Information Technology Reference
In-Depth Information
Thus far we have seen how applying a single causal relationship generates
one particular indirect eect. The direct eects of an action may of course
give rise to several indirect eects. Moreover, these eects may in turn cause
further eects, possibly triggering even more and so on and so forth. Closing
switch
s
3
in our circuit involving the relay (Fig. 2.4), for example, causes an
activation of that relay, which in turn triggers an indirect eect by attracting
switch
s
2
. These chains of indirect eects are modeled by serial application
of causal relationships.
Example 2.4.2.
Let
D
be the basic action domain formalizing the electric
circuit of Fig. 2.4 as in Example 2.3.2. As for the various causal dependencies
among the components, we notice, rst, that light turns on if either of the
two switches
s
1
and
s
2
is caused up with the other one already being
in its upper position. Conversely, light is o if either of these switches is
caused down, regardless of the other switch's position. This is reflected by
introducing the following four causal relationships:
up
(
s
1
) causes
light
if
up
(
s
2
)
:
up
(
s
1
) causes
:
light
if
>
(2.5)
(
s
2
) causes
if
(
s
1
)
:
(
s
2
) causes
:
if
>
up
light
up
up
light
Analogously, the state of the relay causally depends upon the two switches
s
1
and
s
3
as follows:
if
>
up
(
s
3
) causes
relay
if
:
up
(
s
1
)
:
up
(
s
3
) causes
:
relay
if
>
(2.6)
Finally, the activated relay forces switch
s
2
be down, that is,
relay
:
(
s
1
) causes
if
(
s
3
)
(
s
1
) causes
:
up
relay
up
up
relay
causes
:
up
(
s
2
) f
>
(2.7)
Now, let
S
=
f:
up
(
s
1
)
;
up
(
s
2
)
; :
up
(
s
3
)
; :
light
; :
relay
g
be the current
state, as depicted in Fig. 2.4. Performing the action
toggle
(
s
3
) yields the
following state-eect pair.
s
3
)
g
)
The one and only applicable causal relationship is the bottom left one in (2.6),
which activates the relay:
(
f:
(
s
1
)
;
(
s
2
)
;
(
s
3
)
; :
; :
g ; f
(
up
up
up
light
relay
up
(
f:
up
(
s
1
)
;
up
(
s
2
)
;
up
(
s
3
)
; :
light
;
relay
g ; f
up
(
s
3
)
;
relay
g
)
As a consequence of this indirect eect, the relationship of (2.7) is now ap-
plicable, which results in
(
f:
up
(
s
1
)
; :
up
(
s
2
)
;
up
(
s
3
)
; :
light
;
relay
g ; f
up
(
s
3
)
;
relay
; :
up
(
s
2
)
g
)
This state-eect pair allows no further application of causal relationships.
Incidentally, its rst component is acceptable wrt. the underlying state con-
straints (c.f. formulas (2.1)) and constitutes the (unique) resulting state ex-
pected when we close the third switch in initial state
S
.
