Last month a stray neuron fired and I wrote these piece on what I called the
seven facets of classes, which I think is restating some of what this
conversation has been about. (01)
Would love to hear your feedback on it. (02)
http://semanticarts.com/articles/seven-facets-of-class (03)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed Barkmeyer
Sent: Friday, January 21, 2011 9:03 AM
To: doug@xxxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] Ontology of Rough Sets (04)
+1 Thanks, Doug. This is almost exactly what I replied to John on the
other exploder. (05)
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. (06)
Typo: Doug means membership in a _set_ cannot change, while membership
in a class can. (07)
> The set is either
> defined extensionally or generated as the extension of a predicate in a
> given context. (08)
For "context", I would have said "domain of discourse". (09)
> 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.
> (010)
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. (011)
> 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
>
> (012)
-Ed (013)
>> 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. (014)
--
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 (015)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (016)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (017)
|