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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 03:20, 19 June 2007
, 03:20, 19 June 2007→Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>: wiki table
The component notation ''F'' = ‹''F''<sub>1</sub>, ''F''<sub>2</sub>› = ‹''f'', ''g''› : ''U''<sup> •</sup> → ''X''<sup> •</sup> allows us to give a name and a type to this transformation, and permits us to define it by means of the compact description that follows:
The component notation ''F'' = ‹''F''<sub>1</sub>, ''F''<sub>2</sub>› = ‹''f'', ''g''› : ''U''<sup> •</sup> → ''X''<sup> •</sup> allows us to give a name and a type to this transformation, and permits us to define it by means of the compact description that follows:
<pre>
<br><font face="courier new">
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
| |
|
| <x, y> = F<u, v> = <((u)(v)), ((u, v))> |
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| |
| ‹''x'', ''y''›
| =
</pre>
| ''F''‹''u'', ''v''›
| =
| ‹((''u'')(''v'')), ((''u'', ''v''))›
|}
|}
</font><br>
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.