A van Benthem Theorem for Atomic and Molecular Logics

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