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Axioms 2012, 1(1), 38-73; doi:10.3390/axioms1010038
Article

Foundations of Inference

1,*  and 2
Received: 20 January 2012; in revised form: 1 June 2012 / Accepted: 7 June 2012 / Published: 15 June 2012
(This article belongs to the Special Issue Axioms: Feature Papers)
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Abstract: We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information.
Keywords: measure; divergence; probability; information; entropy; lattice measure; divergence; probability; information; entropy; lattice
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Knuth, K.H.; Skilling, J. Foundations of Inference. Axioms 2012, 1, 38-73.

AMA Style

Knuth KH, Skilling J. Foundations of Inference. Axioms. 2012; 1(1):38-73.

Chicago/Turabian Style

Knuth, Kevin H.; Skilling, John. 2012. "Foundations of Inference." Axioms 1, no. 1: 38-73.


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