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Re: [ontolog-forum] Ontology of Rough Sets

To: "doug@xxxxxxxxxx" <doug@xxxxxxxxxx>, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Fri, 21 Jan 2011 11:02:54 -0500
Message-id: <4D39AE2E.2060603@xxxxxxxx>
+1 Thanks, Doug. This is almost exactly what I replied to John on the 
other exploder.    (01)

doug foxvog wrote:
> On Thu, January 20, 2011 0:27, John F. Sowa said:
>> A question about types, sets, and classes arose on the AESIG
>> mailing list, which is related to the earlier discussion in
>> this thread.  See, in particular, the slides by Peter Aczel.
>> John
>> -------- Original Message --------
>> Subject: Re: [architecture-strategy] Relationship between types, classes
>> and sets
>> Date: Wed, 19 Jan 2011 23:54:43 -0500
>> From: John F. Sowa <sowa@xxxxxxxxxxx>
>> To: architecture-strategy@xxxxxxxxxxxxxxx
>> Cory,
>>> The terms "type", "class" and "set" are used within many
>>> modeling
>>> languages, formal languages and natural language.  A precise
>>> specification of languages involving these terms must have them
>>> precisely specified.
>> ...
>>> Rick murphy referenced this paper:
>>> http://www.cs.man.ac.uk/~petera/what-is-a-set-leeds-nov-2010.pdf
>> These slides by Peter Aczel distinguish the terms 'type', 'class',
>> and 'set' as used by logicians who talk about higher orders of
>> infinity.  Most of that discussion is irrelevant to AESIG.
>> ...
>> Summary:
>>   1. A set is extensional: it is uniquely determined by its elements.
>>   2. Type is an informal notion has been formalized in different ways.
>>      But a very common and useful way is to choose some predicate
>>      that specifies the type.
>>   3. A class is the extension of some predicate.
>>   4. Every set is a class, but some classes could be too big to
>>      be sets -- but those are hyper-infinite monsters that are
>>      irrelevant to computer systems.
>>> If an object could change types...
>> No object can "change" types without becoming a different object.
> I think that John refers to a mathematical object here.
>> [Example of type Integer vs. floating point number]
> However, for a temporal object, such as a person, the specific "type" of
> that object can change.  For example, at one time Barak Obama was of type
> HumanChild, while at another he was of type HumanAdult.  Of course, there
> is some more generic type of which the object is an instance throughout
> its existence.  But sets, classes, and types can be generated or defined
> using narrower predicates.
> A standard distinction between a set and a class, is that membership in
> a class cannot change, while membership in a class can.      (02)

Typo: Doug means membership in a _set_ cannot change, while membership 
in a class can.    (03)

> The set is either
> defined extensionally or generated as the extension of a predicate in a
> given context.      (04)

For "context", I would have said "domain of discourse".    (05)

> Once the set is generated, the extension of the predicate
> in a different context (which might merely mean a different time) is no
> longer necessarily the same set.
>       (06)

Agreed. A set _is_ the collection of things in it. A different 
collection of things is a different set.
But that does get into issues of identity.    (07)

> If the extension of the predicate is context-independent, membership in
> the associated class is fixed.  An instance of a context-free type (such
> as Integer) can not change whether or not it is an instance of that type.
> -- doug f
>       (08)

-Ed    (09)

>> John
> =============================================================
> doug foxvog    doug@xxxxxxxxxx   http://ProgressiveAustin.org
> "I speak as an American to the leaders of my own nation. The great
> initiative in this war is ours. The initiative to stop it must be ours."
>     - Dr. Martin Luther King Jr.    (010)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                Cel: +1 240-672-5800    (011)

"The opinions expressed above do not reflect consensus of NIST, 
 and have not been reviewed by any Government authority."    (012)

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