Next Article in Journal
Gradings, Braidings, Representations, Paraparticles: Some Open Problems
Next Article in Special Issue
Fat Triangulations, Curvature and Quasiconformal Mappings
Previous Article in Journal / Special Issue
Introduction to the Yang-Baxter Equation with Open Problems
Article Menu

Export Article

Open AccessArticle
Axioms 2012, 1(1), 38-73;

Foundations of Inference

Departments of Physics and Informatics, University at Albany (SUNY), Albany, NY 12222, USA
Maximum Entropy Data Consultants Ltd., Kenmare, County Kerry, Ireland
Author to whom correspondence should be addressed.
Received: 20 January 2012 / Revised: 1 June 2012 / Accepted: 7 June 2012 / Published: 15 June 2012
(This article belongs to the Special Issue Axioms: Feature Papers)
Full-Text   |   PDF [347 KB, uploaded 18 June 2012]   |  


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. View Full-Text
Keywords: measure; divergence; probability; information; entropy; lattice measure; divergence; probability; information; entropy; lattice

Figure 1

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top