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\address
Professor Gian-Carlo Rota
Department of Mathematics
M. I. T.
Cambridge, MA 02139
\body
Dear Gian-Carlo:

	I was reading the issue of {\it Los Alamos Science} dedicated
to Stan Ulam, and I came across the transcript of your conversation
with him concerning ``but''.  You'll pardon me for saying so, but
you and he didn't get very far in that conversation.

	Recalling our discussions of formalized nonmonotonic reasoning, I
was not sure you were convinced that anything significant had been achieved.
Since I had previously thought about ``but'' in connection with
nonmonotonic reasoning, it immediately occurred to me to write you
about it.

	``A but B'' may be taken to mean
%
$A ∧ B ∧ (completion(A∧C) ⊃ ¬B),$
%
where $C$ is additional information that the speaker assumes the hearer
has, and $completion(A∧C)$ is a sentence that is obtained from $A∧C$ in
some way that depends on the kind of nonmonotonic formalism being used.
In the case of an abnormality theory using circumscription,
$completion(A∧C)$ would be the formula obtained from $A∧C$ by assuming
that the predicate $ab$ (for abnormal) is minimized.  This is one way of
adding to $A∧B$ the fact that the speaker expects that given $A$, the
hearer would expect $B$ to be false.

	The key question is why it is desirable to give this additional
information.  I think this is related to the sketchiness of the information
usually given in a conversation.  The speakers do not first agree on what
information they hold in common, and must take into account the possibility
that their states of information differ in some relevant respect.
$A\ but\ B$ permits the hearer to keep track of what the hearer expects
he has been inferring and would infer from the statement $A$.

	I have been asking myself whether ``but'' will be required in
communication among computer programs.  I think so, but
I don't have a definite answer yet.

	The {\it Daedalus} issue on AI, about which I had considerable
misgivings, seems to be moderately respectable.
\closing
Sincerely,
John McCarthy
Professor
\endletter
\end