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

 To: "[ontolog-forum]" "John F. Sowa" Fri, 01 May 2009 08:27:28 -0400 <49FAEAB0.4000108@xxxxxxxxxxx>
 ```Dear Matthew,    (01) To avoid distractions of 3-D vs 4-D ontologies, I'll focus on the importance of intensional definitions even in set theory itself.    (02) JFS>> But note that even for finite sets, an intensional definition >> is necessary.    (03) MW> I would challenge necessary, but I agree they are useful. There > is nothing to prevent sets having intensional definitions, just > as long as that definition does not lead to varying memberships.    (04) 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.    (05) To emphasize the importance of intensional definitions, consider just sets of integers. First, note that a finite set can be specified by extension:    (06) S = {6, 9, 12, 15, 18, 21}    (07) The same set could also be specified by intension:    (08) S = { x | x is an integer, x>4, x<23, and x is divisible by 3}    (09) 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,    (010) 1. Let 6 be an element in the set S.    (011) 2. If x is an element of S, then so is x+3.    (012) 3. S is the smallest set that satisfies conditions #1 and #2.    (013) 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.    (014) For any 4D region that includes the future, no specification by extension is possible even for much smaller sets. I can, for example, specify such a set by intension:    (015) The winning numbers for next week's New York State Lottery.    (016) But there is no way to evaluate the denotation before the date. (If you have such a method, please send me the denotation by email, but please don't cc it to the list.)    (017) John    (018) _________________________________________________________________ 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    (019) ```
 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, Rich Cooper Re: [ontolog-forum] Last Call: OWL 2 and rdf:text primitive datatype, Richard H. McCullough