Intensional systems deal with uncertainty in a context sensitive manner. They try to model the interdependencies and relevance relationships of the variables in the system. If an extensional system has the rule, if A then B with some certainty factor m. and observes A in its database it will infer something about the state of B regardless of any other knowledge available to it. What we believe about B in this system is dependent on our whole view of the problem and how relevant information interacts. The difference between these two systems boils down to a trade-off between semantic accuracy and computational feasibility.
Extensional systems are computationally efficable but semantically clumsy.
Intensional systems on the otherhand were thought by some to be computationally intractable even though they are semantically clear. It uses certainty factor calculus to manipulate generalised truth values which represent the certainty of particular formulae. The certainty of a formula is calculated as some function of the certainty of it subformulae. We know that fire causes smoke but it is definitely not true that smoke causes fire. Quite simply, smoke is considered evidence for fire, therefore if we see smoke we may be led to believe that there is a fire nearby.