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
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
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