A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Errata: “The relationship between knowledge, belief, and certainty”
Annals of Mathematics and Artificial Intelligence
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It is shown that probabilistic beliefs and estimation of quantities give rise to the same model, that of a type space, and can be viewed as the two sides of the same coin. We study the axiom of correct estimation, which states that an agent's estimation of his own estimation is correct, showing it to be weaker than the introspection axiom, according to which an agent is certain of his own probabilistic beliefs. The correct estimation axiom implies, however, that the agent is certain that he is introspective, and it is equivalent to the axioms of averaging and conditioning, which are expressed in terms of probabilistic beliefs.