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In-Depth Information
causal relationship
:
(
x
)if
>
are applicable to the state-
eect pair (
S
0
;E
). Suppose we rst apply instance
fx 7!
(
x
) causes
down
up
g
. This yields
lhs
the state-eect pair
(
f
(
)
; :
(
g ;
f:
down
(
lhs
)
; :
down
(
rhs
)
;
up
(
lhs
)
g
)
)
; :
(
)
; :
(
)
; :
up
lhs
down
lhs
up
rhs
down
rhs
stain
We can proceed with the second instance,
fx 7!
rhs
g
, of the above relation-
ship, thus obtaining
f
up
(
lhs
)
; :
down
(
lhs
)
;
up
(
rhs
)
; :
down
(
rhs
)
; :
stain
g
as
a causal successor state. Yet we can also rst insert the application of
up
(
lhs
) causes
stain
if
:
up
(
rhs
). Followed by the conversion of
:
up
(
rhs
),
we thus obtain
f
g
as an-
other possible causal successor, where surprisingly a stain has been produced!
The identical two causal successor states can be obtained in case relationship
instance
:
(
)
; :
(
)
;
(
)
; :
(
)
;
up
lhs
down
lhs
up
rhs
down
rhs
stain
(
) causes
(
)if
>
is applied rst, allowing to produce
down
rhs
up
rhs
a stain via
(
) causes
if
:
(
).
up
rhs
stain
up
lhs
The general problem which causes the unexpected possibility of a stain
here, is that causal relationships introduce an articial causal lag between
coupled eects. Some other causal relationship may exploit this lag for
`squeezing in' a triggered eect which can never occur in reality. As a conse-
quence, our approach to the Ramication Problem needs to be rened in that
it respects the distinction between virtually and truly instantaneous indirect
eects.
To this end, some state constraints are distinguished as being
steady
. All
denitional constraints enjoy this property, but others might as well. Con-
sider, as an example, the situation depicted in Fig. 2.10. The corresponding
state constraint
8x
[
;x
) ] is to be regarded as
steady. The criterion for characterizing a state constraint as steady is that not
even for an instant a situation is imaginable where this constraint is violated.
All indirect eects determined by steady state constraints have causal lag
zero, i.e., are coupled. As argued, during the application of causal relation-
ships the insertion of an eect with real causal lag in between the generation
of coupled eects needs to be prohibited. This is achieved by rst apply-
ing only causal relationships stemming from steady state constraints, until
none of these constraints is violated. Only thereafter a triggered eect may
be generated, again followed by accounting for all coupled eects necessary
to satisfy the steady constraints, and so on until an overall acceptable state
obtains. This strategy is formalized in the following denition of successor
state.
Denition 2.7.1.
Let E , F , A, and L be sets of entities, fluent names, ac-
tion names, and action laws, respectively. Furthermore, let C be a set of state
constraints and R a set of causal relationships, and let C
s
C and R
s
R
be designated sets of steady constraints and relationships, respectively. If S
is an acceptable state and a an action, then a state S
0
(
;x
)
(
location
a
location
b
is a
successor
of S
