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## Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

 To: "[ontolog-forum]" "John F. Sowa" Thu, 04 Feb 2010 08:17:24 -0500 <4B6AC8E4.2030807@xxxxxxxxxxx>
 ```Dear Matthew and Duane,    (01) MW> It is the most basic thing about sets that they are defined > by their membership, which does not change.    (02) Yes. If you write something like the following,    (03) S1 = S union {x}    (04) mathematicians don't say that S has changed, but that S1 is a different set.    (05) In programming languages, it is common to write    (06) x = x + 1;    (07) but when that operation is carefully analyzed and described, it's described as "the value stored at the location designated by x has been replaced or updated with a new value."    (08) There are also some programming languages, such as ML or Haskell, called *functional* or *single-assignment* languages in which no variable can be reassigned a different value -- i.e., no statement of the form x=x+1 is permitted.    (09) MW> So if you have something that has members, but the membership > can change, then what you know for certain is that it is not a set. > Some people use the word type for such things. A type will have, > at a point in time, a set which is its membership.    (010) The usual distinction:    (011) The identity conditions for a set are *extensional*: if S1 and S2 have the same members, they are identical; otherwise they are two different sets.    (012) The identity conditions for a type are *intensional*; two types T1 and T2 are identical if their definitions are equivalent; their set of instances in a particular world w is called their *denotation* in w. Those worlds may be, for example, the physical world or a particular computer system at different times.    (013) John    (014) _________________________________________________________________ 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    (015) ```
 Current Thread Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, (continued) Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Patrick Cassidy Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Patrick Cassidy Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Patrick Cassidy Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, doug foxvog Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Duane Nickull Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa <= Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Duane Nickull Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Chris Partridge Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, John F. Sowa Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Chris Partridge Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Matthew West Re: [ontolog-forum] Foundation ontology, CYC, and Mapping, Christopher Menzel