Information Technology Reference
In-Depth Information
attracts the second switch,
sw
2
. Hence, the latter is open in the nally re-
sulting state. Notice, however, that as soon as the rst switch is in the upper
position, the sub-circuit involving the light bulb gets closed. This may ac-
tivate the light bulb for an instant, that is, before the second switch jumps
its position as a result of the relay activation. If this is indeed the case,
then this `flash' might be registered by the photo device. Hence, while it is
clear that the light bulb is o in the resulting state, fluent
detect
possi-
bly becomes true.
17
Accordingly, two causal successor states exist for ini-
tial state
f:
up
(
s
1
)
;
up
(
s
2
)
;
up
(
s
3
)
; :
light
; :
relay
; :
detect
g
and action
toggle
s
1
), which are obtained as follows. The unique preliminary successor
state along with the corresponding direct eect is
(
(
f
(
s
1
)
;
(
s
2
)
;
(
s
3
)
; :
; :
; :
g ; f
(
s
1
)
g
)
(2.14)
up
up
up
light
relay
detect
up
The rst component violates both the rst and the second constraint of (2.13).
There are several ways to proceed. First, we can apply causal relationship
up
(
s
1
) causes
relay
if
up
(
s
3
) followed by
relay
causes
:
up
(
s
2
)if
>
, which
results in
(
f
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
;
relay
; :
light
; :
detect
g ;
f
s
2
)
g
)
The rst component satises all of the state constraints and, consequently, is
a causal successor state.
Another possibility to process the state-eect pair (2.14) is to apply the
following sequence of causal relationships:
up
(
s
1
)
;
relay
; :
up
(
(
s
1
)
causes
if
(
s
2
)
up
light
up
up
(
s
1
)
causes
if
up
(
s
3
)
relay
(2.15)
causes
:
up
(
s
2
) f
>
relay
:
up
(
s
2
)
causes
:
light
if
>
In words, we rst conclude the light bulb turns on due to the second switch
being on. However, since the activation of the relay causes
up
(
s
2
) to become
false, we have to `turn o' the light bulb again via the nally applied causal
relationship. In this way we obtain the following overall resulting state-eect
pair.
(
f
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
;
relay
; :
light
; :
detect
g ;
f
g
)
Though dierent from the chain of causal relationships we considered rst,
the extended chain results in the identical causal successor state. But we have
17
up
(
s
1
)
;
relay
; :
up
(
s
2
)
; :
light
What actually happens depends on the physical properties of both the relay and
the light detector. Lacking this precise information, common sense interprets
the situation as giving rise to non-determinism. See the following section for a
detailed discussion on this phenomenon.
