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

Foundations of Inference

Kevin H. Knuth 1,* email and John Skilling 2 email
1 Departments of Physics and Informatics, University at Albany (SUNY), Albany, NY 12222, USA 2 Maximum Entropy Data Consultants Ltd., Kenmare, County Kerry, Ireland
* Author to whom correspondence should be addressed.
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)
PDF Full-text Download PDF Full-Text [347 KB, Updated Version, uploaded 18 June 2012 11:38 CEST]
The original version is still available [211 KB, uploaded 15 June 2012 11:02 CEST]
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

Article Statistics

Click here to load and display the download statistics.

Cite This Article

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.

Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert