  We introduce a generic expression language describing behaviours of finite
coalgebras over sets; besides relational systems, this covers, e.g., weighted,
probabilistic, and neighbourhood-based system types. We prove a generic
Kleene-type theorem establishing a correspondence between our expressions and
finite systems. Our expression language is similar to one introduced in
previous work by Myers but has a semantics defined in terms of a particular
form of predicate liftings as used in coalgebraic modal logic; in fact, our
expressions can be regarded as a particular type of modal fixed point formulas.
The predicate liftings in question are required to satisfy a natural
preservation property; we show that this property holds in particular for the
Moss liftings introduced by Marti and Venema in work on lax extensions.
