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exists a preferred model
M
0
of (
O; D
) such that
M
0
M
. This implies the
existence of a corresponding prioritized extension
E
0
of
(
O;D
)
according
to the rst part (\
(
") of this proof. From
M
0
M
we conclude that there
exists some
f
ab
0
2 D
D
which is applied in
E
0
n E
but no
f
ab
2 D
D
with
higher priority and which is applied in
E n E
0
. This contradicts
E
being
prioritized extension.
Qed.
An immediate consequence of this one-to-one correspondence is that, as
far as observations are concerned, the notion of skeptical entailment in pri-
oritized default theories resulting from our axiomatization and the notion of
entailment suggested by our action theory coincide.
Corollary 3.6.2.
Let
(
O; D
)
be a qualication scenario with axiomatization
(
O;D
)
. An observation is entailed by
(
O; D
)
i the corresponding formula
(c.f. (3.10) and (3.11), respectively) is skeptically entailed by
(
O;D
)
.
Proof.
The claim is a consequence of Theorem 3.6.2 following the lines of the
proof of Corollary 3.6.1.
Qed.
3.7 Bibliographic Remarks
The Qualication Problem was introduced and so named in [76] as one of
several arguments making manifest the urge for nonmonotonic representation
and reasoning frameworks. The very article already anticipated the solution
of introducing abnormality predicates which are to be (globally) assumed
away by default. This solution was formally elaborated in [78] based on the
by then existing nonmonotonic formalism of so-called circumscription [77]. It
has rst been observed in [64], however, that globally minimizing abnormal
disqualications of actions fails to suitably account for disqualications that
occur for reasons of causality.
10
Rather than oering a solution, however,
10
It is remarkable that the proposal put forth in the very article [78] to address
the Frame Problem by globally minimizing change has been proved erroneous
by a counter-example that shows some striking similarities to the refutation of
global minimization as means to tackle the Qualication Problem. Suppose we
consider abnormal any change of a fluent's truth value during the execution
of an action, as suggested in [78]. Then the
Yale Shooting
problem, which we
already touched upon earlier in this topic, arises as follows (c.f. [49]): Given
that shooting at a turkey with a loaded gun causes the former to drop dead,
we should expect exactly this to happen when we load the gun, wait for a short
period, and then shoot. Yet globally minimizing abnormalities in this scenario
produces a second model where the gun surprisingly becomes unloaded during
the intermediary action of waiting and the turkey survives! While the magical
change of the gun's status is abnormal, the turkey surviving the shot is normal
in the above sense|as opposed to the change of its life status in the intended
model. Hence, this second model minimizes abnormality as well, though it
is obviously counter-intuitive. The problem here is essentially that uniformly
considering abnormal all changes is ill-dened. A gun that becomes magically
unloaded while waiting deserves being called abnormal but not the death of
the turkey if being shot at with a loaded gun, which is perfectly normal from
