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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 14 Sep 2008 12:48:44 -0400
Message-id: <48CD406C.4040206@xxxxxxxxxxx>
Azamat and Leonid,    (01)

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:    (02)

    delta:  Types x Worlds -> Sets    (03)

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.    (04)

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.    (05)

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.    (06)

 > Accordingly, there is extensional classification, called taxonomy,
 > and intensional classification, called meronomy, or mereology.    (07)

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.    (08)

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.    (09)

John    (010)

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