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.
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
Included in
Artificial Intelligence and Robotics Commons, Probability Commons, Statistical Theory Commons
Terms of Use
This work is made available under the Scholars Archive Terms of Use.
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/)