Information Technology Reference
In-Depth Information
The second point to be made, which completes the overall argument, is
to justify our minimizing abnormalities initially. But given that causality
is eective only forward in time, it is clear that no causal reason for an
abnormality in the initial state can possibly be known of. This by no means
implies that such a causal reason does not exist. But if it does, then it must
lie outside the scenario specication, hence has no influence on the correct
reasoning about this scenario.
Having justied our strategy of how to cope with the Qualication Prob-
lem, we proceed with developing a formal account of this approach. To begin
with, any so-called qualication domain is supposed to include, for each ac-
tion
a
, the fluent
disq
(
a
) stating whether or not action
a
is abnormally
disqualied in a state. Abnormal disqualications indicate abnormal circum-
stances. The latter might be specied with the help of fluents which, too,
are expected to be assumed false by default. Example fluents of this kind
might be
in
(
pt
) and
heavy
(
pt
), as normally tail pipes are not clogged by
potatoes, let alone the possibility of a potato being too heavy to lift. Fluents
describing abnormal circumstances can be combined in state constraints to
describe the conditions for a particular action being abnormally disqualied.
We make no formal presuppositions as to the structure of these constraints,
but we will later, in the following section, argue for a general strategy of how
to design them.
Denition 3.3.1.
A
plain
6
qualication domain
D is a ramication do-
main with a distinguished subset F
ab
, called
abnormality fluents
, of the set
of all fluents so that disq
(
a
)
2F
ab
for each action a. The
transition model
of D is a mapping from pairs of an acceptable state and an action into
(possibly empty) sets of states such that S
0
2
(
S; a
)
i :disq
(
a
)
2 S and
S
0
is successor of S and a.
Notice that the transition model of a qualication domain assigns no next
state whenever an action is abnormally disqualied, regardless of whether
successor states exist.
Like in the approach based on global minimization, the new minimiza-
tion policy is realized by means of a model preference criterion. Informally
speaking, the less abnormality fluents are initially true the better.
Denition 3.3.2.
A
plain qualication scenario
is a pair
(
O; D
)
where D
is a plain qualication domain and O is a set of observations. An
interpreta-
tion
for
(
O; D
)
is a pair
(
;Res
)
where is the transition model of D and
Res is a partial function which maps nite (possibly empty) action sequences
to acceptable states and which satises the following:
1. Res
([ ])
is dened.
2. For any sequence a
=[
a
1
;:::;a
k−
1
;a
k
]
of actions (k>
0
),
6
The reason for calling \plain" these qualication domains is that for the mo-
ment all abnormalities are considered equally likely.
