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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 04:52, 4 July 2007
, 04:52, 4 July 2007→Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>: wiki table
The information that defines the logical transformation ''F'' can be represented in the form of a truth table, as in Table 60. To cut down on subscripts in this example I continue to use plain letter equivalents for all components of spaces and maps.
The information that defines the logical transformation ''F'' can be represented in the form of a truth table, as in Table 60. To cut down on subscripts in this example I continue to use plain letter equivalents for all components of spaces and maps.
<pre>
<font face="courier new">
Table 60. Propositional Transformation
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
|+ '''Table 60. Propositional Transformation'''
| u | v | f | g |
|- style="background:paleturquoise"
| width="25%" | ''u''
| | | | |
| width="25%" | ''v''
| 0 | 0 | 0 | 1 |
| width="25%" | ''f''
| | | | |
| width="25%" | ''g''
| 0 | 1 | 1 | 0 |
|-
| | | | |
| width="25%" |
| 1 | 0 | 1 | 0 |
{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| | | | |
| 0
| 1 | 1 | 1 | 1 |
|-
| | | | |
| 0
|-
| | | ((u)(v)) | ((u, v)) |
| 1
|-
</pre>
| 1
|}
| width="25%" |
{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| 0
|-
| 1
|-
| 0
|-
| 1
|}
| width="25%" |
{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| 0
|-
| 1
|-
| 1
|-
| 1
|}
| width="25%" |
{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| 1
|-
| 0
|-
| 0
|-
| 1
|}
|-
| width="25%" |
| width="25%" |
| width="25%" | ((''u'')(''v''))
| width="25%" | ((''u'', ''v''))
|}
</font><br>
Figure 61 shows how one might paint a picture of the logical transformation ''F'' on the canvass that was earlier primed for this purpose (way back in Figure 30).
Figure 61 shows how one might paint a picture of the logical transformation ''F'' on the canvass that was earlier primed for this purpose (way back in Figure 30).