  We introduce and study several notions of computability-theoretic
reducibility between subsets of $\omega$ that are "robust" in the sense that if
only partial information is available about the oracle, then partial
information can be recovered about the output. These are motivated by
reductions between $\Pi^1_2$ principles in the context of reverse mathematics,
and also encompasses generic and coarse reducibilities, previously studied by
Jockusch and Schupp (2012).
