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 to 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


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 though we don't know which. Formalizing this sort of probability is the primary goal of the field of logical uncertainty....

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