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∂18-Mar-90  2237	hewitt@ai.mit.edu 	the uses of Circumscription    
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Date: Mon, 19 Mar 90 01:38 EST
From: Carl Hewitt <hewitt@ai.mit.edu>
Subject: the uses of Circumscription
To: JMC@sail.stanford.edu
Cc: hewitt@ai.mit.edu, kirsh%cogsci@ucsd.edu
Message-Id: <19900319063820.8.HEWITT@DUE-PROCESS.AI.MIT.EDU>

John,

I have enclosed the section of my AIJ paper that deals with
Circumscription in case you would like to comment or make
suggestions.

Thank you very much for correcting some of my misunderstandings
about Circumscription.

Sincerely,

Carl

\subsubsection{The Deductive Indecision Problem in Circumscription}

In this section I present an example to show how the Deductive
Indecision Problem arises in the use of Circumscription in OIS.
Circumscription [McCarthy: 1980, McCarthy: 1986] has been introduced
as a way to close logical axiom systems to provide qualifications that
are useful in compactly expressing axioms and their qualifications.
Circumscription and related nonmonotonic logics are very useful
for this purpose.

This section of the paper uses Circumscription to illustrates some points
about Deductive Indecision in Microtheories.  We illustrate how
Circumscription can be used as a powerful tool to analyze the
qualifications of Microtheories.

Consider the question of the safety of the Diablo Canyon nuclear power
plant which came up as a crucial issue as part of the process of
deciding whether or not it should be given an operating license.

Let's suppose that all participants accept the following propositions:

\procedure %
trained-operators

earthquake-zone
\endproc

\noindent
which state that the operators are trained and that the nuclear plant is in an
earthquake-zone

\procedure %
{\rm Axiom 1:}
\keyword{If} trained-operators, \keyword{then} safe-plant
\endproc

\noindent
which states that if the operators are trained then the plant is safe

\procedure %
{\rm Axiom 2:}
\keyword{If} earthquake-zone, \keyword{then} \keyword{not}(safe-plant)
\endproc

\noindent
which states that if the plant is in an earthquake zone then
it is not safe.

The above propositions taken together are inconsistent in they
imply both \code{safe-plant} and \code{\keyword{not}(safe-plant)}.

Using Circumscription, we can remove the contradiction by
replacing each axiom \code{$A_{i}$} with an new axiom of the form

\procedure %
\keyword{If} \keyword{not}($C_{i}$), \keyword{then} $A_{i}$
\endproc

where \code{$C_{i}$} is a new unique propositional variable which I
call a {\em Caveat} and which McCarthy calls a {\em Normality
Condition}.

So Axiom 1 is transformed to Axiom 1':

\procedure %
{\rm Axiom 1':}
\keyword{If} trained-operators \keyword{and} \keyword{not}(caveat-1), \keyword{then} safe-plant
\endproc

and Axiom 2 is transformed to Axiom 2': 

\procedure %
{\rm Axiom 2':}
\keyword{If} earthquake-zone \keyword{and} \keyword{not}(caveat-2), \keyword{then} \keyword{not}(safe-plant)
\endproc

\noindent

Circumscription provides that conclusions can be drawn from the
maximal consistent models of the axioms by varying which Caveats are
taken to be true and false.  In this way Circumscription eliminates the
contradiction in the Microtheory obtained by joining the Microtheories of
the proponents and opponents of licensing the reactor.  However, note
that the Deductive Indecision Problem has been enlarged by
Circumscription because in addition to be being Undecided about
\code{safe-plant}, the new Circumscription Microtheory is undecided
about \code{caveat-1} and \code{caveat-2} as well.  There are two
inconsistent extensions: one in which \code{caveat-2} is true along with
\code{safe-plant} and vice-versa.

In response to the above discussion, the utility proposes the
following axiom:

\procedure %
{\rm Interaction Axiom 3:}
\keyword{If} trained-operators, \keyword{then} caveat-2
\endproc

\noindent
because it maintains that its operators have been trained to deal with
earthquakes and so the fact that power plant is in an earthquake zone
does not imply that it is not safe.  If the above proposition is
accepted and the discussion ends here, then by Circumscription, we can
conclude that the power plant is safe.

However, the opponents to the plant also have a new axiom to propose:

\procedure %
{\rm Interaction Axiom 4:}
\keyword{If} earthquake-zone, \keyword{then} caveat-1
\endproc

\noindent
because they maintain that being in an earthquake zone implies that
having trained operators does not imply that the plant is safe.

The machinery that Circumscription establishes to join together two
formally inconsistent microtheories has become part of the content of
the dispute between the participants!  Actually this is not to surprising
given the entrenched nature of the conflict.

Neither side is willing to accept each others new proposals for axioms
and so Circumscription is applied to produced Axioms 3' and 4':

\procedure %
{\rm Interaction Axiom $3'$:}
\keyword{If} trained-operators \keyword{and} \keyword{not}(caveat-Interaction-Axiom-3),
\keyword{then} caveat-2
\bline
{\rm{Interaction Axiom $4'$:}}
\keyword{If} earthquake-zone \keyword{and} \keyword{not}(caveat-Interaction-Axiom-4),
\keyword{then} caveat-1
\endproc

There is no resolution and the Deductively Undecided atomic
propositions have been enlarged to include
\code{caveat-Interaction-Axiom-3} and \code{caveat-Interaction-Axiom-4}.

But the discussion is not done yet!  The utility proposes the following
axiom:

\procedure %
{\rm{Second-Order Interaction Axiom 5:}}
\keyword{If} trained-operators, \keyword{then} caveat-Interaction-Axiom-4
\endproc

\noindent
because it believes that if the operators are trained to handle
earthquakes, then the power plant being in an earthquake zone does not imply
that trained operators will not have a safe plant.

\noindent
while the opponents counter with:

\procedure %
{\rm{Second-Order Interaction Axiom 6:}}
\keyword{If} earthquake-zone, \keyword{then} caveat-Interaction-Axiom-3
\endproc

\noindent
because they believe that if the power plant is in an earthquake zone,
then having trained operators does not imply that the
earthquake zone does not make the plant unsafe because
even though the operators are trained, they will not be able
to keep the plant safe. 

The participants are arguing about the {\em process} of the forum in
which they make their representations in a way which is couched in
logical language.  The same kind of behavior should be expected in any
other forum that is provided to the participants:  they will use
whatever machinery is available to them in order to further
incompatible entrenched commitments specifically including all the
various nonmonotonic logics.

Determination of the safety of the power plant is a very difficult issue.
So it is not surprising that it cannot be solved using Deduction.
However the Deductive Indecision Problem can be made
worse!  Deduction is concerned exclusively with the {\em internal}
structure of Microtheories.  Its great power stems from the ability to
analyze Microtheories from any context in which they
might have arisen.  However, it seems that it has left out something
crucial by concentrating only on the {\em logical} relationships among
Microtheories.