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is identical to that of abnormal action disqualications, is then determined
by the model theoretic component of our action theory as it stands.
4.2 Disqualied Causal Relationships
Each state, including the initial one, resulting from the performance of action
sequences is supposed to be acceptable, that is, to satisfy all state constraints.
This implies that every constraint, as it stands, is universally valid, hence so
is the occurrence of indirect eects it triggers. In order to account for possible
exceptions to the strict truth of a state constraint, the latter is to be suitably
weakened by restricting its range of applicability to normal circumstances.
Formally, this is accomplished by rewriting a constraint
C
as
:ab
C
C
,
where
ab
C
is a new fluent which, if true, shall indicate that there happens
to be an exception to
C
. Validity of the state constraint is thus conned to
`normal', in a specic sense, states.
Any restriction to the applicability of a state constraint should of course
be transmitted to all corresponding causal relationships. If an exception to
a constraint occurs, then the indirect eects it usually triggers are no longer
expected. The following proposition shows that this comes for free if causal
relationships are automatically extracted from the modied state constraints
following the guidelines of Section 2.5.
Proposition 4.2.1.
Let E and F be sets of entities and fluent names, re-
spectively. Furthermore, let C be a variable-free state constraint and I some
influence information. If R and R
0
are the output of the generation proce-
dure depicted in Fig. 2.6 on input
(
C; I
)
and
(
:ab
C
C; I
)
, respectively,
then
"
causes
%
if
^:ab
C
2R
0
"
causes
%
if
2R implies
Proof.
Let
C
1
^ :::^ C
n
be the minimal CNF of
C
, then the minimal CNF
of
:ab
C
C
is (
C
1
_ ab
C
)
^ :::^
(
C
n
_ ab
C
). Let
^
:`
j
causes
`
k
if
:`
l
l
=1
;:::;m
l
6
=
j; l
6
=
k
be any member of
R
, then there exists some
C
i
=
`
1
_ ::: _ `
m
(where
1
i n
) such that (
k`
j
k; k`
k
k
)
2I
and 1
j 6
=
k m
. Accordingly, the
disjunct
`
1
_ :::_ `
m
_ ab
C
determines the causal relationship
^
:`
j
causes
`
k
if
:`
l
^:ab
C
l
=1
;:::;m
l
6
=
j; l
6
=
k
in
R
0
.
Qed.
