COMMENT ⊗   VALID 00003 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	%contex[e86,jmc]	Formalization of contexts
C00009 00003	\noindent The first version of contex.tex[e86,jmc] is dated 1986 July 5.
C00010 ENDMK
C⊗;
%contex[e86,jmc]	Formalization of contexts
%
%CONTEX[S76,JMC] 24-Jul-76	CONTEXT DEPENDENT SEMANTICS
%ideas[e84,jmc]	
%contex[f84,jmc]		Ideas about context
%contex[s85,jmc]		Notes on contexts
%The best: contex[w86,jmc]		Contexts and mental situations
%notes[s86,jmc]		Amarel model and contexts
%genera[w86,jmc]		Generality in AI, for old Turing lecture
\input memo.tex[let,jmc]
\centerline{draft draft draft}
\vskip .5in
\centerline{\bf NOTES ON FORMALIZED CONTEXTS}
\vskip .1in
\centerline{John McCarthy, Stanford University}
\vskip .3in
%
\noindent {\bf Abstract:} (TO BE SUPPLIED)
\vskip .5in
%
\noindent {\bf Introduction.}

	These notes are part of the ``logicist'' approach to AI, which
involves expressing what an intelligent program knows as sentences
in logic and having it decide what to do by logical inference.  It
has already turned out that the required logical inference cannot merely be
deduction.  Deduction must be supplemented by nonmonotonic reasoning.

	Now it further seems that we need to formalize the notion of
context and relations among contexts and between sentences and contexts.
This should have been expected, because every formal mathematical
theory applied to the real world is preceded in its exposition by
natural language prose describing what is assumed and describing the
connections between the terms of the theory and the real world.
These natural language explanations, while they describe what
is assumed by the theory, in turn depend on assumptions and
terminology common to the author and the reader.  If computer
programs are to behave intelligently, they will also require
some way of expressing the contexts.  Some ideas for this are
described in these notes.

	Consider the sentence ``The cat is on the mat''.  When
discussed in logic it is often formalized $on(cat,mat)$.  However,
when we need to consider change and use the situation calculus,
we are inclined to use $on(cat,mat,s)$, so that we can also consider
the truth-value of (say) $on(cat,mat,result(e,s))$, where $result(e,s)$
is the situation that results from the event $e$ occurring in situation
$s$.  Even this is not specific enough when it is not obvious which
cat and which mat.  Our goal is to have it both ways --- to be able
to ``enter'' a context and say $on(cat,mat)$, but also to be able
to say the equivalent of ``John McCarthy's youngest cat was on
John McCarthy's front door mat on July 12, 1986 at 17:35
Pacific Daylight time''.  Even that assumes a context in which
a particular John McCarthy is identified.
%
\vskip .3in
\noindent {\bf Formalized contexts.}

	We begin by introducing some abstract objects called
contexts denoted by the letter $c$ with appropriate subscripts
and other decorations.  Denoting propositions by $p$, a basic
relation is
%
$$holds(p,c),$$
%
asserting that the proposition $p$ holds in the context $c$.
%
\vskip .3in
\noindent {\bf What is a context?}

	Contexts are abstract entities with the following properties.

	1. A context involves a set of
assumptions.  The assumptions peculiar to a given context may
be definitional, i.e. they may involve what certain terms mean.
They may be temporal and/or spatial, i.e. they may prescribe that
the sentences refer to a particular time and place.

	2. The set of assumptions in a context are only partially
known to the user of the context.  Indeed there may be an infinite
set of assumptions.

	3. Contexts may be related by specialization.
$c1 ≤ c2$ means that $c1$ is a more specialized context than $c2$.
We have

$$c1 ≤ c2 ⊃ (∀p.holds(p,c2) ⊃ holds(p,c1)).$$

	4. Some contexts make assumptions about time and/or place.
Thus $holds(on(A,B),c1)$ will be meaningful if $c1$ assumes a time.

	5. If $c0$ doesn't assume a time $t$ and  $c1$ is like $c0$
except that it does, we'll have $c1 ≤ c0$ and something like
$holds(on(A,B),assumetime(t,c0))$.
\noindent The first version of contex.tex[e86,jmc] is dated 1986 July 5.

\noindent This version \TeX ed on \jmcdate\space at \theTime.
\vfill\eject\end