Information Technology Reference
In-Depth Information
A formalization of this approach requires just a marginal renement of
our concept of minimizing-change successors (recall Denition 2.2.1). Namely,
the notion of distance shall now respect the preference for minimizing change
of primary fluents. Otherwise our denition remains unchanged.
Denition 2.3.1.
Let D
=(
E; F; A; L
)
be a basic action domain. Further-
more, let F
p
(
primary
fluents) and F
s
(
secondary
fluents) be two sets of
fluents such that F
p
\F
s
=
fg and F
p
[F
s
is the set of all fluents composed
of fluent names F and entities E .If S; T; T
0
are states, then T is
closer
to S than T
0
wrt.
F
p
; F
s
, written T
S
T
0
j
F
p
;F
s
,i
1. kT n Sk\F
p
kT
0
n Sk\F
p
,or
2. kT n Sk\F
p
=
kT
0
n Sk\F
p
and kT n Sk\F
s
kT
0
n Sk\F
s
.
Let C be a set of state constraints, S a state which is acceptable (wrt. C),
and a an action. A state T is
categorized minimizing-change successor
of S
and a i the following holds: There exists a preliminary successor S
0
of S
and action a obtained through direct eect E such that
1. E T ,
2. T is acceptable, and
3. there is no T
0
S
0
T j
F
p
;F
s
such that E T
0
and T
0
is acceptable.
With the rened notion of closeness of states we rst concentrate on primary
fluents (clause 1) when comparing distances. Only in case the distances are
equal with this regard, secondary fluents become the decisive factor (clause 2).
Example 2.3.1.
Let domain
D
be as in Example 2.2.2 (recall the circuit of
Fig. 2.3, with two switches). Suppose that
F
p
=
f
up
(
x
):
x 2f
s
1
;
s
2
gg
and
F
s
=
f
light
g
be the fluent categorization for
D
. When perform-
ing
toggle
(
s
1
) in the acceptable state
S
=
f:
up
(
s
1
)
;
up
(
s
2
)
; :
light
g
,
the (unique) preliminary successor is
S
0
=
f
g
, which
results through direct eect
E
=
f
up
(
s
1
)
g
as before. There exist two ac-
ceptable states containing
E
, namely,
T
1
=
f
up
(
s
1
)
;
up
(
s
2
)
;
light
g
and
T
2
=
f
up
(
s
1
)
; :
up
(
s
2
)
; :
light
g
. From
kT
1
n S
0
k\F
p
=
f
light
g\F
p
=
fg
and from
kT
2
n S
0
k\F
p
=
f
up
(
s
1
)
;
up
(
s
2
)
; :
light
s
2
)
g
we can conclude that
T
1
S
0
T
2
j
F
p
;F
s
(but not vice versa, of course). Hence
T
1
is the unique
categorized minimizing-change successor of
f:
up
(
s
1
)
;
up
(
s
2
)
; :
light
g
and
toggle
(
s
1
).
The distinction between primary and secondary fluents allows to recog-
nize `phantom' eects whenever these are obtained by changing a generally
independent property where changing a dependent one would suce to satisfy
a state constraint. In this way we have avoided, for instance, the conclusion
that a switch magically leaves its position where it was sucient to turn on
the light. On the other hand, it is obvious that this approach to the Ramica-
tion Problem relies on the existence of a suitable categorization for a domain.
The following example with a newly extended electric circuit shows that this
is not guaranteed.
up
(
s
2
)
g\F
p
=
f
up
(
