SUO: Graph Theory and ontology
All,
Just got back and began to filter my e-mail box. In the process I found the
response of Jon Awbrey to Adam Apease' raised question "need graph-theoretic
notions to support codifying concepts rivers, plumbing, roads and traffic,
electrical systems etc."
I wonder if we could take this thought of a Graph Theory a little bit
further towards the SUO as a whole.
Ontology maps very well in to the concept of graphs. For example a single
term can be a node, and an axiomatic relationship can represent an
edge/branch. The next question is whether we can cluster nodes and edges to
form conceptual paths. (I would like to thank John Sowa who's work on
Conceptual Nets stimulated my thoughts on this matter a while ago)
The ontology can become an enormously large corpus of "data". The
navigation/search for relationships, within this huge body, perhaps can be
simplified by applying Graph Theory based algorithms.
Enjoy the holidays.
Edward
Tel: (732) 427-4122 DSN 987-4122
Fax (732) 427-3440
E-Mail edward.dawidowicz@mail1.monmouth.army.mil
-----Original Message-----
From: Jon Awbrey [mailto:jawbrey@oakland.edu]
Sent: Monday, December 18, 2000 1:01 PM
To: Stand Up Ontology
Cc: John F Sowa; Douglas McDavid; Adam Pease
Subject: SUO: Graph Theory
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Earlier I wrote:
>
> Adam Pease wrote:
> >
> > Douglas,
> >
> > You make a good point about needing general concepts in the SUO.
> > While river source might be a little too specific, we certainly
> > need graph-theoretic notions to support codifying concepts like
> > rivers, plumbing, roads and traffic, electrical systems etc.
> >
> > Would anyone be willing to make a start on this area?
> > We need fleshed out concepts like
> >
> > node
> > path
> > juncture
> > flow
> > source
> > sink
> > rate
> > etc
> >
> > Adam
>
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>
> Adam,
>
> I will try to be con-tributary to this,
> so long as you understand that there
> are stylistic variations even here,
> between the four coasts of the US,
> especially.
>
> I hale from what is called "The MiGhTy School"
> of "Midwestern Graph Theory", and will try to
> represent their "way of thinking about graphs" (WOTAG)
> as faithfully as I can muster the Mistic Memories to do so.
>
> Will now go, post haste,
> to look for some dusty
> old books in my nooks --
> When I say "post haste",
> I mean "after the hurry is
> hurried, sung, and danced"!
>
> Cheers,
>
> Jon
>
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Graph Theory SIG,
Just by way of a rudimental bibliography, here are what I,
in my book, yet to be writ, consider to be three classics:
Elementary Graph Theory:
| Frank Harary,
| 'Graph Theory', Addison-Wesley, Reading, MA, 1969.
Enumerative Graph Theory:
| Frank Harary & Edgar M. Palmer,
| 'Graphical Enumeration', Academic Press, New York, NY, 1973.
Asymptotic Graph Theory:
| Edgar M. Palmer,
| 'Graphical Evolution: An Introduction to the Theory of Random Graphs',
| John Wiley & Sons, New York, NY, 1985.
Do not worry too much about the dates --
things do not move all that fast in mathematics --
anyway, I believe that I referred to them as "classics" ...
More, Later,
Jon Awbrey
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