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fail to produce light. But globally minimizing abnormality in this scenario
does not yield this conclusion. Obviously, some abnormality is inevitable.
One minimal model is therefore given by
:ab
2
with regard to the rst ac-
tion, and
ab
1
with regard to the second. This reflects the expected course of
events. Yet we can just as well assume the rst ramication unqualied (i.e.,
ab
2
), which then would avoid the necessity of assuming a disqualication of
the following ramication (i.e.,
:ab
1
). For if the bulb does not break as a
consequence of toggling
s
2
, then light turns on as the usual indirect eect
of toggling
s
1
afterwards. This gives us a second, unintended model, where
the more powerful battery is supposed down and light is on in the end.
4.3 Causing Exceptions to State Constraints
Global minimization being inappropriate when assuming away exceptions to
state constraints, too, our solution to the Qualication Problem furnishes a
ready approach to satisfactorily tackling abnormalities in the new context.
Since exceptional circumstances can be brought about as side eect of per-
forming actions, fluents representing these circumstances should be made
subject to both ramication and, otherwise, persistence. Being
a priori
un-
likely to occur, these fluents are to be minimized initially to the largest rea-
sonable extent, just like the fluents that describe abnormal disqualications
of actions.
To summarize, the amalgamation of the Ramication and Qualication
Problem is addressed as follows. Each state constraint
C
which admits ex-
ceptions is replaced by the weaker fluent formula
ab
C
C
, with
ab
C
being
a distinct new fluent name. The reading of the modied constraint is that
now
C
holds only under normal circumstances. As for the case of action
disqualications, the fluent
ab
C
should be engaged in additional state con-
straints dening conditions for an exception to
C
. In order to reflect that
ab
C
indicates an exceptional situation, this fluent is subject to minimization,
i.e., belongs to the set of abnormality fluents of the domain at hand.
Example 4.3.1.
Let
D
be the qualication domain of Example 4.2.1, and let
F
ab
=
f
malfunc
1
;
malfunc
2
;
;
; ab
1
; ab
2
g
broken
wiring-problem
Let
be the transition model of
D
, and suppose
O
consists of the obser-
vation
:
up
(
s
1
)
^:
up
(
s
2
) after []
Since no abnormality needs to be granted, the qualication scenario (
O; D
)
admits a unique preferred model (
;Res
) where
:
s
2
)
2 Res
([ ])
and
Res
([ ])
\F
ab
=
fg
. Performing
toggle
(
s
2
)in
Res
([ ]) has the direct
eect
up
(
s
2
) and the indirect eects
broken
and, hence,
ab
1
according to
the following causal relationships.
(
s
1
)
; :
(
up
up
