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then the only model for (
O
2
; D
)is
M
2
from above, which thus is preferred.
The state
Res
2
([
ignite
]) is not dened due to our disqualifying condition.
Hence, (
O
2
; D
) entails the observation
inexecutable after [].
This example demonstrates that our account of the Qualication Problem
meets the basic requirement: Abnormal disqualications may be assumed
away by default, and in fact are so whenever this oers a coherent account of
the observations. Consequently, the new entailment relation is nonmonotonic.
Our way of assuming away unlikely action disqualications for the gener-
ation of preferred models can be characterized as globally minimizing abnor-
malities. No preference is given in case an action scenario implies that there
be one out of two alternative abnormalities without necessitating a partic-
ular one. Suppose, for instance, observation suggests that there either be a
potato in the tail pipe or a used chewing gum in the car's door lock thus
rendering unexecutable the action of unlocking the door. This gives rise to
two preferred models, one of which accounts for the rst and the other for
the second abnormal disqualication. The two models are considered equally
plausible, which raises the question whether so doing might not be overly
credulous. If, say, the neighborhood where we have left the car unattended
for some time suers from frequent strikes of a tail pipe marauder, then like-
lihood might favor the conclusion that we will be unable to start the engine
while succeeding in unlocking the door.
One solution to this problem is the explicit introduction of probability val-
ues for each potential abnormal disqualication. In most real-world domains,
however, it seems dicult if not impossible to acquire knowledge this pre-
cise. The Qualication Problem is therefore concerned with qualitative rather
than quantitative reasoning about unlikely disqualications of actions.
2
Ac-
cordingly, we will later (in Section 3.5) provide means to distinguish dierent
degrees of (im-)probability. This will enable us to prefer minimization of ab-
normalities that are
a priori
more unlikely to occur than others.
The question remains whether global minimization of abnormal action
disqualications risks to ignore other fundamental reasons for preferring an
abnormality over another one|that is, reasons which are not grounded on
a priori
dierences in likelihood. Within an isolated state, preference can
also be caused by observations entailing a certain abnormality. Our approach
accounts for this via the notion of disqualifying conditions. On the other
hand, the various states that are passed during the evolution of a system are
not at all isolated. Consequently, preference of some abnormality over another
one may also be caused by the dynamics of action theories. That is to say,
a particular abnormal disqualication might naturally come about by state
transition, in which case causality may provide good reasons for preferring
this very abnormality over alternatives. The following simple extension of
our introductory example illustrates this point and shows that our account
ignite
2
More to nonmonotonic vs. probabilistic reasoning in the brief historical account
in Section 3.7.
