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Denition 3.2.1.
Let E , F , and A be sets of entities, fluent names, and
action names, respectively. A
disqualication observation
is of the form
a
inexecutable after [
a
1
;:::;a
n
]
where each of a; a
1
;:::;a
n
is an action (n
0
). If Res is a partial map-
ping from nite (possibly empty) action sequences to states, then this dis-
qualication observation is
true
in Res i Res
([
a
1
;:::;a
n
])
is dened but
Res
([
a
1
;:::;a
n
;a
])
is not.
In what follows, the term \observation" refers both to observations in the
original sense as introduced in Chapter 1 (c.f. Denition 1.2.5) and to dis-
qualication observations.
For a formal account of the approach to the Qualication Problem
sketched above we need means to connect abnormal disqualications of ac-
tions with the situations that give rise to them. The following notion serves
this purpose.
Denition 3.2.2.
Let E , F , and A be sets of entities, fluent names, and
action names, respectively. A
disqualifying condition
is an expression of the
form F disq
(
a
)
where F is a fluent formula and a an action.
For notational convenience, both
F
and
a
may contain variables, in which
case the disqualifying condition
F disq
(
a
) is regarded as representative
for all its ground instances. An example is
), stating
that any object clogging the tail pipe unqualies the action of starting the
engine.
A disqualifying condition
F disq
(
a
) indicates that whenever formula
F
is true, then action
a
cannot be performed even if all of its regular precondi-
tions are satised. Having disqualifying conditions requires an extended no-
tion of interpretations and models (
;Res
) of action scenarios. If an action
a
is disqualied in a particular state
Res
([
a
1
;:::;a
n
]), then this dictates that
Res
([
a
1
;:::;a
n
;a
]) is undened regardless of whether the underlying tran-
sition model,
, suggests a successor state of
Res
([
a
1
;:::;a
n
]) and
a
.To
allow for comparison of models in view of preferring those with the fewest pos-
sible abnormal disqualications, a third component is introduced into both
interpretations and models. This new argument, denoted
Ab
, reflects all situ-
ations where an action cannot be performed on account of some disqualifying
condition.
Denition 3.2.3.
Let
(
O; D
)
be a ramication scenario, and let Q be a set
of disqualifying conditions. An
interpretation with abnormalities
for
(
O; D
)
is a triple
(
;Res ; Ab
)
where is the transition model of D, Res is a
partial function which maps nite (possibly empty) action sequences to ac-
ceptable states, and Ab is a set of non-empty action sequences such that the
following holds:
1. Res
([ ])
is dened.
2. For any sequence a
=[
a
1
;:::;a
k−
1
;a
k
]
of actions (k>
0
):
(
x
)
disq
(
in
ignite
