  It is by now well known that the Boltzmann-Gibbs-von Neumann-Shannon
logarithmic entropic functional ($S_{BG}$) is inadequate for wide classes of
strongly correlated systems: see for instance the 2001 Brukner and Zeilinger's
{\it Conceptual inadequacy of the Shannon information in quantum measurements},
among many other systems exhibiting various forms of complexity. On the other
hand, the Shannon and Khinchin axioms uniquely mandate the BG form
$S_{BG}=-k\sum_i p_i \ln p_i$; the Shore and Johnson axioms follow the same
path. Many natural, artificial and social systems have been satisfactorily
approached with nonadditive entropies such as the $S_q=k \frac{1-\sum_i
p_i^q}{q-1}$ one ($q \in {\cal R}; \,S_1=S_{BG}$), basis of nonextensive
statistical mechanics. Consistently, the Shannon 1948 and Khinchine 1953
uniqueness theorems have already been generalized in the literature, by Santos
1997 and Abe 2000 respectively, in order to uniquely mandate $S_q$. We argue
here that the same remains to be done with the Shore and Johnson 1980 axioms.
We arrive to this conclusion by analyzing specific classes of strongly
correlated complex systems that await such generalization.
