RE: SUO: RE: The Plumbing Theorem(s)
Dear John,
> Dear Matthew,
>
> I was trying to state the plumbing theorems in a way that was
> independent of any choice of representation. I never said which
> if any of the physical objects corresponded to any elements of
> KIF, conceptual graphs, or any other notation. I used the
> terms "dyads", "triads", "tetrads",... as names for connectors
> that have 2 holes, 3 holes, 4 holes, respectively. I did not
> say whether any of those pipes or connectors should be called
> "relations", "concepts", "entities", "variables", or whatever.
>
> If you want to use that story as a metaphor for any kn. rep.
> language, you can choose to map the physical objects in my
> story or your further elaboration in many different ways
> to many different kinds of notation. But the point I was
> making is that the plumbing theorems hold, no matter what you
> call the connections or how you map them to any notation:
>
> 1. If you want to connect one source to one sink, you can
> do so without using anything more complex than pipes with
> at most dyadic connections to other pipes.
>
> 2. But if you want to connect one source to multiple sinks,
> you must have some connections that involve more than two
> pipes.
>
> 3. It is possible to connect one source to any number of
> sinks by a collection of pipes and connections, in which
> no connection involves more than 3 separate pipes.
>
> You can relabel or rename the physical objects in any way
> you like, but those theorems will always be true.
>
> John
>
MW: Ah, then you were illustrating the graph theory results.
I misunderstood, my apologies.
MW: The graph theory stuff I have no problem with. It seems
to me to be a matter of what you map to nodes, and what you
map to edges. Most of our nodes would have a somewhat higher
number of connections than 3, with not great sense of any
need to reduce the number.
MW: On the other hand the analysis of the representation I
unwittingly put in your mouth stands, and the use of the
EPISTLE approach to representing that problem also stands.
Regards
Matthew
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Matthew West http://www.matthew-west.org.uk/
Principal Consultant Shell Visiting Professor
Operations & Asset Management The Keyworth Institute
Shell Services International The University of Leeds
http://www.shellservices.com/ http://www.keyworth.leeds.ac.uk/
H3229, Shell Centre, London, SE1 7NA, UK.
Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
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