Information Technology Reference
In-Depth Information
a) Res
(
a
)
is dened if and only if Res
([
a
1
;:::;a
k−
1
])
is dened and
(
Res
([
a
1
;:::;a
k−
1
])
;a
k
)
is not empty, and
b) Res
(
a
)
2
(
Res
([
a
1
;:::;a
k−
1
])
;a
k
)
.
If I
=(
;Res
)
and I
0
=(
;Res
0
)
are interpretations, then I is
less
abnormal
than I
0
, written I I
0
,i Res
([ ])
\F
ab
Res
0
([ ])
\F
ab
.A
model
of a plain qualication scenario
(
O; D
)
is an interpretation
(
;Res
)
such that each o 2O is true in Res. A model is
preferred
i there is no
other model which is less abnormal. An observation o is
entailed
i it is true
in all preferred models of
(
O; D
)
.
Example 3.3.1.
Let
D
be the ramication domain of Example 3.2.2 but now
including the fluent names
disq
(
ignite
)
0
and
disq
(
insert
)
1
plus the steady
state constraints
9x:
)
8x
[
heavy
(
x
)
disq
(
insert
(
x
)) ]
(
x
)
disq
(
in
ignite
Consider
F
ab
=
f
))
g
, then
D
is a (plain) qualication domain. Let
O
consist of the observation
in
(
pt
)
;
heavy
(
pt
)
; disq
(
ignite
)
; disq
(
insert
(
pt
:
runs
after []
then (
O; D
) is a qualication scenario. Suppose
be the transition model
of
D
. The domain being deterministic, interpretations (
;Res
) are uniquely
characterized by the initial state
Res
([ ]), e.g.
Res
1
([ ]) =
f:
; :
(
)
; :
(
)
; :disq
(
)
; :disq
(
(
))
g
runs
in
pt
heavy
pt
ignite
insert
pt
Obviously, (
;Res
1
) is a model of (
O; D
) as it satises
:
runs
2 Res
1
([ ]).
Since
Res
1
([ ])
\F
ab
=
fg
, this model is preferred. Moreover, it is unique in
that respect because the initial value of the only existing non-abnormality
fluent, viz.
, is xed by the given observation. Thus whatever is true
in this model is also entailed by our scenario, (
O; D
). In particular, we have
in
(
pt
)
2 Res
1
([
insert
(
pt
)]) and, hence,
disq
(
ignite
)
2 Res
1
([
insert
(
pt
)])
according to transition model
. Consequently, (
O; D
) entails both the two
observations
runs
in
(
pt
) after [
insert
(
pt
)]
inexecutable after [
(
)]
ignite
insert
pt
