At 10:35 PM -0400 6/26/08, Bob Futrelle wrote:
>If I have a database of *all* employees in a company and a query for a
>person returns nothing, then that failure allows me to assert that
>that person is not an employee.
As long as you know that the database has that all-encompassing
quality, yes. But then, since that knowledge is crucial to the
conclusion being correct, it - the knowledge of the completeness -
should be made explicit as a premis in the argument. And then the
reasoning is classical.
Heres a way to say it. Logic is about what entails what. Now, suppose that:
John is not listed in database D of employees. Does it follow -is it
entailed - that John is not an employee? Well, no, actually. But NAF
would say that it does.
Now, in your scenario, we also know that the database is a list of
ALL the employees. So add this as another assumption, since this is
an important fact. NOW indeed it does follow that John is not an
employee. But we don't need NAF to conclude this: it follows by
classical logic from the two assumptions. Either way, in order to
express the reasoning correctly, classical logic is exactly what we
want. Using NAF on just the failure is an enthymeme: it has a missing
premis, like saying "Plato is a man, so Plato is mortal", forgetting
to add the 'obvious' premis that all men are mortal. As this example
might suggest, this is a VERY old mistake in reasoning.
>It's a matter of deciding what your
>universe of discourse is, is it not?
Well, if your entire universe of discourse is just the employees of
one company, then sure. But by and large, most ontologies have a
rather wider view of the universe. And if you plan to publish stuff
on a Web, then expecting everyone who reads it to agree with you that
the entire universe comprises nothing but the employees listed in
your database is asking rather a lot.
Bear in mind that the start of this thread was John Sowa's suggestion
that CL be adopted as a basic notation for ontologies in general, a
kind of super-OWL, and Adrian's response suggesting that there was
something inherently wrong with classical negation for such a role.
Pat
--
---------------------------------------------------------------------
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
http://www.ihmc.us/users/phayes phayesAT-SIGNihmc.us
http://www.flickr.com/pathayes/collections