Foundations of Inference

Authors

Kevin H. Knuth, University at Albany, State University of New YorkFollow
John Skilling, Maximum Entropy Data Consultants Ltd.

Document Type

Article

Publication Date

Summer 6-15-2012

DOI

10.3390/axioms1010038

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.

Comments

Publisher Acknowledgment

This is the Publisher's PDF of the following article made available by MDPI © 2012 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/)

Recommended Citation

Knuth, Kevin H. and Skilling, John, "Foundations of Inference" (2012). Physics Faculty Scholarship. 8.
https://scholarsarchive.library.albany.edu/physics_fac_scholar/8