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Symbolic versus statistical reasoning

The (Symbolic) methods basically represent uncertainty belief as being

Some methods also had problems with

Statistical methods provide a method for representing beliefs that are not certain (or uncertain) but for which there may be some supporting (or contradictory) evidence.

Statistical methods offer advantages in two broad scenarios:

Genuine Randomness
-- Card games are a good example. We may not be able to predict any outcomes with certainty but we have knowledge about the likelihood of certain items (e.g. like being dealt an ace) and we can exploit this.
-- Symbolic methods can represent this. However if the number of exceptions is large such system tend to break down. Many common sense and expert reasoning tasks for example. Statistical techniques can summarise large exceptions without resorting enumeration.