  We investigate four well-known negative translations of classical logic into
intuitionistic logic within a substructural setting. We find that in affine
logic the translation schemes due to Kolmogorov and G\"odel both satisfy
Troelstra's criteria for a negative translation. On the other hand, the schemes
of Glivenko and Gentzen both fail for affine logic, but for different reasons:
one can extend affine logic to make Glivenko work and Gentzen fail and vice
versa. By contrast, in the setting of Lukasiewicz logic, we can prove a general
result asserting that a wide class of formula translations including those of
Kolmogorov, G\"odel, Gentzen and Glivenko not only satisfy Troelstra's criteria
with respect to a natural intuitionistic fragment of Lukasiewicz logic but are
all equivalent.
