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Date: Sat, 24 Sep 94 08:19:39 CDT From: fritz@rodin.wustl.edu (Fritz Lehmann) Message-id: <9409241319.AA19917@rodin.wustl.edu> To: cg@cs.umn.edu, interlingua@isi.edu, srkb@cs.umbc.edu Subject: _Pure_ graphs have genuine value Sender: owner-srkb@cs.umbc.edu Precedence: bulk

A recent private email exchange on time ontologies had the following light digression (quoted with permission): FRITZ LEHMANN: > Glad you see the light; notation should be beneath the >notice of an ontologist (unless some iconic quality of the notation >is being exploited).. PAT HAYES: Glad I see the light!! Cheeky bastard! Ive been preaching this loudly since 1972. LEHMANN: Yeah but you keep lapsing, and grumbling about Sowa's rebarbative graphs, semantic networks, "frames", etc. HAYES: 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 whatever. ------------ I hazard that some of my reply could be of interest to these lists: ---- LEHMANN: ... 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 fritz@rodin.wustl.edu ============================================================= * 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.