SUO: Re: An idea for making progress
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Jim, I correct some typos, continue, and focus my last comment.
JA: I agree with Bob. I do not think that we should have
any more voting, except to admit additional documents
to preliminary consideration, for another year or so.
Scientific and technical issues are simply not best
decided that way. Nor will it do anything in support
of your recent remarks about achieving consensus, since
all of our voting periods have been extremely divisive,
putting the contributors of documents in a defensive,
if not evasive position, instead of encouraging them
to seek out the advice and critique that they need.
JA: The ongoing discussions and debates of this membership have
been positively full of "serious comments on what members
want to see incorporated in the document[s]", and though
I know that you did not mean it that way, it is perhaps
a little insulting to the membership to suggest that
comments are not "serious" unless they are directed
toward an active ballot.
JA: My present comment is this. My consistent, long-standing,
and very serious suggestion as to what should be incorporated
in the prospective SUO, at least, any component or module of it
that is intended in support of critical, educational, engineering,
research, and scientific applications, is that it absolutely must
incorporate, in a usable manner, the content of basic undergraduate
knowledge, hopefully extendible in the direction of graduate expertise,
in all of the relevant subject matters and methods. I am taking it on
faith, but only provisionally, that IFF has staked out a big enough tent
for this, and John Sowa has told us that this was an initial intention of
Doug Lenat in the Cyc project. But it will take an order of work far more
"serious" than the mere casting of ballots in order to accomplish these very
worthwhile goals.
JA: In particular, there are several miles of stratosphere, and not a little
vacuum of space, between where we stand and the exalted heights of IFF.
And though I would not for a moment wish to block anybody's view of
this nor any other of the beautiful blue skies that are constantly
being gesticulated at over our heads, I am a building up from
the earth sort of worker, and there is much to do within my
demesne in humble support of all these grand mansions and
greater visions. So I will now get back to work on that.
I've been making the motto of my contributions to this working group
for the last month or so to be "keep it concrete and simple" (KICAS).
In that spirit, let me focus the thrust of my comment on a single
very critical point. It's a single point, but it goes under two
names: "logical equivalence" and "mathematical isomorphism".
The beginning of wisdom in mathematics and computer science
turns on being able to recognize when people who appear to
be talking about very different-looking things are really
talking about the exact same thing. That ought to sound
familiar. This idea is crucial to category theory, one
of the recognized cornerstones of which is the paper by
Eilenberg & Mac Lane on the "General Theory of Natural
Equivalences" (GTONE) from 1945, and RK has recently
and rightly stressed its place in the IFF approach.
These ancient names of equivalence and isomorphism --
much like rabbits there's no such thing as just 2 --
are about to multiply their names beyond all hope
of recapture now that the hutches of the webfloks
have latched onto them, but they have amounted
to the first stepping stones of logical and
mathematical maturity for a long time now.
That is not the KICAS part, but I'm getting to it now.
A humble instance of the concept of isomorphism shows up in
the basic distinction between "graphs" and "labeled graphs",
where graph theorists generally use the unadorned term for
their default concept, namely, the abstract graph, or the
graph defined only "up to isomorphisms", as they say.
This distinction is a first element of the minimal curriculum,
usually taken up just after midterms of the typical undergrad
course in combinatorics or discrete math, and refreshed right
after drops-&-adds of the typical grad course in graph theory.
I have looked with some diligence through the SUMO document,
and a little more half-heartedly through the OpenCyc text,
for any hint that they recognize the distinction between
graphs and labelled graphs, under any of its commonly
used aliases. And I can find no expression of this
basic bit of knowledge in these "knowledge bases".
Now, it's certainly conceivable to me that the
needle is there in some hayestack of disguise
or another, so I will just ask:
Can any of the champions or familiars of these two systems,
OpenCyc and SUMO, point me to where the fundamental distinction
between graphs and labeled graphs is encrypted in their documents,
so that I might examine its cogency with respect to the established
standards in graph theory?
Thanks In Prospect,
Jon Awbrey
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