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:
up
(
s
1
)
:
up
(
s
2
)
Figure 2.5.
Two switches are mechanically connected through a tight spring, whose
tension does not allow the switches occupy dierent positions.
Now, suppose we switch up the rst switch in the state
f:
up
(
s
1
)
; :
up
(
s
2
)
g
.
This yields the preliminary successor
S
0
=
f
s
2
)
g
. On the other
hand, suppose we switch down the second switch in the state
f
up
(
s
1
)
;
up
(
s
2
)
g
.
This obviously yields the very same preliminary successor
S
0
. Nonetheless
the expected outcomes in these two situations dier considerably: In the rst
case the nal result should be that both
up
(
s
1
)
; :
up
(
s
2
are in the upper po-
sition, as opposed to the second case where both are expected down! This
distinction can only be made by referring to the diering direct eects, viz.
E
1
=
f
up
(
s
1
)
g
as opposed to
E
2
=
f:
up
(
s
2
)
g
. The former enables only
the application of the very rst relationship in (2.4) to the intermediate re-
sult, the latter only the application of the very last one. The two resulting
state-eect pairs are
s
1
and
s
2
)
g
)
(
f:
up
(
s
1
)
; :
up
(
s
2
)
g ; f:
up
(
s
2
)
; :
up
(
s
1
)
g
)
Thus in either case we obtain the intended successor state.
(
f
(
s
1
)
;
(
s
2
)
g ; f
(
s
1
)
;
(
up
up
up
up
Incidentally, this example also illustrates the necessity of distinguishing trig-
gering eects from contexts in causal relationships: There is an obviously
crucial dierence between the situation where
up
(
s
1
) became true in the
context
:
up
(
s
2
) and the situation where
:
up
(
s
2
) became true in the con-
text
up
(
s
1
).
7
Curious as the last example may seem at rst glance, such tight cou-
pling between fluents frequently occurs in an important class of state con-
straints. So-called \denitional" constraints dene, for the sake of conve-
nience, a fluent as abbreviation for a complex fluent formula. The constraint
7
Let us add the marginal note that dividing the condition for the occurrence of
an indirect eect into two components matches the distinction often made in
philosophical accounts of causality between so-called \triggering" and \predis-
posal" causes.
