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Professor Raymond Reiter
Department of Computer Science
University of Toronto
Toronto, Ontario M5S 1A4
CANADA

Dear Ray:

	Thanks for your draft ``Nonmonotonic Reasoning''.
Here are some comments.

page 6.  The part about natural kinds isn't clear and may be wrong.
The reason that natural kinds lack definitions isn't that their
boundaries are fuzzy.  It's rather that a person or computer program
doesn't know all about a particular natural kind; more can be found
by scientific or other investigation.  In particular, the some of
the features that allow objects of that kind to be distinguished
from other objects may be unknown.  For example, lemon is a natural
kind.  The lemons that I know about are yellow and much smaller
than grapefruit, but geneticists or plant breeders may have bred
blue lemons the size of grapefruit.  I'm not sure this affects the
examples of nonmonotonic reasoning you gave, but I am pretty sure
that this affects the presumptions about natural kinds such as lemons.
For example,  our formalism needs to allow the presumption that
lemons can always be distinguished from oranges because no chain
of indiscernable intermediates exists.

	We may also want a rule saying that a noun normally designates a
natural kind such that objects of that kind are distinguished from other
kinds of objects --- not necessarily by immediately observable criteria.
Thus children ask for criteria separating hills from mountains and are
disappointed when told there isn't a sharp criterion.

	With regard to databases, it might be worth mentioning
that the if-and-only-if assertions can be made quite compactly
if this is wanted.  For example, we can give the airline guide
as a list and then state that all flights have their names,
origins and destinations listed in the guide.  For example,
we may have the sentences
%
$$airline\-guide = '((ua473 sfo dfw) (aa3371 dfw tyl)\ldots)$$
%
and
%
$$(∀ f)(airline\-flight(f) ≡ member(list(name(f),origin(f),destination(f)),
airline\-guide)).$$