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Re: [ontolog-forum] Ontology of Rough Sets

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 18 Jan 2011 15:32:28 -0500
Message-id: <4D35F8DC.5080908@xxxxxxxxxxx>
On 1/18/2011 12:40 PM, Tara Athan wrote:
> What happens when an Employee is fired or a new Employee is hired. The
> type doesn't change. But the set of Employees becomes a different set -
> does the class change? Or does the class disappear, to be replaced by a
> new class? Or are we talking about the set of all Employees, past,
> present and future?    (01)

Those are good questions.  To avoid them, I prefer to use the terms
'type' and 'set' and avoid using the word 'class'.  However, there
are many languages and tools (Java and OWL, for example) that use the
word 'class'.    (02)

When I write an article about my own approach, I have no need for the
word 'class'.  But when I'm writing a textbook that I hope will be used
by a wider audience, I have to relate my terminology to the terms that
are common in the field.    (03)

Therefore, I would define the word 'class' to be consistent with the
way it's used in Java, OWL, and related languages:  For any situation
(which may be possible or actual with arbitrary space-time coordinates),
a class is the set of entities in that situation for which the type
predicate is true.    (04)

For the question of what happens during a change, I would say that
the class and its definition (i.e., the type predicate) does not
change, but the old set is replaced with the new set.    (05)

> The example I frequently see used to illustrate this point is the
> classes "three-sided polygon" and "three-angled polygon", which
> have the same extension but different definitions, so they are
> different classes.    (06)

This gets into the identity conditions for prepositions (and a
predicate or relation can be defined as a lambda-abstraction of
a proposition).  If you distinguish the two predicates, I would
distinguish the two classes.    (07)

For a short note about propositions, see    (08)

    http://www.jfsowa.com/logic/proposit.htm    (09)

According to the recommendations in that article, sentences that
use different vocabulary (e.g., 'angles' and 'sides') would not
be considered statements of the same proposition.  Therefore,
they would not be considered the same definitions.    (010)

Therefore, the two classes would be distinct, but they would
have the same elements.    (011)

John    (012)

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