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supports unsound conclusions. For illustration purpose, let us formalize a
scenario mentioned by [88].
Example 3.7.1.
Suppose we park our car overnight in a neighborhood that
is known for its suering from a tail pipe marauder. Then chances are good
that the rascal has struck by the next morning so that we had better check
for a potato in the tail pipe before trying to start the car. Let
D
be the qual-
ication domain of Example 3.2.2 but with action name
replaced by
stay-overnight
0
. The latter having a non-deterministic eect, it is specied
by a pair of non-exclusive action laws, viz.
insert
transforms
fg
into
fg
stay-overnight
stay-overnight
transforms
f:
in
(
pt
)
g
into
f
in
(
pt
)
g
Let
O
consist of the observation
:
runs
^:
in
(
pt
) after [ ], then the qualica-
tion scenario (
O; D
) admits two categories of preferred models (
;Res
), one
of which satisfy
:
(
)
2 Res
([
]) while the others claim
in
pt
stay-overnight
that
]). Hence nothing is entailed
as to whether there is an abnormal disqualication of
ignite
or not after
staying overnight.
Now to the problems of chronologically minimizing in this scenario. The fol-
lowing formula species the new, non-deterministic action:
(
) be true in
Res
([
in
pt
stay-overnight
2
T
rue
(
stay-overnight
;t
)
^ 2
T
rue
(
:
in
(
pt
)
;t
)
2
T
rue
(
in
(
pt
)
;t
+1)
_ 2
T
rue
(
:
in
(
pt
)
;t
+1)
(3.17)
That is to say, if at time
t
we stay overnight and there is no potato in the tail
pipe, then at time
t
+1 this may or may not have changed. Consider this for-
mula in conjunction with the specication of action
as given by im-
plication (3.16), and suppose given
2
T
rue
(
:
in
(
pt
)
;
1) in conjunction with
the events
2
T
rue
(
stay-overnight
;
1) and
2
T
rue
(
ignite
;
2). Then im-
plication (3.17) allows no denite conclusion about T
rue
(
ignite
(
)
;
2), hence
in
pt
3
T
rue
(
:
)
;
2) following the principle of chronological ignorance, which
in turn implies
2
T
rue
(
runs
;
3) according to (3.16). Thus the conclusion
that
ignite
be qualied at time 2 is sanctioned despite the possibility that
the tail pipe marauder has struck by then. This undesired conclusion proves
that the \what-you-don't-know-won't-hurt-you" principle is not suited for in-
determinate information. While the Qualication Problem requires assuming
away abnormal circumstances whenever they do not provably hold, this is in
general too credulous if the performance of a non-deterministic action ren-
ders quite possible such circumstances. A \what-you-can't-expect-won't-hurt-
you" principle would be appropriate|clearly, an abnormal disqualication of
ignite
after carelessly leaving unattended the car in the dangerous neigh-
borhood is to be expected from one of the possible eects of staying overnight,
which is why this potential disqualication ought not be assumed away.
Exploiting ramication as the key to the Qualication Problem shares
with
Motivated Action Theory
(MAT, for short) [104, 2] the basic insight
(
in
pt
