Information Technology Reference
In-Depth Information
The minimal CNF of
C
is
(
9x: :
up
(
x
)
_
light
)
^
(
8y:
up
(
y
)
_:
light
)
1. Regarding conjunct
C
1
=
9x: :
up
(
x
)
_
light
we obtain the following:
{ In case
j
=1
;k
= 2 we have (
up
(
x
)
;
light
)
2I
, which yields
up
(
x
) causes
if
8x:
up
(
x
)
light
(
x
))
62 I
.
2. Regarding conjunct
C
2
=
8y:
up
(
y
)
_:
light
we obtain the following:
{ In case
j
=1
;k
= 2 we have (
up
(
y
)
;
light
)
2I
, which yields
{ In case
j
=2
;k
= 1 we have (
light
;
up
:
up
(
y
) causes
:
light
if
>
(
y
))
62 I
.
Thus closing either switch causes light provided all other switches are closed;
and conversely, opening either switch causes the light be o afterwards re-
gardless of other switches|as one would expect.
{ In case
j
=2
;k
= 1 we have (
light
;
up
With this extension of our basic algorithm we conclude the discussion on
how causal relationships may be automatically generated whenever suitable
influence information can be provided. It is, however, not claimed that the
latter is always possible with our basic notion of influence information. More
sophisticated means to specify potential influence may be required in certain
domains. E.g., a fluent having the potential to aect another fluent may
depend on whether the former occurs armatively or negated. To reflect this,
the concept of influence information needs to be extended so as to relate fluent
literals and not just fluents. Further generalization may allow for restricting
potential influence to circumstances expressed by arbitrary fluent formulas.
15
Whichever sophistication is required depends on the domain at hand. The
simpler the notion of potential influence|provided it suces|, the more is
gained by the automatic extraction of causal relationships compared to these
drawing up all by hand.
2.6 Non-minimal Successor States
The attempts to solve the Ramication Problem which we have discussed
prior to causal relationships were based on the idea of minimizing change to
the largest reasonable extent. The employment of causal relationships does
15
Notice that this is unnecessary in case the circumstances follow from the state
constraints. Of course, fluent
relay
can aect
up
(
s
2
) only in case
relay
is
true (in our circuit depicted in Fig. 2.4). However, the very state constraint
relay
:
up
(
s
2
) encodes this knowledge, which is why it needs not be inte-
grated into the information of potential influence.
