Information Technology Reference
In-Depth Information
:
up
(
s
1
)
up
(
s
2
)
:
light
Figure 2.3.
The electric circuit of Fig. 2.1 enhanced by a second switch. What
would you expect as to the outcome of closing
s
1
in the current state?
toggle
(
x
)
transforms
f
up
(
x
)
g
into
f:
up
(
x
)
g
toggle
(
x
)
transforms
f:
up
(
x
)
g
into
f
up
(
x
)
g
The two switches and the light bulb being serially connected, we introduce
the state constraint
light
up
(
s
1
)
^
up
(
s
2
).
Let the current state be the acceptable
f:
(
s
1
)
;
(
s
2
)
; :
g
as
up
up
light
depicted in Fig. 2.3. Now suppose
s
1
) be performed in this state,
then the unique preliminary successor is
S
0
=
f
up
(
s
1
)
;
up
(
s
2
)
; :
light
g
,
which is obtained through the direct eect
E
=
f
up
(
s
1
)
g
. This state violates
the state constraint. There are two acceptable states containing
E
, namely,
T
1
=
f
(
toggle
g
.Asfor
the respective distance to
S
0
, we observe that
T
1
n S
0
=
f
light
g
and
T
2
n
S
0
(
s
1
)
;
(
s
2
)
;
g
and
T
2
=
f
(
s
1
)
; :
(
s
2
)
; :
up
up
light
up
up
light
=
f:
up
(
s
2
)
g
. Thus neither
T
1
S
0
T
2
nor
T
2
S
0
T
1
. Consequently,
both
T
1
and
T
2
are minimizing-change successors.
So instead of coming to the obvious conclusion that the light must turn on as
a side eect of toggling
s
1
, an equally possible course of events is suggested,
namely, that switch
s
2
leaves its position and the light stays o!
What is the reason for this unexpected outcome? A closer examination of
the underlying state constraint reveals it. From
s
2
)we
can deduce that
up
(
s
1
)
light
_:
up
(
s
2
) but not the stronger implication
up
(
s
1
)
light
(nor, of course,
up
(
s
1
)
:
up
(
s
2
)). In words, suppose we
know that switch
(
s
1
)
^
(
light
up
up
is in the upper position, then it follows that light is
s
1
on
or
switch
s
2
is down. It does not necessarily follow that the light is on.
Therefore, if the state constraint becomes violated by
up
(
s
1
) becoming true,
the mere disjunction
light
_:
up
(
s
2
) needs to be satised. Obviously, this
can be achieved either by changing
:
light
to
light
or,
voila
, by changing
up
s
2
). The pure state constraint does not allow to distinguish
between these two possibilities in view of preferring the former, as one would
like. Hence the two minimizing-change successor states.
(
s
2
)to
:
(
up
