Information Technology Reference
In-Depth Information
a
b
loc
1
loc
2
Figure 2.10.
These two blocks are connected by a rm bar. Whenever one of them
changes its location, e.g., from
loc
1
to
loc
2
, then the other block moves as well.
Not even for an instant can the two blocks occupy dierent locations. Hence the
state constraint
8x
[
location
(
a
;x
)
location
(
b
;x
) ] is to be considered steady.
and a i the following holds: Set L contains an applicable action law in-
stance a
transforms
C
into
E and there exist states S
0
;S
0
;:::;S
n
;S
0
n
and
sets of fluent literals E
0
;E
0
;:::;E
n
;E
0
n
(n
0
) such that S
0
=(
S n C
)
[ E,
E
0
=
E,
;
R
s
(
S
0
n
;E
0
n
)
and, for each
0
i n, S
i
is acceptable wrt. C
s
and S
0
n
is acceptable.
Example 2.7.2.
Consider
E
=
f
lhs
;
rhs
g
,
F
=
f
up
1
;
down
1
;
stain
0
g
, and
A
=
f
;
R
s
(
S
0
;E
0
)
;
R
(
S
1
;E
1
)
;
R
s
(
S
1
;E
1
)
;
R
:::
(
S
0
;E
0
)
lift-both-sides
0
g
, and let
L
consist of
lift-both-sides
transforms
f
down
(
lhs
)
;
down
(
rhs
)
g
into
f:
down
(
lhs
)
; :
down
(
rhs
)
g
as above. Furthermore, let
C
s
=
f8x
[
down
(
x
)
:
up
(
x
)]
g
, and let
C
be
C
s
plus
up
(
lhs
)
^:
up
(
rhs
)
_
up
(
rhs
)
^:
up
(
lhs
)
stain
. Then the steady
causal relationships
R
s
are
down
(
x
) causes
:
up
(
x
)if
>
up
(
x
) causes
:
down
(
x
)if
>
:
down
(
x
) causes
up
(
x
)if
>:
up
(
x
) causes
down
(
x
)if
>
and
R
is
R
s
plus
up
(
lhs
) causes
stain
if
:
up
(
rhs
)
:
up
(
rhs
) causes
stain
if
up
(
lhs
)
(
) causes
if
:
(
)
:
(
) causes
if
(
)
up
rhs
stain
up
lhs
up
lhs
stain
up
rhs
As above, suppose
S
=
f:
up
(
lhs
)
;
down
(
lhs
)
; :
up
(
rhs
)
;
down
(
rhs
)
; :
stain
g
be the current state. Performing
lift-both-sides
produces the following
state-eect pair.
(
f:
up
(
lhs
)
; :
down
(
lhs
)
; :
up
(
rhs
)
; :
down
(
rhs
)
; :
stain
g ;
f:
(
)
; :
(
)
g
)
down
lhs
down
rhs
