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of abstraction. However, such representations are not always appropriate, since
the continuous variation of some quantity is the salient feature of the domain in
question. Continuous change is particularly hard to represent in the situation
calculus, and this is one of the motivations for study in the event calculus, in
which continuous change can be represented without too much difficulty.
The final criterion in the list is elaboration tolerance. A representation is
elaboration tolerant to the extent that the effort required to add new information
to the representation is proportional to the complexity of that information. During
the process that argument a situation calculus theory a new action, if there are n
fluents which will be directly affected, then it might require the addition of
roughly n new sentences. But it should not necessitate the complete
reconstruction of the old theory; facts about the effects should be gracefully
absorbed into the old theory.
When the domain includes actions with ramifications, it is not enough to
simply expand the explanation closure axioms. It calls for reconstruction and
bring a great improvement to the original system. Such a reconstruction is
expensive for any monotonic mechanisms. The goal of elaboration tolerance
seems to be impossible to achieve if we remain in the realm of monotonic
mechanisms. To solve this problem, many nonmonotonic reasoning mechanisms
were proposed by AI researchers, such as the circumscription proposed by
McCarthy and the default logic proposed by Reiter. In fact, frame problem is one
of the driving forces for the study of nonmonotonic reasoning. The core idea of
nonmonotonic solution to the frame problem is to formalize the common sense
law of inertia. One component of this law is as follows: normally, given any
action and any fluent, the action doesn't affect the fluent.
More generally, we want to write down just the effect axioms, declare the
default assumption that “nothing else changes”, and then appeal to some
nonmonotonic formalism to work out the consequences. Since the early Eighties
of the last century, there have been several candidates for such a formalism. Two
of the most common are default logic and circumscription. Logic programming's
negation-as-failure is another candidate, so long as its semantic is properly
defined.
2.11.3
Nonmonotonic solving approach of the frame problem
Nonmonotonic reasoning was firstly adopted by McCarthy to solve the frame
problem. Circumscription was proposed by McCarthy and applied in a solution
