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fluents, one of which is always subject to the assumption of persistence while
the other fluents may vary freely (in view of satisfying the state constraints).
More elaborated methods dene a partial preference ordering among all pos-
sible changes|as we did in Section 2.3. Even further renement is obtained
by state-dependent categorization.
22
The report [92] presented an extension
of \Features-and-Fluents" (c.f. Section 1.3) to provide a formal methodol-
ogy for assessing the range of applicability of dierent approaches based on
categorization.
An early approach which exploits a specic notion of causality to address
the Ramication Problem was proposed in [26]. This formalism supports
indirect eects deriving from complete descriptions of how the truth-value
of a particular fluent might be caused to change. As an example, recall the
electric circuit consisting of two switches and a light bulb of Fig. 2.3. The
approach of [26] would encode the various possibilities to aect the state of
the bulb by these axioms:
Causes
(
a; s;
light
)
Causes
(
a; s;
up
(
s
1
))
^ Holds
(
up
(
s
2
)
;s
)
_ Causes
(
a; s;
up
(
s
2
))
^ Holds
(
up
(
s
1
)
;s
)
Cancels
(
a; s;
light
)
Cancels
(
a; s;
up
(
s
1
))
_ Cancels
(
a; s;
up
(
s
2
))
(2.43)
where
Causes
(
a; s; f
) should be read as \executing action
a
in situation
s
causes fluent
f
to become true,"
Cancels
(
a; s; f
) as \executing action
a
in
situation
s
causes fluent
f
to become false," and
Holds
(
f; s
) as \fluent
f
is true in situation
s
." Suppose we are given a specication of how
up
(
s
1
)
may become true (resp. false), namely,
Causes
(
a; s;
up
(
s
1
))
a
=
toggle
(
s
1
)
^:Holds
(
up
(
s
1
)
;s
)
Cancels
(
a; s;
up
(
s
1
))
a
=
toggle
(
s
1
)
^ Holds
(
up
(
s
1
)
;s
)
plus this general axiom meant to express persistence of all non-aected flu-
ents:
Holds
(
f;Do
(
a; s
))
Causes
(
a; s; f
)
_
(
Holds
(
f; s
)
^:Cancels
(
a; s; f
))
(2.44)
where
Do
(
a; s
) denotes the situation obtained by executing action
a
in situ-
ation
s
. One then obtains, e.g., that
:Holds
(
up
(
s
1
)
;S
0
)
^Holds
(
up
(
s
2
)
;S
0
)
^
:Holds
(
light
;S
0
) implies
Causes
(
toggle
(
s
1
)
;S
0
;
up
(
s
1
)) and, hence, also
Causes
(
s
1
)
;S
0
)), as
intended. No eort has to be made to suppress an unwanted change of
up
(
s
2
)
since no causal relation like the ones in (2.43) exists that may support this.
On the other hand, the use of denitional descriptions of causal dependencies,
as in (2.43), is restricted to domains where these dependencies are acyclic,
toggle
(
s
1
)
;S
0
;
light
). Thus
Holds
(
light
; Do
(
toggle
(
22
We note, however, that this renement would not help with our counter-
example involving a relay introduced at the end of Section 2.3.