Talk: New Foundations for Information Theory

These are the slides for a number of talks on logical information theory as providing new foundations for information theory. The Shannon definitions can all be derived by a uniform transformation from the logical definitions which, unlike the Shannon notions of entropy, is a measure in the sense of measure theory. In fact, the logical entropy of a partition is a probability measure, the probability that in two independent draws from the underlying set that one will obtain a distinction, i.e., elements in different blocks of the partition. Boolean subset logic (usually mis-specified as the special case of propositional logic) and partition logic are dual in a category-theoretic sense, and logical information theory is the quantitative version of a partition just as logical probability is the quantitative measure of a subset (event).

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