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Let ∆ be the conjunction of these formulas. Then, ∆∧Σ entails many of the
conclusions we would expect. For example, we have
∆∧Σ |= Holds(On(A, D), Result(Move( A, D), S
0
))
However, many conclusions we would like to be able to draw are absent. For
example, although B is on C in S0, and moving A to D doesn't change this fact,
we do not have
∆∧Σ |= Holds(On(B, C), Result(Move( A, D), S0))
In another words, although we have captured what does change as the result
of an action, wehave failed to represent what doesn't change. In general, the
effect of an action is limited to certain range, majority of fluents are unaffected
by the action. We need to capture the persistence of fluents that are unaffected by
an action. To do this, we have to add some frame axioms.
For example, the following is a frame axiom for the fluent “On”:
Holds(On(
))
â
Holds(On(
It states that if v is on w in the situation s and v is not the block x which will be
moved, then v is still on w as while as the action Move(x, y) is executed. Based
on this axiom, the set ∆ and Σ, the formula Holds(On(B,C), Result(Move(A,D),
S0)) can now be deduced.
Similarly, we can add the following frame axiom for the fluent “Clear”:
Holds(Clear(
v, w
), Result(Move(
x, y
),
s
v, w
),
s
) ∧
x
≠
v
))
â
Holds(Clear(
Next, we introduce a fluent “Color” and an action “Paint” for the Block
World:
x
), Result(Move(
y, z
),
s
x
),
s
) ∧
x
≠
z
(1) Color(x, c): block x has color c.
(2) Paint(x, c): painting block x color c.
Paint(x, c) has no preconditions since painting is always successful; the effect
of Paint(x, c) is that x has color c. Therefore, the following formula should be
added into ∆:
Holds(Color(
))
Correspondingly, suppose each block has the Red color in the initial situation
S0 and therefore we add the following formula into Σ:
x, c
), Result(Paint(
x, c
),
s
