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nonmon[w85,jmc]		Article for Scientific American on non-monotonic reasoning

Dear Mr. Flanagan:

	I would like to write an article for Scientific American
about non-monotonic reasoning and its application to giving
computers common sense knowledge and reasoning ability.

	Non-monotonic reasoning has been studied by artificial intelligence
researchers for about the last ten years.  About 100 papers have
been published.  I believe the results that have
been obtained will be of interest to Scientific American readers.
Moreover, they as accessible, if well explained, to a lay scientific
reader as most of the topics treated in Scientific American.

	Besides my general qualification to write about AI, I am
the originator of one of the three approaches to formalizing
non-monotonic reasoning.  Mine is called circumscription, and is
perhaps the most popular currently.

	The general ideas of non-monotonic reasoning are elaborated
in the non-mathematical sections of my 1980 paper which is enclosed.
However, a capsule summary may be useful to you.

	Whenever we humans reason we must limit the facts we take
into account.  Some of the conclusions we draw are guaranteed to
remain if we take additional facts into account.  These are
the consequences of monotonic rules of inference.  Other conclusions
reasonably made from a given collection of facts may be withdrawn
when more facts become available.  These are non-monotonic
inferences.  Mathematical logic, as developed over the last 150
years has covered mononotic reasoning only.  Until about the middle
1970s whenever logicians, philosophers and computer scientists
encountered examples of non-monotonic reasoning they tended to
regard them as hopelessly informal.  According to their prejudices
one either regarded them as evidence that human reasoning could
not be formalized or as inadequate reasoning --- to be replaced
later by proper deductions.

	From about 1975, several people independently realized that
non-monotonic reasoning could be treated mathematically by
extensions of mathematical logic.  A landmark was the publication
in 1980 of a special issue of the journal {\it Artificial Intelligence}
that included three formal systems of non-monotonic reasoning:
non-monotonic logic by Drew McDermott and Jon Doyle, a logic of
defaults by Raymond Reiter, and circumscription by myself.
The first computer program using non-monotonic reasoning in
an extensive and systematic way was Jon Doyle's earlier ``Truth maintenance
system''.

	Since that time non-monotonic reasoning has
been studied by increasing numbers of computer scientists, mathematical
logicians and philosophers.

	The major application has been to the formalization of facts
about the common sense world.  The goal is to prepare a database
of common sense facts that can be used by any intelligent computer
program needing them.  Non-monotonic systems have made it much more
feasible to put this information into a computer.  Unfortunately,
we humans have several more mysteries to solve before we can program
computers to exhibit our own ability at common sense reasoning.

	Nevertheless, the present state of the problem is worth
presenting to a {\it Scientific American} audience.

Sincerely,

	Suppose a conclusion $p$ is inferred from a set $A$ of
premises by ordinary deductive reasoning.  Then $p$ will still
follow if $A$ is enlarged by adding more premises.  This property
is called monotonicity by analogy with monotonic numerical functions.

	Common sense human reasoning is often non-monotonic.  For example,
knowing that I own a car you may infer that it is appropriate
to ask for a ride to some meeting.  When you later learn that my
car is in the repair garage, you no longer draw this conclusion.

	Since about 1975 AI researchers have determined that
intelligent computer programs must also reason non-monotonically
and have developed various ways of representing this kind of
reasoning in mathematical logic and making computer programs
to do it.

	It was first thought that non-monotonic reasoning was
hopelessly informal and would therefore be very difficult to
program into computers.  However, by 1980 a special issue of
the journal {\it Artificial Intelligence} appeared with three
systems of non-monotonic reasoning.  Non-monotonic logic
was proposed by Drew McDermott and Jon Doyle.  A logic of
defaults was proposed by Raymond Reiter, and I proposed a
method of non-monotonic reasoning called circumscription.

	Circumscription is a precise way of jumping to the
conclusion that the set of objects that have a certain property
is minimal given the facts we take into account.