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Re: [ontolog-forum] Ontology of Rough Sets

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Tue, 18 Jan 2011 12:45:15 -0800
Message-id: <20110118204550.04509138CEC@xxxxxxxxxxxxxxxxx>

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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