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∂CSL Prof. Ma Xiwen↓Department of Mathematics↓Peking University
↓Peking↓Peoples Republic of China∞
Dear Prof. Ma:
Mrs. Zhang Guang, who brought me a letter from Professor Wu,
told me that her husband, Victor Kuo, is working with you on the
logic and semantics of knowledge. I had supposed that you had
lost interest in these questions.
I lectured in France recently and talked about the axiomatization
of Mr. S and Mr. P, and I presented your axioms. Then I noticed
what seems to be an error in the last two axioms. It seems to me
that in order to axiomatize learning correctly, the times associated
with these axioms should be 1 and 2 respectively instead of 0.
What is your opinion? Also, if you agree that the times should
be 1 and 2, does your proof depend on having taken them to be 0?
I met two specialists in modal logic there and challenged
them to formalize Mr. S and Mr. P in modal logic without direct use
of the accessibility relation. I have tried to do it several times
without success. So far they haven't responded. Have you considered
trying to axiomatize the problem without the accessibility relation?
Recently I have been working on what I call "ambiguity tolerant"
formalisms that will permit computers to use concepts that are
unambiguous in the cases encountered so far but which may turn
out to be ambiguous when new cases arise. I think this is essential
for common sense reasoning.
Enclosed are an abstract of a paper I expect to give on
ambiguity tolerance and a copy of the axioms of yours to which I
referred above.
I hope your work is going well.
.reg