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New Foundations for Information Theory: Logical Entropy and Shannon Entropy (SpringerBriefs in Philosophy) by David P. Ellerman is a nonfiction available to read on EtoBox.

What is New Foundations for Information Theory: Logical Entropy and Shannon Entropy (SpringerBriefs in Philosophy) about?

This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or "dit" of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory)  and its compound notions are then derived from a non-linear dit-to-bit transform

Who reads New Foundations for Information Theory: Logical Entropy and Shannon Entropy (SpringerBriefs in Philosophy)?

Author

David P. Ellerman

Publisher

Springer International Publishing : Imprint: Springer

Published

2021

Language

EN

ISBN

9783030865535

Category

nonfiction

Subjects

Philosophy, Science, Computer Science