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els M
0
=(
;Res
0
)
of
(
O; D
)
and all f
ab
2F
ab
:If f
ab
2 Res
([ ])
n Res
0
([ ])
,
then there is some f
ab
0
f
ab
such that f
ab
0
2 Res
0
([ ])
n Res
([ ])
.
In words, a preferred model is obtained by rst choosing a minimization
strategy, that is, a strict ordering which respects the given partial one. Then
the model is preferred whose evolution function
Res
satises the following:
Suppose some abnormality fluent
f
ab
is initially true in
Res
but false in the
evolution function
Res
0
of some other model. Then there must be another
abnormality fluent
f
ab
0
of higher priority than
f
ab
according to the chosen
strict ordering and which is initially false in
Res
but true in
Res
0
.
Example 3.5.1.
Let
D
be the qualication domain of Example 3.4.1 but with
abnormality fluent
mysterious
(
ignite
) added as an additional cause for
disq
(
ignite
). Furthermore, let the following information regarding degrees
of abnormality be given:
tank-empty
<
low-battery
<
in
(
pt
)
<
mysterious
(
ignite
)
tank-empty
<
engine-problem
<
mysterious
(
ignite
)
Suppose
be the transition model of
D
, and let
O
consist of the observa-
tions
:
after []
runs
inexecutable after []
ignite
:
after []
tank-empty
Given that
is false initially in any model of (
O; D
), each
of
low-battery
;
engine-problem
;
in
(
pt
)
;
mysterious
(
ignite
) oers as ex-
planation for the observed disqualication. Following the
a priori
knowl-
edge of likelihood given by
<
, we obtain two preferred models, namely,
M
1
=(
;Res
1
), where
Res
1
([ ])
\F
ab
=
f
tank-empty
low-battery
; disq
(
ignite
)
g
, and
)
g
.
8
Consequently,
low-battery
_
engine-problem
after [ ] is entailed by the
qualication domain (
O; D
), as is
:
in
(
pt
)
^:
mysterious
(
ignite
) after [].
Highly unlikely causes such as a potato being in the tail pipe, let alone a
mysterious disqualication, are thus assumed away.
M
2
=(
;Res
2
), where
Res
2
([ ])
\F
ab
=
f
; disq
(
engine-problem
ignite
This completes our formal account of the Qualication Problem. Let us
summarize: A qualication domain is supposed to contain a distinguished set
of fluents
F
ab
, each of which describes abnormal circumstances and thus is
to be assumed false by default. This assumption, however, needs to be re-
stricted to the initial state, so that these fluents are subject to the general
law of persistence but are also potentially (directly or indirectly) aected by
the performance of actions. Among these so-called abnormality fluents are
expressions, denoted
disq
(
a
), which represent the property of action
a
be-
ing abnormally disqualied. State constraints relating
disq
(
a
) with possible
8
Tacitly assuming that both
Res
1
and
Res
2
are otherwise arbitrary but satisfy
the conditions of Denition 3.3.2.