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## Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype

 To: "'[ontolog-forum] '" Matthew West Fri, 1 May 2009 14:42:34 +0100 <49fafc65.0a04d00a.41b1.3f69@xxxxxxxxxxxxx>
 ```Dear John,    (01) We are I think agreed.    (02) > The identity conditions for sets ensure that equality is determined > by their elements. That principle is independent of whether the > elements are specified by extension or intension.    (03) [MW] Exactly. > > To emphasize the importance of intensional definitions, consider > just sets of integers. First, note that a finite set can be > specified by extension: > > S = {6, 9, 12, 15, 18, 21} > > The same set could also be specified by intension: > > S = { x | x is an integer, x>4, x<23, and x is divisible by 3}    (04) [MW] Indeed. I would probably to both in a case like this. > > But note that no infinite set can be specified by extension in > any finite statement in any language with a finite alphabet. > It's always *necessary* to state some rule or predicate that > defines the set by intension. For example, > > 1. Let 6 be an element in the set S. > > 2. If x is an element of S, then so is x+3. > > 3. S is the smallest set that satisfies conditions #1 and #2.    (05) [MW] Yes. Though as you note, only having an intensional definition does not stop it being a set, since the extension is unchanging. > > For many finite sets, such as the set of all cows or the set > of all molecules on planet earth at a given time slice, a > specification by extension is not possible by any known method. > > For any 4D region that includes the future, no specification > by extension is possible even for much smaller sets.    (06) [MW] Only if you have a fully deterministic system - in practice a rarity.    (07) > I can, > for example, specify such a set by intension: > > The winning numbers for next week's New York State Lottery. > > But there is no way to evaluate the denotation before the date.    (08) [MW] Quite.    (09) Regards    (010) Matthew West Information Junction Tel: +44 560 302 3685 Mobile: +44 750 3385279 matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx http://www.matthew-west.org.uk/    (011) This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177. Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.    (012) > (If you have such a method, please send me the denotation by > email, but please don't cc it to the list.) > > John > > > _________________________________________________________________ > 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 >    (013) _________________________________________________________________ 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    (014) ```
 Current Thread Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype, Richard H. McCullough Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype, John F. Sowa Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype, Matthew West <= Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype, Rich Cooper Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype, Richard H. McCullough