By Rudolf Carnap and Yeshoua Bar-Hillel

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**Example text**

Table V gives the values of the absolute and relative contD for the first six values of m and for the last six values of m. We see from this that if a series of messages is received, each being an E, contD grows by every one of these messages by the same amount, from 0 to 1. infD , however, unequal amounts. behaves in a different way. contributes less than 1/2. by Every further The last-but-three message The last-but-two contributes more than 1/2. And the last message contributes m. by 1/64, It grows from 0 to The first message contributes only a small fraction.

_ -1_111_1_-·1 __ -- 1-- -- ~ -- - following general situations. Whenever one is interested in knowing whether a certain event out of an exhaustive system of events, H, has happened (or is going to happen) but is unable, for some reason, to observe directly the occurrence of these events and has to content oneself with the observation of some event out of another exhaustive system, K, where not all of the kq are irrelevant to the h on e (cf. ] § 65), one can regard K as a distortion or a transformation through noise of H.

P=l Various formulas for est(cont, H, e), est(inf, H, e), and other functions based upon them are derived. The concepts of posterior estimate of amount of information, amount of specification, estimate of the posterior estimate, and estimate of the amount of specification are defined, and various theorems concerning them proved. A simple illustrative application is given. If an experiment is performed, the possible results of which are expressed sentences h, .. , in n h n (or in n sentences L-equivalent to them), we can compute the amounts of information which each possible outcome would convey, assuming that an m-function has been defined for all the sentences of the language in which the h's are formulated.