  We provide a categorical notion called uncertain bisimilarity, which allows
to reason about bisimilarity in combination with a lack of knowledge about the
involved systems. Such uncertainty arises naturally in automata learning
algorithms, where one investigates whether two observed behaviours come from
the same internal state of a black-box system that can not be transparently
inspected. We model this uncertainty as a set functor equipped with a partial
order which describes possible future developments of the learning game. On
such a functor, we provide a lifting-based definition of uncertain bisimilarity
and verify basic properties. Beside its applications to Mealy machines, a
natural model for automata learning, our framework also instantiates to an
existing compatibility relation on suspension automata, which are used in
model-based testing. We show that uncertain bisimilarity is a necessary but not
sufficient condition for two states being implementable by the same state in
the black-box system. To remedy the failure of the one direction, we
characterize uncertain bisimilarity in terms of coalgebraic simulations.
