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to the set of abnormality fluents since each describes rather unusual circum-
stances. Consequently, not only do models exist which entail no explanation
for
disq
(
ignite
) in case the latter is known to be true, these models are
even preferred.
The desired proliferation of explanations can, however, be achieved by a
modication known as
completion
of the fluent formula (3.3). The problem
with this implication, as it stands, being that it does not support any further
conclusions from
disq
(
ignite
), it is transformed into a bi-conditional:
9x:
(
x
)
_
_
_
in
tank-empty
low-battery
engine-problem
(3.4)
disq
(
)
ignite
Let this formula replace the state constraints listed in (3.2). Then any ac-
ceptable state which satises
disq
(
ignite
) must also satisfy at least one
of
9x:
(
x
),
,
,or
. The three
in
tank-empty
low-battery
engine-problem
observations
:
runs
after []
inexecutable after []
8x: :
in
(
x
)
^:
tank-empty
^:
low-battery
ignite
after []
for instance, entail
engine-problem
after [ ] on the basis of the completed
state constraint.
The mechanism of completion provides us with a general strategy of
how to design state constraints so as to automatically supply explanations
for observed action disqualications. Suppose
n
dierent abnormal condi-
tions, specied by fluent formulas
F
1
;:::;F
n
, are known to render impos-
sible the execution of action
a
. Instead of introducing the
n
implicational
state constraints
F
1
disq
(
a
)
;:::;F
n
disq
(
a
), we employ a (stronger)
bi-conditional as follows.
_
F
i
disq
(
a
)
(3.5)
i
=1
It obviously entails the aforementioned
n
implications, but in addition allows
to reason the other direction, i.e., from abnormalities to their possible causes.
While this is an invaluable gain of using completion, there is, however, an im-
portant objection against state constraints of the form (3.5). Namely, equat-
ing a disqualication with a disjunction of conditions presupposes complete
knowledge as to the possible reasons for an action to fail. No doubt, abnormal
action disqualications being rare exceptions by denition, the situation is
even more exceptional where this disqualication cannot be explained. Yet,
not accounting for these cases seems to ignore the fact that generally only
partial knowledge can be acquired of real-world domains. Completion being
too valuable to abandon, however, we favor the development of additional
means to deal with inexplicable abnormalities.
Prior to so doing, let us mention another crucial issue when dealing with
action disqualications, which stresses the importance of completed state
