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i.e., hierarchical. Otherwise, that is, if fluents depend mutually, unmotivated
changes cannot be precluded. To see why, consider the elementary cyclic
specication
s
2
))
Cancels
(
a; s;
up
(
s
1
))
Cancels
(
a; s;
up
(
s
2
))
Causes
(
a; s;
up
(
s
1
))
Causes
(
a; s;
up
(
(2.45)
modeling the two switches connected by a tight spring of Fig. 2.5. Suppose
both
up
(
s
1
) and
up
(
s
2
) be true in initial situation
S
0
, and let
A
be
some action whose execution does not aect
s
2
). Then the
two formulas (2.45) in conjunction with the persistence axiom (2.44) are
too weak to conclude that
up
(
s
1
) and
up
(
s
2
) remain true. For neither
:Cancels
(
A; S
0
;
up
(
s
1
)) nor
:Cancels
(
A; S
0
;
up
(
s
2
)) is entailed.
Cyclic causal dependencies are no obstacle to the approach developed
in [14]. This method is based on so-called \causal implications," which, by
virtue of being directed, cannot be applied in a non-causal way. For instance,
the causal implication
up
(
s
1
)
^
up
(
s
2
)
)
light
has a dierent meaning than,
say,
up
(
s
1
)
^:
light
):
up
(
s
2
). In the original approach, successor states
are obtained by minimizing change while respecting domain-specic causal
implications. A far more simple denition of successor states based on causal
implications was presented in [73]. As opposed to [14], this subsequent method
moreover allows for the distinction between implicit qualications and rami-
cations deriving from state constraints (recall Section 2.8), the necessity of
which was rst pointed out by [38]. The reason is that in the approach [14]
one always strives for a successor state no matter how many changes are nec-
essary to this end, while [73] additionally requires all changes be explicitly
grounded on some causal implication. A more detailed comparison between
the two approaches can be found in [73]. A closely related approach, [30, 31],
is based on a nonmonotonic theory of \conditional entailment" and uses ex-
pressions similar to causal implications.
The nature of causal implications resembles the concept of causal rela-
tionships propagated in this topic. In fact, our xpoint characterization of
causal minimizing-change successors was borrowed from [73] and transferred
to causal relationships. A crucial dierence between causal implications and
relationships is that only the latter distinguishes between a context an ex-
plicitly occurred eect. E.g., the two relationships
`
1
causes
`
if
`
2
and
`
2
causes
`
if
`
1
are not interchangeable while both corresponding to the
identical causal implication, viz.
`
1
^ `
2
) `
. The following simple scenario
illustrates the usefulness of causal relationships being more expressive in this
sense.
(
s
1
) nor
(
up
up
Example 2.10.1.
Consider a more subtle, ancient method to hunt turkeys,
namely, by using a (manually activated) trapdoor. The state of this trapdoor
is formalized by the fluent name
trap-open
0
. The fluent
)
describes whether the victim is in the dangerous zone or not, and the fluent
name
at-trap
(
turkey
alive
1
is used as before. The ground underneath the trapdoor is
