One of the key benefits of
the propositional representation was our ability to represent our knowledge
without explicit enumeration of the worlds.In turns out that we can do the same in the probabilistic framework.The key idea, introduced by Pearl in the
Bayesian network framework, is to use locality of interaction.This is an assumption which seems to be a
fairly good approximation of the world in many cases.
This representation supports
many interesting reasoning patterns.For example, if we observe that the student gets an A, the probability
that he is smart goes up.But if we
then find out that the class was easy, it reduces the impact of this
evidence, and our probability goes down, although not all the way.