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:
up
(
s
1
)
up
(
s
2
)
:
relay
:
light
:
up
(
s
3
)
Figure 2.4.
Yet another enhancement of our electric circuit: It now includes a
third switch,
s
3
, and a relay, whose state is represented by the nullary fluent
relay
. When activated, the relay forces switch
s
2
downwards.
Example 2.3.2.
Consider the electric circuit depicted in Fig. 2.4. Let this be
modeled by domain
D
consisting of entities
s
1
,
s
2
, and
s
3
; fluent names
up
1
,
light
0
, and
relay
0
; action name
toggle
1
; and the action laws
toggle
(
x
)
transforms
f
up
(
x
)
g
into
f:
up
(
x
)
g
toggle
(
x
)
transforms
f:
up
(
x
)
g
into
f
up
(
x
)
g
Let
C
be the three state constraints
light
up
(
s
1
)
^
up
(
s
2
)
relay
:
up
(
s
1
)
^
up
(
s
3
)
relay
(2.1)
:
(
s
2
)
up
The last formula states that the activated relay attracts switch
s
2
. Let the
current state be
S
=
f:
up
(
s
1
)
;
up
(
s
2
)
; :
up
(
s
3
)
; :
light
; :
relay
g
, as shown
in Fig. 2.4.
Now, for a suitable account of possible indirect eects of toggling switches
in this circuit we are supposed to categorize the involved fluents. This is
straightforward in case of
up
(
s
1
) and
up
(
s
3
) (being primary) and
light
and
relay
(being secondary); it is easy to verify that any other choice would
immediately cause undesired eects. But what about the second switch, rep-
resented by
up
(
s
2
)? On the one hand, we naturally tend to consider it pri-
mary as before. For if
s
2
is sup-
posed not to change where light is expected to do so. On the other hand,
there is reason to consider
is toggled in the current state, then
s
1
s
3
in the current state, then the relay gets activated and, hence, is expected
to cause switch
up
(
s
2
) secondary. Namely, if we close switch
s
2
leave its position. Formal examination reveals that this
would not be the only categorized minimizing-change successor in this sce-
nario had we
F
p
=
f
up
(
s
1
)
;
up
(
s
2
)
;
up
(
s
3
)
g
and
F
s
=
f
light
;
relay
g
: The
unique preliminary successor of state
S
from above and action
toggle
(
s
3
)
