What is it about?
There is a logic of partitions that is category-theoretic dual to the usual Boolean logic of subsets. Probability starts as the quantitative version of a subset and information starts as the quantitative version of a partition. This leads to the notion of logical entropy that compares favorably to the notion of Shannon entropy as a foundation of information theory. This is the introductory article in a special issue of 4Open on Logical entropy.
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Why is it important?
The Shannon entropy is key for the theory of communications and coding, but it does not provide a foundational notion of information and entropy. The logical entropy provides that foundation.
Perspectives
This open-access paper, https://www.4open-sciences.org/component/toc/?task=topic&id=1575, is a summary of my book: New Foundations for Information Theory.
David Ellerman
School of Social Science, University of Ljubljana, Slovenia
Read the Original
This page is a summary of: Introduction to logical entropy and its relationship to Shannon entropy, 4open, January 2022, EDP Sciences,
DOI: 10.1051/fopen/2021004.
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