Information Technology Reference
In-Depth Information
a) Res
(
a
)
is dened if and only if Res
([
a
1
;:::;a
k−
1
])
is dened;
(
Res
([
a
1
;:::;a
k−
1
])
;a
k
)
is not empty; and no F disq
(
a
k
)
2Q
exists such that F is true in Res
([
a
1
;:::;a
k−
1
])
.
b) Res
(
a
)
2
(
Res
([
a
1
;:::;a
k−
1
])
;a
k
)
.
c) a
2 Ab if and only if Res
([
a
1
;:::;a
k−
1
])
is dened and there is
some F disq
(
a
k
)
such that F is true in Res
([
a
1
;:::;a
k−
1
])
.
Put in words, whenever
Res
([
a
1
;:::;a
k−
1
]) entails the antecedent of a dis-
qualifying condition for action
a
k
, then
Res
([
a
1
;:::;a
k
]) is not dened and
Ab
includes the sequence [
a
1
;:::;a
k
].
The appropriate preference criterion and entailment relation can then be
dened straightforwardly on the basis of comparing the additional compo-
nents,
Ab
. Informally speaking, the less action sequences are declared dis-
qualied by a model the less abnormal the latter. Entailment is then decided
on the basis of least abnormal models, which thus are the preferred ones.
Denition 3.2.4.
Let
(
O; D
)
be a ramication scenario with transition
model and Q a set of disqualifying conditions. If I
=(
;Res ; Ab
)
and
I
0
=(
;Res
0
; Ab
0
)
are interpretations with abnormalities for
(
O; D
)
, then I
is
less abnormal
than I
0
, written I I
0
,i Ab
Ab
0
.A
model with abnor-
malities
of
(
O; D
)
is an interpretation
(
;Res ; Ab
)
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
with abnormalities of
(
O; D
)
.
Let us see how this account of abnormal action disqualications solves
our initial example.
Example 3.2.1.
Let
D
be the ramication domain consisting of entity
pt
,
fluent names
runs
0
in
1
, and action name
and
accompanied by
ignite
the action law
g
. Furthermore, let
in
(
x
)
disq
(
ignite
) be a disqualifying condition. Suppose
be the tran-
sition model of
D
, and let
O
1
consist of the single observation
ignite
transforms
f:
runs
g
into
f
runs
:
runs
after []
Two models
M
1
=(
;Res
1
; Ab
1
) and
M
2
=(
;Res
2
; Ab
2
) exist for
the scenario (
O
1
; D
), namely, where
Res
1
([ ]) =
f:
)
g
and
Res
2
([ ]) =
f:
runs
;
in
(
pt
)
g
. Since the antecedent of the instance
fx 7!
pt
g
of the underlying disqualifying condition,
; :
(
runs
in
pt
), is true in
Res
2
([ ]), we have
Ab
2
=
f
[
ignite
]
g
. In contrast, the rst model entails no
abnormal disqualication, that is,
Ab
1
=
fg
. Hence,
M
1
M
2
. Model
M
1
being the unique preferred one, we see that our scenario entails the observa-
tion
runs
after [
ignite
].
Let, on the other hand,
O
2
consist of the two observations
(
x
)
disq
(
in
ignite
:
runs
after
[]
in
(
pt
)
after
[]