Information Technology Reference
In-Depth Information
:
up
(
s
1
)
:
light
Figure 2.1.
An electric circuit consisting of a battery, a switch, and a light bulb,
which lights up if and only if the switch is closed. The two dynamic components
are described by two fluents, both of which are false in the current state.
to be true in any state, are called
state constraints
. States satisfying all
constraints of a domain shall be called
acceptable
.
State constraints, as we have seen, give rise to additional eects if vi-
olated after the direct eects of an action have been considered. Actions
having indirect eects conflicts with the general assumption that nothing
changes except what is mentioned in an action law. This can easily be seen
with our example circuit: Let
S
=
f:
g
be the current state
as depicted in Fig. 2.1. Performing a
toggle
(
s
1
) action in
S
produces the
state
S
0
=
f
up
(
s
1
)
; :
light
g
following the known action laws (1.2) and ac-
cording to the denition of how to apply them. This is not the expected
successor state, as is formally evident by its violating the underlying state
constraint,
light
up
(
s
1
). Fortunately we were foresighted enough to call
\preliminary" states like
S
0
. The fact that often it does not suce to com-
pute, via the application of action laws, the mere direct eects is called the
Ramication Problem
.
3
One straightforward `solution' to the Ramication Problem is to circum-
vent it. That is, one could stick to the assumption that action laws be com-
plete in specifying the entire eect. To this end, all indirect eects must
somehow be compiled into the action laws. This procedure, however, bears
two major problems demonstrating its inadequacy. First, it may require an
enormous number of action laws to account for every possible combination
of indirect eects. To see why, consider a model of an electric circuit where a
distinguished switch is involved in
n
sub-circuits each of which additionally
contains a switch-bulb pair; see Fig. 2.2. Dening all eects of toggling the
separate switch solely by means of action laws then requires 2
n
+1
dier-
ent laws, one for each possible combination of truth-values assigned to the
(
s
1
)
; :
up
light
3
The name shall suggest the picture that a state description literally ramies
into various directions, each following a possible chain of indirect eects.
