  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 -- 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.
