Reiter asks about representing, ``Quakers are normally pacifists and Republicans are normally non-pacifists. How about Nixon, who is both a Quaker and a Republican?'' Systems of nonmonotonic reasoning that use non-provability as a basis for inferring negation will infer that Nixon is neither a pacifist nor a non-pacifist. Combining these conclusions with the original premiss leads to a contradiction. We use
When we circumscribe 
using these three sentences as
A(ab,pacifist), we will only be able to conclude that Nixon is either abnormal
in aspect1 or in aspect2, and we will not be able to say whether he
is a pacifist. Of course, this is the same conclusion as would be reached
without circumscription. The point is merely that we avoid contradiction.
Reiter's second example is that a person normally lives in the same city as his wife and in the same city as his employer. But A's wife lives in Vancouver and A's employer is in Toronto. We write
we will again only be able to conclude that A lives either in Toronto
or Vancouver. In this circumscription, the function city must be taken
as variable. This might be considered not entirely satisfactory. If one knows
that a person either doesn't live in the same city as his wife or doesn't live
in the same city as his employer, then there is an increased probability that
he doesn't live in the same city as either. A system that did reasoning of
this kind would seem to require a larger body of facts and perhaps more
explicitly metamathematical reasoning. Not knowing how to do that, we might
want to use 
in both (26) and (27). Then
we would conclude nothing about his city once we knew that he wasn't in the
same city as both.
