  We introduce Hyper$^2$LTL, a temporal logic for the specification of
hyperproperties that allows for second-order quantification over sets of
traces. Unlike first-order temporal logics for hyperproperties, such as
HyperLTL, Hyper$^2$LTL can express complex epistemic properties like common
knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The
model checking problem of Hyper$^2$LTL is, in general, undecidable. For the
expressive fragment where second-order quantification is restricted to smallest
and largest sets, we present an approximate model-checking algorithm that
computes increasingly precise under- and overapproximations of the quantified
sets, based on fixpoint iteration and automata learning. We report on
encouraging experimental results with our model-checking algorithm, which we
implemented in the tool~\texttt{HySO}.
