Re: SUO: Re: W3C approves RDF and OWL as recommendations
Adam,
AP> This issue has been discussed at some length before.
> Guarino/Welty argue for the same distinction even more
> strongly than I with their notion of 'identity'.
> When a class hierarchy is non-monotonic it does make
> reasoning problematic.
Who said anything about nonmonotonic logic? If you have
a parentOf relation, the set of parents is every bit as
precisely defined as the relation: it's the set of
all people who are related to somebody by the parentOf
relation. 100% correspondence. No problems there.
AP> Unlike Guarino/Welty I don't think this issue can
> be made completely strict, but it's certainly
> advantageous to maintain identity criteria that
> are as strict as possible.
Talking about something being not completely strict
is like saying someone is not completely pregnant.
In any case, I'm glad that you agree that their notion
is not "completely strict". Whenever Nicola gives his
identity criteria, he uses words like "essence", which
he never defines. He claims that it is a modal notion,
which can be represented by a box operator in modal
logic, but he never explains the basis for those boxes.
As I have pointed out repeatedly, every modal notion
is definable in terms of some law that serves as the
basis for the necessity or possibility. And given
any such law p, all you have to do is to parametrize
it by means of a lambda expression (or any similar
mechanism) to get a relation p(x) or p(x,y).
Once you have a relation p(x,y), you go back to
step #1 and define the set of all x's for which
there exist some y that satisfies the relation p(x,y).
The set of all parents may change over time, but
so does the set of all people. In fact, there is
an interesting relationship between their rates
of change.
John