Foundations of Inference

Axioms

Kevin H. Knuth¹ 

[1] Departments of Physics and Informatics, University at Albany (SUNY), Albany, NY 12222, USA

关键词: measure;    divergence;    probability;    information;    entropy;    lattice;   

DOI  :  10.3390/axioms1010038

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.