Information Technology Reference
In-Depth Information
Figure 3.1.
In general, we would consider it abnormal if we failed to start our
car. But would we still do so if we deliberately insert a potato into the tail pipe
beforehand?
of the Qualication Problem so far might fail to recognize intuitively expected
preferences among abnormalities.
Example 3.2.2.
Let
D
be the ramication domain of Example 3.2.1 but in-
cluding the fluent name
heavy
1
, denoting whether its argument is a heavy
object, and the action name
insert
1
, denoting the introduction of an object
into the tail pipe. The new action is accompanied by the law
insert
(
x
) transforms
f:
in
(
x
)
g
into
f
in
(
x
)
g
The action is, however, abnormally disqualied if the object to be inserted is
too heavy, which is accounted for by the disqualifying condition
heavy
(
x
)
disq
(
).
Suppose it is known that the engine is not running and the tail pipe is not
housing a potato. What, then, would be the expected outcome of rst trying
to insert a potato and, afterwards, trying to start the engine (c.f. Fig. 3.1)?
Since there is no reason to believe that the potato is too heavy, the rst action
should be assumed qualied by default. The tail pipe thus becoming clogged
disqualies the second action. While this is the expected conclusion, our for-
mal approach suggests equally plausible a second course of events. To see why,
let
O
consist of the single observation
:
insert
(
x
)) in addition to
in
(
x
)
disq
(
ignite
) after [ ]. Suppose
is the transition model of
D
, and let
Res
1
and
Res
2
be two partial mappings
from action sequences to states designed as shown in Fig. 3.2. Then both in-
terpretations
M
1
=(
;Res
1
; Ab
1
) with
Ab
1
=
f
[
insert
(
pt
)
;
ignite
]
g
and
M
2
=(
;Res
2
; Ab
2
) with
Ab
2
=
f
[
runs
^:
in
(
pt
)]
g
) are models of (
O; D
).
The rst model,
M
1
, suggests that inserting the potato is successful and,
hence, renders it impossible to start the engine afterwards|just as expected.
Model
M
2
, on the other hand, declares the action of inserting the potato
unqualied in the rst place. The crucial point, now, is that by assuming this
disqualication one avoids to grant a disqualication of starting the car. Con-
sequently,
Ab
1
6 Ab
2
, hence
M
1
6 M
2
(nor, of course,
M
2
M
1
). Since
there is obviously no model of (
O; D
) of the form (
;Res ; fg
),
3
insert
(
pt
both
M
1
and
M
2
are preferred. Thus the observation
3
The reason being that either of [
insert
(
pt
)] or [
insert
(
pt
)
;
ignite
] must be
abnormally disqualied according to the underlying transition model in con-
junction with the disqualifying conditions.
