Hi Tara and John,
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.
I prefer the type definition that is static, fixed in time. That
applies if the class type is defined as a plurality of instances of the type
definition, with optional class properties defined for association with the class
definition as well.
That approach lets the type definition be static from creation to
destruction, while the number of instances varies during that period. But
the definition is not changed by the variation in the number of instances.
If a program's purpose is to represent time varying definitions, those
definitions are built upon a set of static type definitions (the primitives of
another thread) having a dynamic number of instances. The program's goal
of representing definitions is to compose structured groups of primitives and
assemblies into ever more complex systems.
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of John F. Sowa
Sent: Tuesday, January 18, 2011 12:32 PM
Subject: Re: [ontolog-forum] Ontology of Rough Sets
On 1/18/2011 12:40 PM, Tara Athan wrote:
> What happens when an Employee is fired or a new Employee is hired.
> type doesn't change. But the set of Employees becomes a different
> does the class change? Or does the class disappear, to be replaced
> new class? Or are we talking about the set of all Employees, past,
> present and future?
Those are good questions. To avoid them, I prefer to use the
'type' and 'set' and avoid using the word 'class'. However, there
are many languages and tools (Java and OWL, for example) that use the
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
by a wider audience, I have to relate my terminology to the terms that
are common in the field.
Therefore, I would define the word 'class' to be consistent with the
way it's used in Java, OWL, and related languages: For any
(which may be possible or actual with arbitrary space-time
a class is the set of entities in that situation for which the type
predicate is true.
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.
> The example I frequently see used to illustrate this point is the
> classes "three-sided polygon" and "three-angled
> have the same extension but different definitions, so they are
> different classes.
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.
For a short note about propositions, see
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.
Therefore, the two classes would be distinct, but they would
have the same elements.
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