  We show that context semantics can be fruitfully applied to the quantitative
analysis of proof normalization in linear logic. In particular, context
semantics lets us define the weight of a proof-net as a measure of its inherent
complexity: it is both an upper bound to normalization time (modulo a
polynomial overhead, independently on the reduction strategy) and a lower bound
to the number of steps to normal form (for certain reduction strategies).
Weights are then exploited in proving strong soundness theorems for various
subsystems of linear logic, namely elementary linear logic, soft linear logic
and light linear logic.
