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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 17:10, 11 November 2012
, 17:10, 11 November 2012→6.27. Differential Logic and Group Operations: format table
Relative to a setting of this kind, the rules of sequential inference are exemplified by the schematism shown in Table 41.
Relative to a setting of this kind, the rules of sequential inference are exemplified by the schematism shown in Table 41.
<pre>
<br>
Table 41. Schematism of Sequential Inference
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
|+ style="height:30px" |
<math>\text{Table 69.} ~~ \text{Schematism of Sequential Inference}\!</math>
|- style="height:40px; background:#f0f0ff"
| width="33%" | <math>\text{Initial Premiss}\!</math>
| width="33%" | <math>\text{Differential Premiss}\!</math>
</pre>
| width="33%" | <math>\text{Inferred Sequel}\!</math>
|-
| valign="bottom" |
<math>\begin{matrix}
~x~ ~\operatorname{at}~ t
\\[4pt]
~x~ ~\operatorname{at}~ t
\\[4pt]
(x) ~\operatorname{at}~ t
\\[4pt]
(x) ~\operatorname{at}~ t
\end{matrix}</math>
| valign="bottom" |
<math>\begin{matrix}
~\operatorname{d}x~ ~\operatorname{at}~ t
\\[4pt]
(\operatorname{d}x) ~\operatorname{at}~ t
\\[4pt]
~\operatorname{d}x~ ~\operatorname{at}~ t
\\[4pt]
(\operatorname{d}x) ~\operatorname{at}~ t
\end{matrix}</math>
| valign="bottom" |
<math>\begin{matrix}
(x) ~\operatorname{at}~ t'
\\[4pt]
~x~ ~\operatorname{at}~ t'
\\[4pt]
~x~ ~\operatorname{at}~ t'
\\[4pt]
(x) ~\operatorname{at}~ t'
\end{matrix}</math>
|}
<br>
It might be thought that a notion of real time <math>(t \in \mathbb{R})\!</math> is needed at this point to fund the account of sequential processes. From a logical point of view, however, I think it will be found that it is precisely out of such data that the notion of time has to be constructed.
It might be thought that a notion of real time <math>(t \in \mathbb{R})\!</math> is needed at this point to fund the account of sequential processes. From a logical point of view, however, I think it will be found that it is precisely out of such data that the notion of time has to be constructed.