Re: SUO: RE: The Plumbing Theorem(s)
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