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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 02:10, 31 May 2007
, 02:10, 31 May 2007→Thematization : Truth Tables: wiki tables
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{| align="center" border="1" cellpadding="0" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
|+ '''Table 28. Propositions on Two Variables'''
|+ Table 28. Propositions on Two Variables
|
|
{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
|- style="background:paleturquoise"
|- style="background:paleturquoise"
| u v ||
| u || v ||
|f<sub>0</sub>||f<sub>1</sub>||f<sub>2</sub>||f<sub>3</sub>
|f<sub>00</sub>||f<sub>01</sub>||f<sub>02</sub>||f<sub>03</sub>
|f<sub>4</sub>||f<sub>5</sub>||f<sub>6</sub>||f<sub>7</sub>
|f<sub>04</sub>||f<sub>05</sub>||f<sub>06</sub>||f<sub>07</sub>
|f<sub>8</sub>||f<sub>9</sub>||f<sub>10</sub>||f<sub>11</sub>
|f<sub>08</sub>||f<sub>09</sub>||f<sub>10</sub>||f<sub>11</sub>
|f<sub>12</sub>||f<sub>13</sub>||f<sub>14</sub>||f<sub>15</sub>
|f<sub>12</sub>||f<sub>13</sub>||f<sub>14</sub>||f<sub>15</sub>
|-
|-
| 0 0 || ||0||1||0||1||0||1||0||1||0||1||0||1||0||1||0||1
| 0 || 0 ||
|0||1||0||1||0||1||0||1||0||1||0||1||0||1||0||1
|-
|-
| 0 1 || ||0||0||1||1||0||0||1||1||0||0||1||1||0||0||1||1
| 0 || 1 ||
|0||0||1||1||0||0||1||1||0||0||1||1||0||0||1||1
|-
|-
| 1 0 || ||0||0||0||0||1||1||1||1||0||0||0||0||1||1||1||1
| 1 || 0 ||
|0||0||0||0||1||1||1||1||0||0||0||0||1||1||1||1
|-
|-
| 1 1 || ||0||0||0||0||0||0||0||0||1||1||1||1||1||1||1||1
| 1 || 1 ||
|0||0||0||0||0||0||0||0||1||1||1||1||1||1||1||1
|}
|}
|}
|}
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{| align="center" border="1" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
Table 29. Thematic Extensions of Bivariate Propositions
|+ Table 29. Thematic Extensions of Bivariate Propositions
|
| u v | f^¢ |!f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| | | 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 |
|- style="background:paleturquoise"
| u || v || f<sup>¢</sup>
| | | |
| φ<sub>00</sub> || φ<sub>01</sub>
| 0 0 | 0 | 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 |
| φ<sub>02</sub> || φ<sub>03</sub>
| | | |
| φ<sub>04</sub> || φ<sub>05</sub>
| 0 0 | 1 | 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 |
| φ<sub>06</sub> || φ<sub>07</sub>
| | | |
| φ<sub>08</sub> || φ<sub>09</sub>
| 0 1 | 0 | 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 |
| φ<sub>10</sub> || φ<sub>11</sub>
| | | |
| φ<sub>12</sub> || φ<sub>13</sub>
| 0 1 | 1 | 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 |
| φ<sub>14</sub> || φ<sub>15</sub>
| | | |
|-
| 1 0 | 0 | 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 |
| 0 || 0 || 0 ||1||0||1||0||1||0||1||0||1||0||1||0||1||0||1||0
| | | |
|-
| 1 0 | 1 | 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 |
| 0 || 0 || 1 ||0||1||0||1||0||1||0||1||0||1||0||1||0||1||0||1
| | | |
|-
| 1 1 | 0 | 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 |
| 0 || 1 || 0 ||1||1||0||0||1||1||0||0||1||1||0||0||1||1||0||0
| | | |
|-
| 1 1 | 1 | 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 |
| 0 || 1 || 1 ||0||0||1||1||0||0||1||1||0||0||1||1||0||0||1||1
| | | |
|-
| 1 || 0 || 0 ||1||1||1||1||0||0||0||0||1||1||1||1||0||0||0||0
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| 1 || 1 || 0 ||1||1||1||1||1||1||1||1||0||0||0||0||0||0||0||0
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| 1 || 1 || 1 ||0||0||0||0||0||0||0||0||1||1||1||1||1||1||1||1
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===Propositional Transformations===
===Propositional Transformations===