----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Sunday, September 14, 2008 7:48 PM
Subject: Re: [ontolog-forum] Thing and Class (01)
> Azamat and Leonid,
> Intensions can be derived from extensions, but the extensions may
> lose or ignore some important distinctions in the definitions. I
> use the Greek letter delta for a *denotation operator* that maps
> a type t and a world w to the set of instances of t in the world w:
> delta: Types x Worlds -> Sets
> However, the mapping by delta is not one-to-one, since for a given
> world w, the set delta(HumanBeing,w) may be the same as the set
> delta(FeatherlessBiped,w). Also, delta(t,w) for any type t that
> has no instances in the world w would be the empty set.
> Therefore, a taxonomy defined by intensions is more fine grained
> than a taxonomy defined by extensions, because the sets may blur
> important distinctions in the definitions.
> Different applications that might use the same taxonomy may depend
> on those distinctions. For example, a taxonomy for the history of
> proposed airplane designs might have the type FlappingWingAircraft,
> but a taxonomy of airplanes that were actually built and survived
> their first test flight might have no instances. But a taxonomy
> defined by descriptions (intensions) could be used for both purposes.
> > Accordingly, there is extensional classification, called taxonomy,
> > and intensional classification, called meronomy, or mereology.
> The confusion between those two classifications is usually caused
> by terminologies that make a vague distinction of broader/narrower.
> That distinction should be clarified by using different dyadic
> relations, subtypeOf and partOf, which define distinct partial
> orderings. Both of them should accommodate hypothetical things
> like unicorns, which have a horn as part, and airplane designs
> that depend on the details of how the parts are assembled.
> People might dismiss unicorns as mythical or fictional animals,
> but biologists commonly talk about, describe, and search for
> instances of fossils of hypothetical organisms. An example
> would be the first tetrapod that crawled out of the water and
> became the ancestor of the amphibians.
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