SUO: Re: Graphs and Labelled Graphs
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Matthew,
In view of recent discussions, I think that it would be worth
the time to go a little further beyond your 1 or 2 paragraph
target length for this subject. You will, of course, recall
the exceeding care and the exceeding number of paragraphs
that I took to bracket this extremely simple example of
the distinction between graphs and labelled graphs in
such a way that its larger points would not fall
under the ban of the sorts of distraction that
we have in this forum come to know so well.
Just by way of reminder, then, here is the
generalization hierarchy for the topic:
o Standard Topics Of Knowledge In Research Support Ontologies (STOKIRSO)
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o Isomorphisms and Isomorphism Classes
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o Graphs and Labeled Graphs
The question of highest significance for the soundness of the SUO effort
is whether the prospective SUO will find some way to provide support for
the standard concepts that are already in use in significant portions of
the various research, scholarly, scientific, and technical disciplines.
Under that heading I choose the concept of isomorphism and the related
concept of mathematical objects that are isormorphism classes of other
mathematical objects as an especially poignant one, especially in view
of its constant deployment in IFF and in category theory more broadly.
Under that heading I choose what amounts to one of the most concrete,
discrete, graphic, intuitive, and just plan simple instances on that
general theme, namely, the so-called "representation" of (abstract)
graphs as isomorphism classes of so-called "labelled graphs".
So, with that bit of re-orientation -- and now that all of our
roses are planted -- just the laying out of the weed barrier
and the spreading of the cypress mulch, maybe next week,
and our garden is done for the summer -- I will return
to the expo in progress.
Jon Awbrey
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