Actually, N^2 applies to the terms of ontologies also. The notion of
using existing equivalence of two terms in two ontologies to reduce the
effort of mapping might work, but only partly because:
(1) one has to know the equivalence mapping in all the other
ontologies -- not a trivial amount of work, and certainly not 0. If
there are a large number of ontologies, one has to inspect the
equivalence mappings of **every one**!! Try it, you won't like it.
(2) exact equivalence of intended meaning occurs in probably less
than half the terms in any two ontologies, and there is often meaning
overlap which is much more work to reduce
(3) *any* structural difference (difference in the relations) of two
terms in two ontologies will make them formally different (different
inferences) even if their intended meanings are the same. (01)
Even if it seemed to work on a very small number of ontologies, it
is totally impractical when you get over 10. If you know of an example
where it has been done, let us know. (02)
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> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> Christopher Menzel
> Sent: Thursday, May 03, 2007 11:09 AM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] A "common basis"
> On May 3, 2007, at 5:03 AM, Patrick Durusau wrote:
> > Adam,
> > Adam Pease wrote:
> >> Hi Chris,
> >> Many thanks. I was really addressing a point that you weren't
> >> making, but which is all too common.
> >> I'm sympathetic to using SUMO for semantic interoperability.
> >> When I've done projects in that area, it has worked well. At the (05)
> >> risk of stating the obvious, the advantage, at least in
> theory, of
> >> a common model over a federated approach is that one has mappings (06)
> >> linear in the number of products needing integration, rather than (07)
> >> potentially N^2.
> > I am glad you mentioned the "potentially N^2" issue. I have seen
> > that claim on a number of occassions but never with what I
> > considered a convincing explanation of why it must be so.
> > For example, assume that I have terms A, B, and C, all of which I
> > wish to say represent the same subject.
> > While I agree that it is possible to say A = B, A = C, B =
> C, ....,
> > isn't that an implementation choice?
> > In other words, if I have the mapping A = B and then later add B = (08)
> > C, do I really need A = C? The effect of the first two mappings is (09)
> > sufficient to reach the desired result.
> > Well, it should be noted that relying upon separate mappings does
> > result in a problem Steve Newcomb has faced with his topic map
> > implementation, that is how to determine when "all" the mappings
> > have been performed.
> > Ah, or is the N^2 claim based on a requirement that in order to
> > apply whatever inferences are available at A to C, a direct
> > is required? Still, that seems to be an implementation
> question and
> > not one of the actual mapping.
> > That is a particular methodology of mapping is being presumed. I
> > would assume once the mapping is complete, then the outcomes of
> > inferencing will be the same. Yes?
> > I have usually encountered the N^2 comment when a particular
> > vocabulary is being advocated. Noting that an implied mapping is
> > being peformed even by those who advocate a particular vocabulary, (010)
> > but that the implied mapping is not (usually) available for others (011)
> > to inspect or use. (The same can be the result using topic maps.
> > There is no requirement that a mapping in an implementation, which (012)
> > may be commercial intellectual property, be disclosed. For
> the most
> > part, I think greater disclosure can potentially lead to more
> > interoperability. But, there are tradeoffs and reasonable people
> > will draw the line on disclosure at different places.)
> I don't think this is the issue Adam had in mind, Patrick. I
> Adam's N^2 remark doesn't have anything to do with the terms in a
> particular vocabulary (though there may in fact *be* an N^2 problem
> of some sort lurking there), but with the number of the languages
> used by the ontologies one is trying to integrate. Suppose we have
> four ontologies, each one written in a separate language --
> say Loom,
> Classic, SNEPS, and KL-1 (chosen because I have some appropriate
> graphics from a presentation I gave a few years ago :-) :
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