Hi Tara and John,
John wrote:
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
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of John F. Sowa
Sent: Tuesday, January 18, 2011 12:32 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
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.
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?
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'.
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.
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.
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
polygon", which
> 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
http://www.jfsowa.com/logic/proposit.htm
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.
John
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