_Pure_ graphs have genuine email@example.com (Fritz Lehmann)
Date: Sat, 24 Sep 94 08:19:39 CDT
From: firstname.lastname@example.org (Fritz Lehmann)
To: email@example.com, firstname.lastname@example.org, email@example.com
Subject: _Pure_ graphs have genuine value
A recent private email exchange on time ontologies had
the following light digression (quoted with permission):
> Glad you see the light; notation should be beneath the
>notice of an ontologist (unless some iconic quality of the notation
>is being exploited)..
Glad I see the light!! Cheeky bastard! Ive been preaching this loudly since
Yeah but you keep lapsing, and grumbling about Sowa's
rebarbative graphs, semantic networks, "frames", etc.
What I grumble about is claims that any of these damn things have magic
semantic powers, or are a New Order of representational adequacy, or
I hazard that some of my reply could be of interest
to these lists:
Also, the "iconic" point is important, I think. Not
so much psychologically as formally. The problem is
when notational artifacts intrude on processing. A
bad example of this is the order imposed on inherently
unordered things by string notations. Of course a
_drawn_ graph has its own bogus order and shape, but
the _abstract_ graph doesn't. This was a main point
of my ICCS-94 paper* with Gerard Ellis, which you saw
me present. With our Boolean-embedding approach we
can at long last deal with the true abstract graph in
a computer without spurious artifacts; what it requires,
though, is painful explicit calculation of the whole
subsumption algebra (poset of of all vivid logical
graphs ordered by graph inclusion). Some
"top people" are working on it...
Incidentally, in the same paper the "fret product"
is a formal condition of a logic's "typedness". A theory
has a fret product as its subsumption algebra iff
it is typed. As you'll see if you look at the paper,
this is a pretty complicated graph-theoretic and
group-theoretic notion. I believe this may be a
justification for having types in KIF just as
LOOM and Conceptual Graphs already have types.
The first-order expressiveness is unaffected, but
the ability to describe the algebraic structure
in the (higer-order) metalanguage may be affected.
Or at least made feasible.
Yours truly, Fritz Lehmann
GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A.
Tel:(714)-733-0566 Fax:(714)-733-0506 firstname.lastname@example.org
* Gerard Ellis and Fritz Lehmann, "Exploiting the Induced
Order on Type-Labeled Graphs for Fast Knowledge Retrieval",
in "Conceptual Structures: Current Practice", W. Tepfenhart,
J. Dick and J. F. Sowa, Ed.s, Springer Lecture Notes in
Artificial Intelligence, No. 835, Springer, Berlin, 1994.