A Short Note on the Logico-Conceptual Foundations of Information Theory in Partition Logic

2 Pages Posted: 28 May 2009

Date Written: May 27, 2009

Abstract

A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets of a fixed universe rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative size as a probability. The analogous construction for the dual logic of partitions gives rise to a notion of logical entropy that is precisely related to Claude Shannon's entropy. In this manner, the new logic of partitions provides a logico-conceptual foundation for information-theoretic entropy or information content.

Keywords: entropy, information theory, partition logic

JEL Classification: D80

Suggested Citation

Ellerman, David, A Short Note on the Logico-Conceptual Foundations of Information Theory in Partition Logic (May 27, 2009). Available at SSRN: https://ssrn.com/abstract=1410847 or http://dx.doi.org/10.2139/ssrn.1410847

David Ellerman (Contact Author)

University of Ljubljana ( email )

School of Social Science
Ljubljana, CA
Slovenia

HOME PAGE: http://www.ellerman.org

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