Logical uncertainty applies the rules of probability to logical facts which are not yet known to be true or false.
Is the googolth digit of pi odd? The probability that it is odd is, intuitively, 0.5. Yet we know that this is definitely true or false by the rules of logic, even we don't know which. Formalizing this sort of probability is the field of logical uncertainty.
The problem with the 0.5 probability is that it gives non-zero probability to false statements. If I am asked to bet on whether the googolth digit of pi is odd, I can reason as follows: There is 0.5 chance that it is odd. Let P represent the actual, unknown, parity of the googolth digit (odd or even); and let Q represent the other parity. If Q, then anything follows. (By the Principle of Explosion, a false statement implies anything.) For example, Q implies that I will win $1 billion. Therefore the value of this bet is at least $500,000,000, which is 0.5 * $1,000,000, and I should be willing to pay that much to take the bet. This is an absurdity. Only expenditure of finite computational power stands between the uncertainty and 100% certainty....