Information Technology Reference
In-Depth Information
classes which we consider of general importance so that a lot is gained by
their special treatment.
First, consider state constraints of the form
8x
1
:::8x
n
:F
(or
8x: F
,
for short) with sub-formula
F
being quantier-free. Suppose further that
for any atomic fluent expression
f
[
x
] occurring in
F
, the underlying in-
fluence information does not dier regarding dierent instances
f
[
e
]. Then
the causal relationships determined by this constraint and influence in-
formation can be obtained by applying our procedure to sub-formula
F
with all occurrences of variables taken as (distinct) entities.
14
As a sim-
ple example, consider state constraint
8x
[
(
x
) ] and influ-
ence information
I
=
f
(
up
(
x
)
;
down
(
x
))
;
(
down
(
x
)
;
up
(
x
))
g
. Four causal re-
lationships are extractible from the corresponding quantier-free constraint,
down
(
x
)
:
up
(
x
), viz.
down
(
x
)
:
up
down
(
x
)
causes
:
up
(
x
) f
>
:
(
x
)
causes
(
x
) f
>
down
up
up
(
x
)
causes
:
down
(
x
) f
>
:
(
x
)
causes
(
x
) f
>
up
down
stating that any entity becoming
(or not
up
) also becomes not
up
down
(or
down
, respectively) and vice versa.
Second, and more sophisticated, we analyze state constraints in which
each occurrence of a quantier is of the form
8x: `
[
x
] or of the form
9x: `
[
x
]
where
`
[
x
] is a (possibly negated) fluent expression with free variables
x
.
Furthermore, it is assumed that, for any such
`
[
x
], the underlying influence
information does not dier regarding dierent instances
k`
[
e
]
k
. When com-
puting the minimal CNF of a state constraint which is restricted in this way,
sub-formulas
8x: `
[
x
] and
9x: `
[
x
] are treated as if they were ordinary liter-
als. If in addition any
:8x: `
[
x
] is replaced by
9x: :`
[
x
] and any
:9x: `
[
x
]
by
8x: :`
[
x
], then each conjunct in the resulting CNF is a disjunction con-
sisting of ground literals and expressions of the form
8x: `
[
x
] and
9x: `
[
x
].
When generating causal relationships, the sub-formulas with quantier are
treated as follows: The reason for a formula
8x: `
[
x
] becoming false must be
the occurrence of any eect
:`
[
e
]. Thus
:`
[
x
] itself may be used, if influ-
ence permits, as triggering eect in a causal relationship. The reason for a
formula
9x: `
[
x
] becoming false must be the occurrence of any eect
:`
[
e
]so
that (now)
8x: :`
[
x
] holds. Thus
:`
[
x
] may be used as triggering eect in a
causal relationship whose context includes
8x: :`
[
x
]. Correcting the violation
of a state constraint by satisfying a formula
8x: `
[
x
] is achieved by satisfying
all instances of
`
[
x
]. Thus
`
[
x
] may be used as indirect eect in a causal
relationship. Correcting the violation of a state constraint by satisfying a for-
mula
9x: `
[
x
] is achieved by satisfying just one instance of
`
[
x
]. Thus
`
[
x
]
14
During this procedure, the underlying influence information should of course
be assumed to treat these entities similar to all others as regards the aforemen-
tioned atomic fluent expressions
f
[
x
] contained in
F
.
