Logical Uncertainty is probabilistic uncertainty about the implications of beliefs. (Another way of thinking about it is: uncertainty about computations.) Probability theory typically assumes logical omniscience, IE, perfect knowledge of logic. The easiest way to see the importance of this assumption is co consider Bayesian reasoning: to evaluate the probability of evidence given a hypothesis, , it's necessary to know what the implications of the hypothesis are. However, realistic agents cannot be logically omniscient.
See Also: Logical Induction