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C00002 00002	%contex[s90,jmc]		Notes on contexts (for CYC)
C00005 00003	\section{References}
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%contex[s90,jmc]		Notes on contexts (for CYC)

These notes will concentrate on just one of the applications
of treating contexts as formal objects.  This is their use
for writing commonsense axioms in a simple way leaving out
parameters.  For example, in the blocks world the relation
$above$ is transitive.  We would like to write
%
$$∀x y z(above(x,y) ∧ above(y,z) ⊃ above(x,z)),$$
%
or even just
%
$$transitive(above),$$
%
but without contexts we would ordinarily have to write something like
%
$$∀s x y z(holds(above(x,y),s) ∧ holds(above(y,z),s) ⊃ holds(above(x,z),s)),$$
%
and the option of writing $transitive(above)$ is available
only if we introduce a special situation calculus version of
$transitive$.  If this were the worst case, we could surely
live with it, but there are much more complex examples.

	Take $c0$ to be a quite general context.  We have
%
$$holds(∀P(transitive(P) ≡ ∀x y z(P(x,y) ∧ P(y,z) ⊃ P(x,z)),c0)$$
%
and
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$$holds(transitive(above),c0).$$
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A reasoner, human or program, can then give the inference command
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$$(infer: transitive(above) entering(c0)).$$
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This results in the wff
%
$$transitive(above),$$
%
but the reasoning system remembers that this was done within
the context $c0$.  Any result $p$ of any inferences using $transitive(above)$
can, if allowed by other premises of the inference, be lifted
to any context specializing $c0$.  Since $c0$ is quite a general context,
perhaps the most general in which the symbol $above$ has its conventional meaning,
a certain problem may involve only contexts specializing $c0$.
As long as we stay within such contexts $transitive(above)$
can be used without any further reference to context.
\section{References}

\noindent {\bf McCarthy, John (1987)}:
``Generality in Artificial Intelligence'', {\it Communications of the ACM}.
Vol. 30, No. 12, pp. 1030-1035.  Also in {\it ACM Turing Award
Lectures, The First Twenty Years}, ACM Press, 1987.
% genera[w86,jmc]

\noindent {\bf McCarthy, John (1989)}:
``Artificial Intelligence, Logic and Formalizing Common Sense'',
in Thomason, Richmond, ed. {\it Philosophical Logic
and Artificial Intelligence}, Kluwer Academic Publishing,
Dordrecht, Netherlands.
% thomas[f88,jmc],  final printed version in thomas[s89,jmc]