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up
(
s
1
)
:
light
1
:
up
(
s
2
)
:
up
(
s
0
)
:
light
2
up
(
s
n
)
:
light
n
Figure 2.2.
An electric circuit consisting of a battery, a separate switch
s
0
, and
n
sub-circuits each containing a switch
s
i
and a light bulb
light
i
. Exponentially
many cases have to be considered when specifying the eect of closing
s
0
solely
by means of action laws.
switch being operated and the other
n
switches. An arbitrary example is the
following:
toggle
(
s
0
) transforms
f:
up
(
s
0
)
;
up
(
s
1
)
; :
light
1
; :
up
(
s
2
)
; :
light
2
;:::g
into
f
light
2
;:::g
The other laws look no less unpleasant than this one. This is clearly far from
what we consider an adequate specication. Full adequacy is achieved only
if the original, simple specication (1.2) of action
(
s
0
)
;
(
s
1
)
;
light
1
; :
(
s
2
)
; :
up
up
up
toggle
(
x
) also applies
to switch
in this more complex domain, and if the
n
state constraints
s
0
light
i
s
i
) do the rest. Notice that the size of this specication
is linear (in
n
) as opposed to the exponential number of action laws.
The second problem with exhaustive action laws containing the entire
eect is that the introduction of a new state constraint may require, in the
worst case, a redenition of the entire set of action laws used before. Just
suppose yet another switch-bulb pair
up
(
s
n
+1
)
;
light
n
+1
be added to the
circuit of Fig. 2.2. Then all of the previously carefully designed action laws
for
(
s
0
)
^
(
up
up
s
0
) |and recall their exponential number|would need revision.
It so seems we have to think about real solutions to the Ramication
Problem.
(
toggle
2.2 Minimizing Change
We have seen that the basic issue with the Ramication Problem is to resolve
the conflict between the possibility of indirect eects and the postulate of
persistence, i.e., that a fluent does not change unless it is explicitly so stated
in the respective action law. The challenge, therefore, is to nd a suitably
