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.

中文翻译：

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当Shannon和Khinchin遇到Shore和Johnson时：信息论和统计推断公理学的对等

我们为Shannon-Khinchin和Shore-Johnson公理系统提出了一个统一的框架。我们通过用Kolmogorov和Nagumo的广义算术表述Shannon–Khinchine公理来做到这一点。我们证明了这两种公理化方案可以产生相同类别的熵泛函—熵的Uffink类。这允许重新建立信息理论和统计推断之间的熵并行性，这似乎已通过使用非香农熵而被“打破”。