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Date: Mon, 24 Jul 95 19:51:24 CDT From: fritz@rodin.wustl.edu (Fritz Lehmann) Message-id: <9507250051.AA01467@rodin.wustl.edu> To: hovy@isi.edu, phayes@cs.uiuc.edu Subject: Re: Good and Bad IS-A hierarchies Cc: cg@cs.umn.edu, fritz@rodin.wustl.edu, srkb@cs.umbc.edu Sender: owner-srkb@cs.umbc.edu Precedence: bulk

Pat Hayes wrote: ---begin quote--- [stuff on graph-theoretic "bundles" of axioms] None of this is usefully reflected in any kind of isa heirarchy: its not a choice between different concepts, but different ways to axiomatise the same collection of concepts. Moreover, there is no way to organize the concepts, or even the axioms, into neat little packets so that the various alternatives can be assembled by choosing some and ignoring others. There just are genuine alternatives, and one has to make committments in selecting a temporal theory to work with. I seem to detect, in the object-oriented flavor which informs so much current work in ontologies, a residue of the old bias against the use of axioms. But theres no way around it: if you want to answer questions, you have to be able to draw conclusions, and conclusions involve making connections between things. The basic unit of meaning is not a concept but a theory, ie a collection of axioms. Pat Hayes ---end quote--- IS-A hierarchies do accomplish (some of) this bundling. IS-A with strict inheritance is a terse second-order specification of a large class of first-order constraints; constraints are in turn a particular kind of axioms. It is exactly the "bundling" effect of hierarchies that makes them desirable. Anytime you can factor out a "BOX" (in the KL-ONE sense) in a knowledge base you have accomplished something. Divide and Conquer. Admittedly the particular axiom-set determined by the hierarchy is only one kind among the many kinds of axiom-sets needed, but it's a practically important one. Aside from conceptual clarity, it gives you the benefits described by Walther and by Cohn for "order-sorted-logics" (= semantic nets with nestable-negation and an IS-A/type-lattice): dramatic theorem-proving speedup. We still need other ("ABOX") axioms, of course, that don't fit in any of the other "BOX"-factors, even if there are multiple, different subsumption hierarchies ("BOXES") having nodes combined in one proposition. For "vivid" models (existential, without nestable negations) Gerard Ellis' and my ICCS-94 paper (which you saw/suffered through?) gives the mathematics of the "fret product" which combines all the "BOXES" into the big hierarchy of all possible descriptions, ordered by subsumption. ("Exploiting the Induced Order on Type Labeled Graphs for Fast Knowledge Retrieval", in Conceptual Structures: Current Practice, Tepfenhart et al., eds., Lect. Notes on A.I. No. 835, Springer, Berlin, 1994.) IS-A isn't everything, but it's still good. Yours truly, Fritz Lehmann GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A. Tel:(714)-856-0671 email: fritz@rodin.wustl.edu ===========================================================