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Non Monotonic Reasoning and Common Sense Inference

	John McCarthy

	Mathematics has often developed new branches from
applied problems, and the use of mathematical logic in artificial
intelligence research seems to be following this path.

	The straightforward mathematical logical approach to
artificial intelligence is the following:  Build a data base of
general common sense facts about the world out of sentences
in a suitable first order language.  Express the facts and goals of a
particular situation as sentences in the same
language.  A suitable computer program then derives a sentence
asserting that a certain
action is appropriate.  This approach is still far from
achieving human level common sense intelligence, but it has led to
several new logical formalisms and problems
including the following:

	1. Formalized non-monotonic reasoning.  Unlike logical deduction,
common sense reasoning often reaches conclusions that would not be
reached with increased premisses.  One way, called circumscription,
of formalizing this is to assume that certain predicates have the
minimal extension compatible with the premisses.  In some sense, this
is a formalization of Ockham's razor.  In logic it leads to extremal
problems analogous to those in other mathematical subjects.

	2. Present modal logical formalisms are too weak to draw
common sense conclusions about what people don't know.  Attempts
to strengthen them often lead to inconsistency.

	3. Common sense requires the ability to reason while still
confused about the fundamental meaning of the concepts being used.
Even this may be subject to mathematically interesting formalization.
Non Monotonic Reasoning and Common Sense Inference

	The straightforward mathematical logical approach to
artificial intelligence involves a data base of
general common sense facts expressed as sentences
in a suitable first order language.  The facts and goals of a
situation are sentences in that
language.  A computer program seeks a sentence
asserting that a certain
action is appropriate.  This
has led to
several new logical formalisms and problems.

	1. Formalized non-monotonic reasoning.  Unlike logical deduction,
common sense reasoning often reaches conclusions that would not be
reached with increased premisses.  One way
of formalizing this is to assume that certain predicates have the
minimal extension compatible with the premisses.
This leads to logical minimization
problems analogous to those in analysis.

	2. Present modal logical formalisms are too weak to draw
common sense conclusions about what people don't know.  Attempts
to strengthen them often lead to inconsistency.

	3. Common sense requires the ability to reason while still
confused about the fundamental meaning of the concepts being used.
Even this may be subject to mathematically interesting formalization.