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Furthermore, corresponding to each frame axiom, we need to introduce an
axiom for the formula ¬Affects(a, f, s). For example, the following axioms
should be introduced for the Block World example:
¬ Affects(Move(
) â
x, y
), On(
v, w
),
s
x
v
¬ Affects(Paint(
z, c
), On(
x, y
),
s
)
) â
¬ Affects(Move(
y, z
), Clear(
x
),
s
x
z
¬ Affects(Paint(
y, c
), Clear(
x
),
s
)
¬ Affects(Move(
y, z
), Color(
x, c
),
s
)
With these frame axioms, we can draw exactly the same conclusions. If we
employ an implication in place of the simple negation, the number of formuas
can be further cut down and resulted in the following three formulas.
Affects(
¬ Affects(Paint(
y, c2
), Color(
x, c1
),
s
) â
x
v
) ã
a
, On(
x, z
),
s
a
= Move(
x, y
)
) ã
Affects(
a
, Clear(
x
),
s
a
= Move(
x, y
)
)
These formulas are known as explanation closure axioms. Explanation
closure axioms are an effective substitute for frame axioms, and are much more
succinct. They form the basis of a whole class of monotonic solutions to the
frame problem.
Affects(
a
, Color(
x, c2
),
s
) ã
a
= Paint(
x, c1
2.11.2 Criteria for a solution to the frame problem
How can we represent the effects of actions in a formal, logical way without
having to write out all the frame axioms? This is the frame problem. Various
approaches have been proposed for the frame problem. This leads us to consider
what the criteria are for an acceptable solution. Shanahan offerred three criteria
on a satisfactory solution (Shanahan, 1997):
Representational parsimony;
Expressive flexibility;
Elaboration tolerance.
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