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Scenarios like the foregoing clearly favor the use of probabilistic theory when
it comes to decision-making based on the available information. On the other
hand, it seems that only for a small fraction of daily-life situations such exact
(conditional) probabilities can be provided. This is the strongest argument
against probabilistic reasoning as an alternative to nonmonotonic logics. 14
The relevance of this argument has revealed in the course of a research project
devoted to formalizing large parts of human common sense knowledge:
\Early on, we allowed each assertion in the knowledge base to have a nu-
meric certainty factor, but this approach led to its own set of increasingly
severe diculties. [ ::: ] There wasn't statistical data to support these num-
bers [ ::: ]. These problems led us to go back to a simple nonnumeric scheme
in which [assertions] [ ::: ] would simply be true (nonmonotonically, that is,
true by default) [ ::: ]." 15
It so seems that the pragmatic answer to the problem of which approach pro-
vides the `right' formalism, nonmonotonic or probabilistic logic, is to com-
promise: Exact probability values should be used whenever both available
and appropriate|as it is the case in the scenario described by the Lottery
Paradox, for instance. When it comes to representing knowledge involving ab-
normalities which are only vaguely known to be unlikely, choosing a nonmono-
tonic framework helps to base decision-making on reasonable conclusions. 16
14
Another argument often brought forward, namely, that probabilistic reasoning
is computationally intractable, has been challenged by the notable practical
success of Bayesian Belief Networks [81], which exploit knowledge of causal
independence to speed up the reasoning process.
15
[46], pp. 34{5
16
To complete this brief discussion, successful attempts to embed nonmonotonic
reasoning in logics of probability should be mentioned, e.g., [42].
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