 For any given logic, it is useful to know whether or not there is an effective procedure to determine, for each sentence in the logic, if it is provable or not. A decidable logic—i.e., one for which there is an effective procedure for provability—is often described by its complexity class, which characterizes how difficult it is to perform the decision procedure. Extensive research work has been dedicated to the study of the complexity and decidability issues for several fragments of propositional linear logic. It is known that