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the car park in the evening he finds that the car has gone. Now the problem is to
reason backward in time to the causes of the car's disappearance. In this case, the
only reasonable explanation is that the car was stolen some time between
morning and evening. Therefore, the default assumption that the car was still in
the car park at lunch time is open to question.
The stolen car problem can be represented by the following three sentences.
Here two successive Wait actions are used to represent the interval between
morning and evening implicitly; the fluent Stolen represent that the car is not in
the car park.
SC1: ¬Holds(Stolen, S
0
) (2.40)
SC2: S
2
= Result(Wait, Result(Wait, S
0
)) (2.41)
SC3: Holds(Stolen,S
2
) (2.42)
Furthermore, let (Arb1) and (Arb2) be the following axioms:
Arb1: Result(
a
1,
s
1)=Result(
a
2,
s
2)
ã
a
1=
a
2 ∧
s
1=
s
2 (2.43)
Arb2: S
0
≠ Result(
) (2.44)
Then, with chronological minimization, it will be manifested that the car
disappeared during the second Wait, i.e.,
a
,
s
Ab(Wait, Stolen, Result(Wait, S
0
)) ∧ ¬Ab(Wait, Stolen, S
0
)
But in fact, the car could equally well have disappeared during the first Wait, and
we would like the formalization of the common sense law of inertia to respect
this possibility. In another word, what we would like is to be able to manifest the
following result
Ab(Wait, Stolen, Result(Wait, S
0
)) ∨ Ab(Wait, Stolen, S
0
)
and also that there exist two models M1 and M2 such that
M1 |= Ab(Wait, Stolen, Result(Wait, S
0
))
and
M2 |= Ab(Wait, Stolen, S
0
).
