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␈↓ ↓H␈↓␈↓βS␈↓∧ Department of Computer Science, STANFORD UNIVERSITY, Stanford, California 94305

␈↓ ↓H␈↓∧Telephone 415 497-4430␈↓ 
-July 9, 1981 




␈↓ ↓H␈↓Prof. Ma Xiwen
␈↓ ↓H␈↓Department of Mathematics
␈↓ ↓H␈↓Peking University
␈↓ ↓H␈↓Peking
␈↓ ↓H␈↓Peoples Republic of China

␈↓ ↓H␈↓Dear Prof. Ma:

␈↓ ↓H␈↓        Mrs.␈αZhang␈α
Guang,␈αwho␈α
brought␈αme␈α
a␈αletter␈α
from␈αProfessor␈α
Wu,␈αtold␈α
me␈αthat␈αher␈α
husband,
␈↓ ↓H␈↓Victor␈αKuo,␈α
is␈αworking␈α
with␈αyou␈α
on␈αthe␈αlogic␈α
and␈αsemantics␈α
of␈αknowledge.␈α
 I␈αhad␈α
supposed␈αthat
␈↓ ↓H␈↓you had lost interest in these questions.

␈↓ ↓H␈↓        I␈α
lectured␈α
in␈α
France␈αrecently␈α
and␈α
talked␈α
about␈αthe␈α
axiomatization␈α
of␈α
Mr.␈αS␈α
and␈α
Mr.␈α
P,␈αand␈α
I
␈↓ ↓H␈↓presented␈α
your␈α
axioms.␈α
 Then␈α
I␈α
noticed␈α
what␈α
seems␈α
to␈α
be␈α
an␈α
error␈α
in␈α
the␈α
last␈α
two␈α
axioms.␈α It␈α
seems
␈↓ ↓H␈↓to␈αme␈αthat␈α
in␈αorder␈αto␈α
axiomatize␈αlearning␈αcorrectly,␈α
the␈αtimes␈αassociated␈α
with␈αthese␈αaxioms␈α
should
␈↓ ↓H␈↓be␈α∞1␈α∞and␈α∞2␈α∞respectively␈α∞instead␈α
of␈α∞0.␈α∞ What␈α∞is␈α∞your␈α∞opinion?␈α
 Also,␈α∞if␈α∞you␈α∞agree␈α∞that␈α∞the␈α
times
␈↓ ↓H␈↓should be 1 and 2, does your proof depend on having taken them to be 0?

␈↓ ↓H␈↓        I␈α
met␈α
two␈α
specialists␈α
in␈α
modal␈α
logic␈α
there␈α
and␈α
challenged␈α
them␈α
to␈α
formalize␈α
Mr.␈α
S␈α
and␈αMr.␈α
P
␈↓ ↓H␈↓in␈α
modal␈αlogic␈α
without␈αdirect␈α
use␈αof␈α
the␈αaccessibility␈α
relation.␈α I␈α
have␈αtried␈α
to␈αdo␈α
it␈α
several␈αtimes
␈↓ ↓H␈↓without␈α∞success.␈α∞ So␈α∞far␈α∞they␈α∞haven't␈α∞responded.␈α∞ Have␈α∞you␈α∞considered␈α∞trying␈α∞to␈α∞axiomatize␈α
the
␈↓ ↓H␈↓problem without the accessibility relation?

␈↓ ↓H␈↓        Recently␈α⊃I␈α⊃have␈α⊃been␈α⊂working␈α⊃on␈α⊃what␈α⊃I␈α⊂call␈α⊃"ambiguity␈α⊃tolerant"␈α⊃formalisms␈α⊃that␈α⊂will
␈↓ ↓H␈↓permit␈αcomputers␈αto␈αuse␈αconcepts␈α
that␈αare␈αunambiguous␈αin␈αthe␈α
cases␈αencountered␈αso␈αfar␈αbut␈α
which
␈↓ ↓H␈↓may␈α
turn␈α
out␈αto␈α
be␈α
ambiguous␈αwhen␈α
new␈α
cases␈α
arise.␈α I␈α
think␈α
this␈αis␈α
essential␈α
for␈α
common␈αsense
␈↓ ↓H␈↓reasoning.

␈↓ ↓H␈↓        Enclosed␈αare␈αan␈αabstract␈αof␈α
a␈αpaper␈αI␈αexpect␈αto␈αgive␈α
on␈αambiguity␈αtolerance␈αand␈αa␈α
copy␈αof
␈↓ ↓H␈↓the axioms of yours to which I referred above.

␈↓ ↓H␈↓        I hope your work is going well.


␈↓ ↓H␈↓Best regards,



␈↓ ↓H␈↓John McCarthy
␈↓ ↓H␈↓Professor of Computer Science