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## Re: [ontolog-forum] borrowing terminology

 To: "'[ontolog-forum] '" Pat Hayes Fri, 9 Mar 2007 11:12:55 -0600
 ```>Pat, > > > >So OWL and as the rest of computer science are using "range" a > > >nonmathematical way: > > > > > > http://en.wikipedia.org/wiki/Range_%28computer_science%29 > > > > No, wait. There is range-math and range-CS, let > > us agree (although in fact 'range' is used in > > both disciplines in both senses). But the > > owl/RDFS sense of 'range' is closer to the first, > > mathematical, sense than the second.  > >Not following, the definitions in the math links say all elements in the >range have mappings from some element in the domain, while the co-domain >can have elements that aren't mapping to by any element in the domain.    (01) Yes. But at least the issue is about sets and relations. The definitions for 'range' in the wikipedia CS entry (pointer above) are to do with boundary values in arrays and limits on values of variables, which are a COMPLETELY different topic. I thought this was your point.    (02) >In OWL, if the range of a property pet is Animal, it isn't required that >all animals are pets.    (03) Right, so the owl:range is a subset of the co-domain, as I said. There is no explicit OWL construction for codomain as such, but if the codomain of P is C, it would not be incorrect to assert that C is (a) range of P. In fact, if S is any set which is a subset of the codomain and which has the math-range as a subset, then it would be correct to assert that S is an owl-range for the property. In OWL there can be many ranges asserted of a property, and 'the' range is somewhere inside their intersection. One can bound it from above, as it were, but one cannot bound it from below with an owl:range assertion.    (04) > Or at least if you tell me it is (and since it's >you, I'd pretty much hafto believe it!), I'd need to ask what the OWL >construct is for co-domain. > > > >Idempotence is another example: > > > > > > http://en.wikipedia.org/wiki/Idempotent > > > http://en.wikipedia.org/wiki/Idempotence_(computer_science) > > > > > > > This isn't a very good example, as these really > > are the same concept, almost word-for-word the > > same definition in fact, but they are applied to > > rather different kinds of application area. But I > > don't think there would be any risk of a > > mathematician seriously misunderstanding what was > > meant here. > >Not the way I've heard idempotence used by software people. They're >referring to calling the same function twice on the same arguments (the >wikipedia ambiguously calls this "used multiple times"), where the >second call has no effect.    (05) Ah, I see your point, sorry. Hmm. I think I see where this happened. If you assume that every application involves a 'state', then multiple applications become nested function applications to a starting state, which maps the computer science sense into the mathematical sense. But I agree the CS folk have kind of diluted the mathematical meaning.    (06) > This is important in cases where you need to >make sure a function has been called on an argument, but aren't sure if >it has already, and don't have a way of finding out. The mathematical >definition "calls" the function once, and calls it again with the result >of the first call, and gets the same result back it did the first time >(the composition of the function with itself is the function). > > >Bummer about the coopting of completeness. > > > Another example which came up on the OWL-1.1 discussion recently was > > the notion of 'disjoint union', which has been given a non-standard > > (and genuinely faulty) interpretation by formal ontologists, which is > > not in line with its established mathematical > >I thought it equivalent to a set of disjoint classes that are also a >union for another. What's the mathematical definition?    (07) It unions distinct 'copies' of the sets, so even if they are identical or share elements, one gets distinct copies in the disjoint union (aka 'separated union'). This can be described formally in various ways, but the key property is that the cardinality of the disjoint union is always the sum of the cardinalities of the unioned sets. So the n-fold disjoint union of A with itself is meaningful and isomorphic to A x n. If the sets are disjoint, then the disjoint union is the ordinary union. But it is defined even if they aren't disjoint; and this is important for the category-theory treatment of set theory.    (08) Pat    (09) > >Conrad    (010) -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 cell phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes    (011) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: 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 Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (012) ```