I don't think the construction actually requires instant propagation. It requires a certain calculation to be made when you wish to assign a probability to a particular statement, and this calculation is provably finite.

In your example, you are free to have X contain "A" and "A=>B", and not contain "B", as long as you don't assign a probability to B. When you wish to do so, you have to do the calculation, which will find that B∈OLC(X), and so will assign P(B)=1. Assigning any other value would indeed be inconsistent for any reasonable definition of probability, because if you know that A=>B, then you have to know that P(A)≤P(B), and then if P(A)=1, then P(B) must also be 1.