We propose a unified framework for both Shannon-Khinchin and Shore-Johnson axiomatic systems. We do it by rephrasing Shannon-Khinchine axioms in terms of generalized arithmetics of Kolmogorov and Nagumo. We prove that the two axiomatic schemes yield identical classes of entropic functionals-the Uffink class of entropies. This allows to re-establish the entropic parallelism between information theory and statistical inference that has seemed to be "broken" by the use of non-Shannonian entropies.

Complexity Science Hub Vienna Josefstädter Strasse 39 1080 Vienna Austria

Faculty of Nuclear Sciences and Physical Engineering Czech Technical University Prague Břehová 7 115 19 Prague Czech Republic

Section for Science of Complex Systems Medical University of Vienna Spitalgasse 23 1090 Vienna Austria

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