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C00002 00002	situat[f83,jmc]		Modifications to the situation calculus
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situat[f83,jmc]		Modifications to the situation calculus

	The situation calculus is based on the equation

	s' = result(e,s)

where  e  is an event, and  s'  is the new situation that results
when  e  occurs in the situation  s.  In the examples treated so
far the events have been mainly actions such as  move(x,l),  denoting
the action of moving the object  x  to the location  l.  Another
example recently treated is  paint(x,c)  standing for the action
of painting the object  x  the color  c.  Another way of handling
painting is  paint1(x,p)  where  p  represents some paint.  Painting
with a particular source of paint is more particular that painting
a color, but obviously the same event can be described in both
ways.

	This suggests regarding events as resembling situations
in being not fully describable.  In the painting case we would
write

	occurs(e,paint(x,c))

or

	occurs(e,paint1(x,c)).

We would then have axioms

	∀x p e s.¬ab aspect1(e,s) ∧ occurs(e,paint1(x,p))
⊃ color(x,result(e,s)) = color1 p,

	∀x c e s.¬ab aspect2(e,s) ∧ occurs(e,paint(x,c))
⊃ color(x,result(e,s)) = c

and

	∀p c e.color1 p = c ∧ occurs(e,paint1(x,p)) ⊃ occurs(e,paint(x,c)).


SITUATIONS AND STATES

	The situation calculus is intended to refer to the real world,
and the real world has much more detail than it is feasible to
take into account.  Therefore, we approximate the real world by
systems with a small finite amount of detail.  For example,
the missionaries and cannibals problem can be solved by a system
with just 32 states - a state being given by a triplet (m c b)
expressing the numbers of missionaries, cannibals and boats on
the initial bank of the river.  The 32 state system is small enough
to be exhaustively searched.  Indeed the usual advantage of
discrete state systems is that search is more often feasible.
  Our object is to study the relation
between the real world as described by the situation calculus and
the finite state systems we use to approximate it.  We also want
to study the relations between two finite state systems approximating
the same real world situation where one of them is more detailed
than the other.