>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 rangemath and rangeCS, 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 codomain
>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
codomain, 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 mathrange as a subset, then it
would be correct to assert that S is an owlrange
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 codomain.
>
> > >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 wordforword 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 OWL1.1 discussion recently was
> > the notion of 'disjoint union', which has been given a nonstandard
> > (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 nfold 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 categorytheory treatment of
set theory. (08)
Pat (09)
>
>Conrad (010)


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