  Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with
quantification over atomic propositions. It has recently come to the fore as a
powerful intermediary framework to study logics for strategic reasoning. We
extend it to include imperfect information by parameterising quantifiers with
an observation that defines how well they observe the model, thus constraining
their behaviour. We consider two different semantics, one related to the notion
of no memory, the other to perfect recall. We study the expressiveness of our
logic, and show that it coincides with MSO for the first semantics and with MSO
with equal level for the second one. We establish that the model-checking
problem is Pspace-complete for the first semantics. While it is undecidable for
the second one, we identify a syntactic fragment, defined by a notion of
hierarchical formula, which we prove to be decidable thanks to an
automata-theoretic approach.
