We study the notion of stratification, as used in subsystems of linear logic
with low complexity bounds on the cut-elimination procedure (the so-called
light logics), from an abstract point of view, introducing a logical system in
which stratification is handled by a separate modality. This modality, which is
a generalization of the paragraph modality of Girard's light linear logic,
arises from a general categorical construction applicable to all models of
linear logic. We thus learn that stratification may be formulated independently
of exponential modalities; when it is forced to be connected to exponential
modalities, it yields interesting complexity properties. In particular, from
our analysis stem three alternative reformulations of Baillot and Mazza's
linear logic by levels: one geometric, one interactive, and one semantic