\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>f_{1000}\!</math>
 +
|-
 +
| <math>f_{1001}\!</math>
 +
|-
 +
| <math>f_{1010}\!</math>
 +
|-
 +
| <math>f_{1011}\!</math>
 +
|-
 +
| <math>f_{1100}\!</math>
 +
|-
 +
| <math>f_{1101}\!</math>
 +
|-
 +
| <math>f_{1110}\!</math>
 +
|-
 +
| <math>f_{1111}\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| 1 0 0 0
 +
|-
 +
| 1 0 0 1
 +
|-
 +
| 1 0 1 0
 +
|-
 +
| 1 0 1 1
 +
|-
 +
| 1 1 0 0
 +
|-
 +
| 1 1 0 1
 +
|-
 +
| 1 1 1 0
 +
|-
 +
| 1 1 1 1
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>x\ y\!</math>
 +
|-
 +
| <math>((x,\ y))\!</math>
 +
|-
 +
| <math>y\!</math>
 +
|-
 +
| <math>(x\ (y))\!</math>
 +
|-
 +
| <math>x\!</math>
 +
|-
 +
| <math>((x)\ y)\!</math>
 +
|-
 +
| <math>((x)(y))\!</math>
 +
|-
 +
| <math>((~))\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|}
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|
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{| align="left" cellpadding="2" style="text-align:left"
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|-
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|
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|}
 
|}
 
|}
 
<br>
 
<br>
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| <math>\mathcal{L}_4</math>
 
| <math>\mathcal{L}_4</math>
 
| <math>\mathcal{L}_5</math>
 
| <math>\mathcal{L}_5</math>
 +
| <math>\mathcal{L}_6</math>
 
|-
 
|-
 +
|
 +
{| align="center" style="background:ghostwhite"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 
|
 
|
 
{| align="right" style="background:ghostwhite; text-align:right"
 
{| align="right" style="background:ghostwhite; text-align:right"
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|-
 
|-
 
| <math>f_{7}\!</math>
 
| <math>f_{7}\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>f_{0000}\!</math>
 +
|-
 +
| <math>f_{0001}\!</math>
 +
|-
 +
| <math>f_{0010}\!</math>
 +
|-
 +
| <math>f_{0011}\!</math>
 +
|-
 +
| <math>f_{0100}\!</math>
 +
|-
 +
| <math>f_{0101}\!</math>
 +
|-
 +
| <math>f_{0110}\!</math>
 +
|-
 +
| <math>f_{0111}\!</math>
 
|}
 
|}
 
|
 
|
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|-
 
|-
 
| <math>f_{15}\!</math>
 
| <math>f_{15}\!</math>
 +
|}
 +
|
 +
{| align="center" cellpadding="2"
 +
| <math>f_{1000}\!</math>
 +
|-
 +
| <math>f_{1001}\!</math>
 +
|-
 +
| <math>f_{1010}\!</math>
 +
|-
 +
| <math>f_{1011}\!</math>
 +
|-
 +
| <math>f_{1100}\!</math>
 +
|-
 +
| <math>f_{1101}\!</math>
 +
|-
 +
| <math>f_{1110}\!</math>
 +
|-
 +
| <math>f_{1111}\!</math>
 
|}
 
|}
 
|
 
|
Jon Awbrey
12,080

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