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.
However, this representation
suffers from the same problem as other propositional representations.We have to create separate representational
units (propositions) for the different entities in our domain.And the problem is that these instances are
not independent.For example, the
difficulty of CS101 in one network is the same difficulty as in another, so
evidence in one network should influence our beliefs in another.