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designed such that nothing being
with the trapdoor open can be
alive. This is represented by the state constraint
at-trap
8x
[
at-trap
(
x
)
^
trap-open
:
alive
(
x
) ]
(2.46)
We can open the trapdoor and entice the turkey, respectively, via these two
action laws:
open
transforms
f:
trap-open
g
into
f
trap-open
g
entice
(
x
)
transforms
f:
at-trap
(
x
)
g
into
f
at-trap
(
x
)
g
While the state of the trapdoor can possibly aect the turkey being alive,
the animal is alert to the extent that it would never kill itself by moving
towards the open trapdoor; hence,
)
but
at-trap
(
turkey
) may not so. The latter is intended to give rise to the
implicit qualication
:
trap-open
for the action
entice
(
turkey
). Therefore
the correct influence information is
I
=
f
(
trap-open
;
alive
(
turkey
))
g
.In
conjunction with our state constraint (2.46), this determines a single causal
relationship, viz.
trap-open
may influence
alive
(
turkey
causes
:
(
) f
(
)
(2.47)
trap-open
alive
turkey
at-trap
turkey
Given the state
S
=
f
g
(say, af-
ter having enticed the turkey), performing the action
open
yields the state
f
alive
(
turkey
)
;
at-trap
(
turkey
)
;
open
g
as preliminary successor, which
violates the state constraint. Since
(
)
;
(
)
; :
alive
turkey
at-trap
turkey
open
occurred as eect, the given
causal relationship is applicable, which results in the unique and expected
successor state
f:
alive
(
turkey
)
;
at-trap
(
turkey
)
;
trap-open
g
.
Consider state
S
=
f
alive
(
turkey
)
; :
at-trap
(
turkey
)
;
trap-open
g
and
action
trap-open
), on the other hand. Performing this action yields the
preliminary successor
f
(
entice
turkey
g
,too,
but now obtained through the direct eect
E
=
f
at-trap
(
turkey
)
g
. There-
fore the only available causal relationship is not applicable; hence, no suc-
cessor state exists. In other words,
:
trap-open
(
)
;
(
)
;
alive
turkey
at-trap
turkey
trap-open
is revealed as additional,
implicit qualication for
), as expected. Notice that we are
only able to distinguish between these two cases by employing causal rela-
tionship (2.47) but not the analogue, namely,
(
entice
turkey
at-trap
(
turkey
) causes
:
alive
(
turkey
) f
trap-open
Since these two relationships both correspond to the same causal implication
at-trap
(
turkey
)
^
trap-open
):
alive
(
turkey
), this distinction goes be-
yond the expressiveness of causal implications.
In [69], which improves previous work where indirect eects are `compiled'
into action descriptions [68], rst-order formulas resembling causal relation-
ships are employed to dene dependencies between eects and their indirect
consequences. These formulas are of the form
