  We develop new abstractions for reasoning about relaxations of differential
privacy: R\'enyi differential privacy, zero-concentrated differential privacy,
and truncated concentrated differential privacy, which express different bounds
on statistical divergences between two output probability distributions. In
order to reason about such properties compositionally, we introduce approximate
span-lifting, a novel construction extending the approximate relational lifting
approaches previously developed for standard differential privacy to a more
general class of divergences, and also to continuous distributions. As an
application, we develop a program logic based on approximate span-liftings
capable of proving relaxations of differential privacy and other statistical
divergence properties.
