  After recalling the definitions of atomic and molecular logics, we show how
notions of bisimulation can be automatically defined from the truth conditions
of the connectives of any of these logics. Then, we prove a generalization of
van Benthem modal characterization theorem for molecular logics. Our molecular
connectives should be uniform and contain all conjunctions and disjunctions. We
use modal logic, the Lambek calculus and modal intuitionistic logic as case
study and compare in particular our work with Olkhovikov's work.
