Probabilistic Rule

A Probabilistic Rule is a Production Rule that is associated with a Probability Value such that if Proposition [math]\displaystyle{ y }[/math] occurs then there is a Probability Value [math]\displaystyle{ p }[/math] that Proposition [math]\displaystyle{ x }[/math] is True and a Probability Value 1 - [math]\displaystyle{ p }[/math] that Proposition Not x is True.

• See: Conditional Probability, Probabilistic Rule Set.

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References

1991

• (Smyth & Goodman, 1991) ⇒ Padhraic Smyth, and Rodney M. Goodman. (1991). “Rule Induction Using Information Theory.” In: Proceedings on the Workshop on Knowledge Discovery in Databases (KDD 1991)
  • We define a probabilistic rule as an if-then statement to the effect that if proposition [math]\displaystyle{ y }[/math] occurs then there is a probability [math]\displaystyle{ p }[/math] that proposition [math]\displaystyle{ x }[/math] is true and a probability 1 - [math]\displaystyle{ p }[/math] that proposition not x is true. It is convenient to define the probability [math]\displaystyle{ p }[/math] as the conditional probability p(X|y). Hence our probabilistic rule corresponds to a simple statement regarding the conditional probability of one event given another. While other methods of representing uncertainty have been proposed and are in common use (such as fuzzy logic (Zaheh 1965) and certainty factors (Adams 1976)), standard probability theory remains the established and preferred uncertainty model due to its theoretical foundations and proven utility.

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