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logical consequences of Σ. But in this time, appluing the default rules, let's
choose to add:
¬Ab(Shoot, Alive, Result(Wait, Result(Load, S
0
)))
This sentence is consistent with S, so the default rule permits its addition. Now
we add in the logical consequences of this new addition with the result that the
following is added:
¬Holds(Loaded, Result(Wait, Result(Load, S
0
)))
Since we already had:
Holds(Loaded, Result(Load, S
0
))
and taken together, these two sentences give us:
Ab(Wait, Loaded, Result(Load, S
0
))
This gives us the undesired consequence:
Holds(Alive, Result(Shoot, Result(Wait, Result(Load, S
0
)))).
Therefore, with respect to the Yale shooting problem, default logic will yield
anomalous extension in just the same way that circumscription yields anomalous
models. In another word, the Hanks-McDermott problem is not merely a problem
for circumscription. The exercise of showing how it arises with default logic
offers an insight into why the difficulty arises. The intended extension arises
when the default rule is applied in chronological order (i.e., earliest abnormalities
are considered first); The anomalous extension arises when the default rules is
applied in reverse chronological order (i.e., later abnormalities are considered
first). Therefore, the intended extension is the result of postponing change until
as late as possible. Based on this result, a technique named chronological
minimization was proposed.
The Hanks-McDermott problem can be solved by the chronological
minimization approach. But the Yale shooting problem is just one example.
There are still other examples where chronological minimization supplies
counter-intuitive conclusions. The best know of these is the stolen car problem.
The stolen car problem is a family of explanation problem. In an explanation
problem, we know that certain fluents hold in some situations other then the
initial situation, and we want to know the cause for holding of these fluents. In
the stolen car scenario, a person parks the car in the morning and goes to work.
According to the common sense law of inertia it can be inferred by default that
the car is still in the car park at lunch time. However, when this person return to
