  Following the idea of Subexponential Linear Logic and Stratified Bounded
Linear Logic, we propose a new parameterized version of Linear Logic which
subsumes other systems like ELL, LLL or SLL, by including variants of the
exponential rules. We call this system Superexponential Linear Logic (superLL).
Assuming some appropriate constraints on the parameters of superLL, we give a
generic proof of cut elimination. This implies that each variant of Linear
Logic which appears as a valid instance of superLL also satisfies cut
elimination.
