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C00002 00002	Non Monotonic Reasoning and Common Sense Inference
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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.
	Mathematical logic suggests making an intelligent
computer program that expresses what it knows in a logical
language and decides what to do by finding a provable
sentence asserting that a course of action is appropriate
for achieving its goals.  This approach to artificial intelligence involves
the following:

	First we express as sentences in a suitable logical language the
following kinds of information:

	1. General facts about the world, its changes in time
and the effects of actions.  These may include laws of physics
and other sciences, but it is even more important to include
common sense qualitative information.  For example, the fact
that a dropped egg will fall to the floor and probably break
is understood by a person quite separately from his knowledge
of the differential equations of gravitation.

	Besides physical facts about the world, it is important
to include facts about information and how it is obtained.
The information-obtaining effects of external and internal actions
are decribed along with their physical effects.

	2. Facts about particular situations in which the machine
is required to act.

	3. The structure of goals and priorities, i.e. how to
evaluate the predicted consequences of various courses of action.
Facts about how humans and other agents will evaluate outcomes
are relevant here as well as relevant to predicting their
behavior.

	The intelligent program then decides what to do by
deducing the consequences of various courses of action and
determining what course of action produces preferred outcomes.
The evaluation will often have to be probabilistic and this
requires that information for computing the required probabilities
be present in the data base at least to the same extent that
humans have it.

	This approach to artificial intelligence was proposed in
(McCarthy 1960), and there have been numerous attempts to implement
parts of it.

	Various difficulties have arisen, and some people believe
they show that the approach can't succeed.  Our view is that
most likely the difficulties will eventually be overcome.

reference to Leibniz approach