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Animated Logical Graphs • 22

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The step of controlled reflection we just took can be repeated at will, as suggested by the following series of forms:

Reflective Series (a) to (a, b, c, d)

Written inline, we have the series {}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime}, {}^{\backprime\backprime} \texttt{(} a \texttt{,} b \texttt{)} {}^{\prime\prime}, {}^{\backprime\backprime} \texttt{(} a \texttt{,} b \texttt{,} c \texttt{)} {}^{\prime\prime}, {}^{\backprime\backprime} \texttt{(} a \texttt{,} b \texttt{,} c \texttt{,} d \texttt{)} {}^{\prime\prime}, and so on, whose general form is {}^{\backprime\backprime} \texttt{(} x_1 \texttt{,} x_2 \texttt{,} \ldots \texttt{,} x_k \texttt{)} {}^{\prime\prime}.  With this move we have passed beyond the graph-theoretical form of rooted trees to what graph theorists know as rooted cacti.

I will discuss this cactus language and its logical interpretations next.

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics


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