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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 05 Sep 2008 10:31:07 -0400
Message-id: <48C142AB.7030403@xxxxxxxxxxx>
Sean,    (01)

That is a strong argument for adopting precise definitions of the
terminology used for ontology and related fields:    (02)

> While I would agree that, say, the CAD model for a part
> describes the shape of a part, the issue is not one of design but of
> configuration management. In particular, the criterion for being a part
> A123 is that it is fit, form and function identical to the "typical
> part" A123. The design is an "ontological commitment" that some class of
> thing exists (will exist). To reject this is to reject the concept of
> "is-a" and of labelling things with the concepts they instantiate.
> Conversely, penguins do not stop being penguins just because some has
> sequenced their DNA (written down their design).    (03)

In particular, the words 'concept' and 'class' have been used with
many different definitions (or with no definitions at all).    (04)

As we discussed, the term 'set' is defined by extension:  two sets A
and B are identical if and only if they have the same members.  That
has some important implications:    (05)

  1. Any change to a set S makes it a different set.    (06)

  2. Two sets may be identical even though their defining properties are
     very different.  For example, the set of human beings happens to
     be identical to the set of featherless bipeds.  But if someone
     generates a dinosaur from ancient DNA, those two sets might become
     distinct.    (07)

  3. Since the empty set is a subset of every set, the set of all
     unicorns is a subset of the set of all cows or the set of
     all bicycles.    (08)

The term 'type', however, is defined by intension:  an entity x
is of type T if and only if x has all the differentiae (defining
properties) of the type T.  That also has important implications:    (09)

  1. A type does not change when new instances are created or destroyed.    (010)

  2. Two types, such as HumanBeing and FeatherlessBiped may be distinct,
     even though they happen to have exactly the same instances.    (011)

  3. A type with no instances, such as Unicorn, is distinct from
     other types that have different definitions, independent of any
     instances those types may have.    (012)

Since the words 'class' and 'concept' have been used in many different
ways with different definitions, any use of them in discussions of
ontology can and frequently does create confusion.    (013)

I realize that many specific *notations* used for ontology happen
to use the words 'concept' and 'class'.  Some examples include the
use of 'concept' in conceptual graphs and 'class' in OWL.    (014)

But for those notations, the words are technical terms with precise
definitions.  In the conceptual graph system, the word 'concept' is
defined as a node in a conceptual graph.  That is a very narrow
definition, which should not be exported outside the context of CGs.
Similarly, the OWL term 'class' has a precise definition, which
should not be used outside the context of a discussion of OWL.    (015)

John Sowa    (016)

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