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(
up
(
s
1
)
;
:
up
(
s
2
)
;
:
light
)
Toggle (s
1
)
(
:
up
(
s
1
)
;
:
up
(
s
2
)
;
:
light
)
(
:
up
(
s
1
)
;
up
(
s
2
)
;
:
light
)
Toggle (s
2
)
(
:
up
(
s
1
)
;
up
(
s
2
)
;
:
light
)
switch-one-up
Toggle (s
1
)
(
:
up
(
s
1
)
;
up
(
s
2
)
;
:
light
)
Toggle (s
1
)
(
up
(
s
1
)
;
:
up
(
s
2
)
;
:
light
)
(
up
(
s
1
)
;
up
(
s
2
)
;
:
light
)
Toggle (s
2
)
(
up
(
s
1
)
;
:
up
(
s
2
)
;
:
light
)
Toggle (s
2
)
switch-one-up
(
up
(
s
1
)
;
up
(
s
2
)
;
:
light
)
Figure 1.1.
Each interpretation suggests possible evolutions of the system's
state. This may be depicted as tree whose nodes are states and whose
edges are labeled with actions. In the example, the state resulting from per-
forming
toggle
(
s
2
) admits only two child nodes, as opposed to, say, the
root node admitting three of them. The reason is that no action law for
switch-one-up
(c.f. (1.3)) is applicable to the state
f
up
(
s
1
)
;
up
(
s
2
)
; :
light
g
.
Thus
Res
([
toggle
(
s
2
)
;
switch-one-up
]) is not dened in this interpretation. No-
tice further that when constructing an interpretation one has to select among the
alternative results whenever a non-deterministic action is performed; in the exam-
ple the result of [
toggle
(
s
1
)
;
switch-one-up
], for instance, has been determined as
f:
up
(
s
1
)
;
up
(
s
2
)
; :
light
g
|we would have a dierent interpretation had we made
the equally possible choice
f
up
(
s
1
)
; :
up
(
s
2
)
; :
light
g
.
version of our running example. Below and from now onwards, by
k
we
indicate that
is of arity
k
.
Example 1.2.1.
Let
E
=
f
s
1
;
s
2
g
be the set of entities,
F
=
f
up
1
;
light
0
g
the set of fluent names, and
A
=
f
toggle
1
;
switch-one-up
0
g
the set of
action names. Furthermore, let
L
consist of the action laws
toggle
(
x
)
transforms
f
up
(
x
)
g
into
f:
up
(
x
)
g
toggle
(
x
)
transforms
f:
up
(
x
)
g
into
f
up
(
x
)
g
transforms
f:
up
(
s
1
)
g
into
f
up
(
s
1
)
g
switch-one-up
transforms
f:
up
(
s
2
)
g
into
f
up
(
s
2
)
g
switch-one-up
