[naveensundar]

Logic is much more than classical AI. The logic culture in classic AI was very ambitious and that was one of the reasons it crashed and not due to fundamental flaws in logic.

Formal classical logic can represent all kinds of truths and even uncertainty with trivial syntactic mechanisms. E.g., "It is true that statement X holds with probability P." can be a syntactically correct statement representing uncertainty with certainty (there can be levels of statements with varying levels of certainty). Classical logic is extremely good at complex nested representations and the objects represented can be probabilistic statements. See the following paper for a syntactically classic FOL of probability (semantically it is a bit different from the standard model-theoretic approach)

http://www.cs.cornell.edu/home/halpern/papers/first-order_pr...

Of course, researchers who posit probabilistic models reason mostly in classical logic when they write papers explaining the math (other than for assumptions of course).