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Re: [ontolog-forum] borrowing terminology (was: [ontology-summit] PLEASE

To: "'Pat Hayes'" <phayes@xxxxxxx>
Cc: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Conrad Bock" <conrad.bock@xxxxxxxx>
Date: Thu, 8 Mar 2007 21:03:56 -0500
Message-id: <002601c761ef$324a8110$84dc0681@xxxxxxxxxxxx>
Pat,    (01)

 > >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.      (02)

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.
In OWL, if the range of a property pet is Animal, it isn't required that
all animals are pets.  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.    (03)

 > >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.    (04)

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.  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).    (05)

Bummer about the coopting of completeness.    (06)

 > 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    (07)

I thought it equivalent to a set of disjoint classes that are also a
union for another.  What's the mathematical definition?    (08)

Conrad    (09)

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