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C00002 00002	.cb COMPUTATION WITH STATES OF KNOWLEDGE
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.cb COMPUTATION WITH STATES OF KNOWLEDGE


	A physical strategy says what to do in each state of the world.
A general strategy says what to do in each state of knowledge about
the world.
We can often find a physical strategy to accomplish a task, but it
may be unrealizable, because the executor of the strategy may now
sufficiently know the state of the world.  Often we can regard
a general strategy as an approximation to a physical strategy
containing only knowable tests and functions of state.
It may be easy to represent the possible physical states
and describe the effects of actions on them in terms of the new
state states that arise.  Of course, the descriiption of the physical
state doesn't ever give the state of the world; we
use an idealized physical state that is a function of the world state
and describe the effects of actions on that idealized physical state.
For the idealization to work, the goal predicate must also be a function
of the idealized state.

	It is often possible and convenient to compute with idealized states
of knowledge in the same way.  We choose a space of "states of knowledge".
In geneal, it will be a function (many-one) of the real state of
knowledge - even of the real state of knowledge of the idealized
physical state.  This is because the number of real states of knowledge
is often unmanageably large, so we gain by taking only certain knowledge
into account.  It will be particularly simple if there are only a
finite number of idealized states of knowledge, and we can give the
effect of an action on such a state of knowledge.  Besides physical
actions there is an action of forgetting that may be useful by reducing
the number of states.

	If there are ⊗n physical states, there are ⊗2↑n_-_1 knowledge states,
so the compression of knowledge states in the idealization had
better be pretty great.

	All this is somewhat vague, so we proceed with an example.
A good example is a generalization of the "rotating table" problem
described in Martin Gardner's column in the February 1979 issue of
%2Scientific American%1 (p. 16).  (Well it looks like "rotating
table" may yield to simpler methods).  The generalization is to
more holes and more arms.