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Directory:Jon Awbrey/Papers/Dynamics And Logic (view source)
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<pre>
The ''differential variables'' <math>\operatorname{d}x_j</math> are boolean variables of the same basic type as the ordinary variables <math>x_j.\!</math> It is conventional to distinguish the (first order) differential variables with the operative prefix "<math>\operatorname{d}</math>", but this is purely optional. It is their existence in particular relations to the initial variables, not their names, that defines them as differential variables.
It is conventional to give the additional variables these inflected
In the case of the conjunction f<p, q> = pq,
In the example of logical conjunction, <math>f(p, q) = pq,\!</math> the enlargement <math>\operatorname{E}f</math> is formulated as follows:
the enlargement Ef is formulated as follows:
{| align="center" cellpadding="6" width="90%"
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<math>\begin{array}{l}
\operatorname{E}f(p, q, \operatorname{d}p, \operatorname{d}q)
\\[6pt]
= \quad (p + \operatorname{d}p)(q + \operatorname{d}q)
\\[6pt]
= \quad \texttt{(} p, \operatorname{d}p \texttt{)(} q, \operatorname{d}q \texttt{)}
\end{array}</math>
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<pre>
Given that this expression uses nothing more than the "boolean ring"
Given that this expression uses nothing more than the "boolean ring"
operations of addition (+) and multiplication (*), it is permissible
operations of addition (+) and multiplication (*), it is permissible