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In-Depth Information
is
S
0
=
f:
g
, obtained through direct
eect
E
=
f
up
(
s
3
)
g
. There are exactly three acceptable states containing
E
,
viz.
(
s
1
)
;
(
s
2
)
;
(
s
3
)
; :
; :
up
up
up
light
relay
T
1
=
f:
(
s
1
)
; :
(
s
2
)
;
(
s
3
)
; :
;
g
up
up
up
light
relay
T
2
=
f
up
(
s
1
)
;
up
(
s
2
)
;
up
(
s
3
)
;
light
; :
relay
g
T
3
=
f
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
; :
light
; :
relay
g
To see why, observe rst that both
are completely deter-
mined by the positions of the switches (c.f. formulas (2.1)). There are four
dierent combinations of switch positions given that
and
light
relay
up
(
s
3
), one of which,
however, is not acceptable, namely, where only
s
1
is down. As for the re-
spective distance to
S
0
,wehave
kT
1
n S
0
k\F
p
=
f
s
2
)
g
kT
2
n S
0
k\F
p
=
f
up
(
s
1
)
;
light
g\F
p
=
f
up
(
s
1
)
g
kT
3
n S
0
k\F
p
=
f
up
(
s
2
)
;
relay
g\F
p
=
f
up
(
(
s
1
)
;
(
s
2
)
g\F
p
=
f
(
s
1
)
;
(
s
2
)
g
up
up
up
up
It follows that both
T
1
S
0
T
3
j
F
p
;F
s
and
T
2
S
0
T
3
j
F
p
;F
s
whereas
T
1
and
T
2
are not comparable wrt.
S
0
. Hence the two are categorized
minimizing-change successors of
S
and
toggle
(
s
3
).
The existence of the unintended successor, i.e.,
T
2
, where switch
s
1
changes
instead of switch
s
2
, can be explained by the necessity of changing a pri-
mary fluent|aside from
up
(
s
3
), which was the direct eect|to arrive at
an acceptable state. In the intended successor, i.e.,
T
1
, this change concerns
switch
s
2
, triggered by the activation of the relay. This very activation is
avoided, however, by moving switch
s
1
instead, as done in
T
2
.Inbothways
we respect the idea of minimizing change of primary fluents. Hence the two
successor states.
The reason for this unexpected result is that we necessarily fail to assign
a unique appropriate category to fluent
up
(
s
2
), whose role is twofold: On the
one hand, it should be considered primary regarding the sub-circuit involving
switch
s
1
and the light bulb, and on the other hand, it behaves like a
secondary fluent as regards the relay. From a general perspective, this proves
that it might be impossible to globally characterize a fluent either as always
being `active' or as always being `passive.' The way a fluent behaves rather
seems a more local property, depending on which of the related components
one considers. In other words, a fluent can be active regarding one aspect
and passive regarding another. As for our example, one might suggest just
introducing an additional category of, say,
tertiary
fluents,
F
t
, with even
lower priority than secondary fluents. Then taking
up
(
s
1
)
;
up
(
s
3
)
2F
p
,
up
(
s
2
)
;
relay
2F
s
, and
light
2F
t
yields the expected unique resulting
state, provided an appropriate extension of our notion of state distance wrt. a
categorization (recall Denition 2.3.1). However, this particular classication
requires a deeper analysis of possible direct and indirect eects in the electric
circuit and seems, at rst glance, quite unnatural. It is, moreover, not hard
