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C00002 00002	%probab[e89,jmc]	Formalized Bayesianism Requires Non-monotonic Logic
C00005 00003	\smallskip\centerline{Copyright \copyright\ 1989\ by John McCarthy}
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%probab[e89,jmc]	Formalized Bayesianism Requires Non-monotonic Logic
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\title{Formalized Bayesianism Requires Non-monotonic Logic}

	Some computer scientists, e.g. (Cheeseman 198xx)
have supposed that Bayesianism and formalized nonmonotonic
reasoning are rivals for dealing with uncertainty in
artificial intelligence.  This is a mistake.  Dealing with
uncertainty in the common sense world sometimes requires
probabilities, but it always requires nonmonotonic reasoning
whenever the system is supposed to be able to deal with
new facts, supplementing but not contradicting old facts,
 that may change conclusions derived on the basis of the
old facts.  Formal consideration of probabilities is required
when their numerical values are significant, i.e. not
infinitesimals or infinitesimally close to 1.

	The required nonmonotonic reasoning has to be formalized
if the facts are represented as sentences of logic.  This
is appropriate when the reasoning is to be done by a computer
program capable of taking a wide variety of facts into account.
The probabilists haven't felt the need for understanding
nonmonotonic reasoning, because they do the nonmonotonic part
informally.

	To fix the ideas consider a simple example.  A computer
program is to be designed that represents what it knows by
sentences of logic and which is capable of advising its user
whether to carry his umbrella when he leaves for work.  Suppose
it to have the following sentences in its memory.

$$prob(rain) = 0.01$$

$$\all day(should.carry.umbrella(day) \iff prob(rain,day) > 0.2).$$
\smallskip\centerline{Copyright \copyright\ 1989\ by John McCarthy}
\smallskip\noindent{This draft of PROBAB[E89,JMC]\ TEXed on \jmcdate\ at \theTime}
%File originated on 06-Aug-89
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