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C00002 00002	%counte[w90,jmc]		Practical Counterfactuals (for Etchemendy conference)
C00005 00003	\section{The uses of counterfactuals in human life and for robots}
C00007 00004	\section{Cartesian counterfactuals and their elaborations}
C00008 00005	\section{Approximate theories}
C00009 00006	\section{Comparison with other approaches}
C00010 00007	\smallskip\centerline{Copyright \copyright\ 1990\ by John McCarthy}
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%counte[w90,jmc]		Practical Counterfactuals (for Etchemendy conference)
\input memo.tex[let,jmc]
\title{Counterfactuals for the Practical Man}

\section{Introduction}

	The object of this paper is to elaborate a theory of a class
of counterfactual conditional propositions.  Practicality comes in
by considering what counterfactuals are good for in human life and
what counterfactuals we shall want robots and other intelligent
computer programs to use.

	There are two main ideas.

	1. Cartesian product counterfactuals and their
elaborations.  Given a representation of a set as a cartesian
product and a point in that set, we can talk about changing one
co-ordinate of the point and leaving the others unchanged.  This
idea leads to a class of counterfactuals like those beginning
``If $x$ were 5 then $\ldots$''.  The idea will also be elaborated
to some cases when the structure isn't actually a cartesian
product.

	2. Counterfactuals defined in an approximate theory of
some aspect of the world.


	The first of these ideas, cartesian product counterfactuals,
can be regarded as a special case of the Lewis-Stalnaker theory of
counterfactuals based on the closest possible world.  The metric is
just the number of components in which the two worlds differ.

	The second idea is less compatible, because approximate theories
don't necessarily provide a correspondence between states of the

\section{The uses of counterfactuals in human life and for robots}

	The first use of counterfactuals is to learn from experience.
We can learn from what might have happened as well as from what did
happen.

Something bad might have happened.

	``If there had been something blocking the road when I
went fast around that corner I would have hit it''.

Something good might have happened.

	``If I had telephoned to find out if the restaurant was
open on Monday, I'd have saved a useless trip.''

	``If there weren't another planet pulling on it, Uranus
would follow a Keplerian orbit.''

	Clearly we want our computer programs also to be able
to do this kind of learning.

	``If kangaroos had tiny tails they would topple over.''

	``If there were no friction objects would continue
at the same velocity forever.''

	``Gravity is that, which if it were not, we should all
fly away.''

	We learn from counterfactuals, because they are in
approximate theories that permit learning general statements
usable in other forms.

Query: As well as general statements, we can consider case law.
\section{Cartesian counterfactuals and their elaborations}

\section{Approximate theories}

	Instead of possible worlds we use possibility sets.
These differ from possible worlds in the following ways.

1. A possibility set does not specify everything.

2. What it does specifiy is indefinite.

3. Nevertheless, possibility sets are first order objects in
a Kripke like theory.
\section{Comparison with other approaches}

\section{Informal examples}

\section{Formalized examples}

\section{References}
\smallskip\centerline{Copyright \copyright\ 1990\ by John McCarthy}
\smallskip\noindent{\fiverm This draft of COUNTE[W90,JMC]\ TEXed on \jmcdate\ at \theTime}
%File originated on 27-Mar-90
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