[jschveibinz]

"Formal reasoning" or "logic" as you suggest is a model for finding "truth" from static inputs and simple operations. However, if the inputs are random variables (they have an associated distribution) then so (likely) are the outputs, and "truth" is still a random variable. The world we live in is better modeled by the latter than the former, and as such the "decision tree" approach of AI seems like a more reasonable approach and model to finding "truth" than a strictly mathematical approach.

[mirekrusin]

You can still have stochastic model that works on and/or produces ie. coq formalism.