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@make(letterhead,Phone"497-4330",Who "John McCarthy", Logo Old, Department CSD)                    
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@begin(address)
Mr. Chin-Chyuan Chen
Institute of Applied Mathematics
National Cheng-Kung University
Tainan, Taiwan 700
R.O.C.
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@greeting(Dear Mr. Chen:)
@begin (body)

	Domain circumscription was the original form that I developed.  I
discussed it in "Epistemological Problems of AI", which you have, and
Martin Davis treats its mathematics in his paper in the 1980 April AI
Journal.  I suggest you also look at Davis's paper for a clearer
mathematical exposition.

	In attempting to apply circumscription to examples, it became
clear that predicate circumscription was needed, and so I wanted to
reduce my previous circumscription to predicate circumscription.
When I wrote the 1980 paper, domain circumscription was fresh in
my mind, and I was too brief in describing it.  Indeed when I received
your letter and looked at the paper again, it took me quite a while
before I convinced myself that the paper was indeed correct.

	Domain circumscription was intended to formalize the
conjecture that the only objects that exist are those that must
exist because of a formula  A.  Predicate circumscription formalizes
the idea that the only objects that satisfy a predicate  P  are
those that must because of the formula  A(P).  How can we consider
domain circumscription as a special case of predicate circumscription?
Answer: We apply predicate circumscription to a predicate
satisfied by   all  objects.  We relativize the original formula
A  to the predicate  all,  because we want to assert that the
objects that exist satisfy  all.  We need   Axiom(all),  because
we need to assert that the objects satisfying  all  include
the constants and if  x  satisfies  all,  so does  f(x)  for any
function  f.

	It seems to me that predicate circumscription and domain
circumscription agree with respect to the definition of the
natural numbers, because the only objects that must exist as a
consequence of that definition are natural numbers.  If we
circumscribe a predicate, say  isblock,  when there are axioms
forcing the existence of other kinds of objects than blocks,
then predicate circumscription gets results that cannot be
obtained with domain circumscription.

	I agree with your correction to the formula on page 362.

	The  Minimal Inference  paper is an early draft of the
circumscription paper and is superseded.
I am sending the First Order Theories and  Ascribing  ... under
separate cover.  I am preparing a new paper on circumscription,
and I'll put you on the list to receive a copy.
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	I will probably visit Taiwan in May, and would be glad
to meet with you then.  I'll write again when the schedule is
arranged.

	I wish you success in your work on non-monotonic reasoning
and would be glad to receive a copy of your thesis even if it is
only in Chinese.
@end(body)
Sincerely,
 
   
    
John McCarthy
Professor of Computer Science