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relay is known to take its time for warming up until it reaches the power to
attract the switch, whereas the light detector registers the shortest flash with
utmost alertness. Then it seems unreasonable to consider the possibility that
the detector stays o when toggling switch
s
1
in the situation depicted in
Fig. 2.8.
One approach to this problem is to introduce an explicit notion of time,
namely, in specifying the exact delay between the occurrence of an eect and
its cause. This, however, is not in the spirit of the Ramication Problem.
For the latter is concerned with accounting for those indirect eects which
so rapidly follow the performance of an action that common sense consid-
ers them virtually instantaneous. Had we assumed precise knowledge of the
relay's delay, then its attracting switches fell into the category of so-called
\delayed" eects. Though certainly of importance, too, these eects need to
be meticulously distinguished from those indirect eects investigated in the
context of the Ramication Problem. For delayed eects deserve a separate
state transition, that is, they should not occur during the same transition step
as its triggering eect. In contrast, solving the Ramication Problem means
to account for all indirect eects that are summarized in a single state tran-
sition. This amounts to performing qualitative reasoning about causal lags,
as opposed to quantitative reasoning, which would require precise knowledge
of virtually indistinguishable time intervals. Qualitative reasoning, which ac-
knowledges the fact that common sense often lacks precise knowledge, con-
siders equal all causal lags greater than zero.
The very last remark, however, reveals one critical aspect which we
have neglected hitherto. Causal lags may indeed dier even qualitatively,
namely, in possibly being zero. An important category of indirect eects
obviously of this nature is eects triggered by so-called denitional state con-
straints, which we have already touched upon in Section 2.4. Recall constraint
8x
[
down
(
x
)
:
up
(
x
)]. Having some instance like
up
(
s
1
) as direct or indi-
rect eect, this gives rise to additional indirect eect
:
s
1
). The causal
lag between these two eects is zero|not even for the tiniest fraction of time
a state is imaginable where
up
(
s
1
) already and
down
(
s
1
) still hold. The to-
tal absence of a causal lag qualitatively distinguishes this ramication from
most ones we have considered throughout the previous sections. Let us call
coupled
all eects which occur with causal lag zero, as opposed to
triggered
eects. Failing to account for this distinction may lead to surprising conclu-
sions even if granted that, as we have argued, temporal dierences between
causal lags are to be neglected. The following scenario illustrates why coupled
and triggered eects must not be treated alike.
(
down
Example 2.7.1.
Suppose a bowl well lled with soup is standing on a rectan-
gular table; see Fig. 2.9. Whenever the left hand side of the table is lifted up
but not the right hand side (or vice versa), then the spilling soup stains the
tablecloth. If, however, both sides are lifted up simultaneously, then no soup
is expected to spill out. Let us model this scenario by a basic action domain
consisting of entities
lhs
and
rhs
(left and right hand side of the table),
