  The literature on concurrency theory offers a wealth of examples of
characteristic-formula constructions for various behavioural relations over
finite labelled transition systems and Kripke structures that are defined in
terms of fixed points of suitable functions. Such constructions and their
proofs of correctness have been developed independently, but have a common
underlying structure. This study provides a general view of characteristic
formulae that are expressed in terms of logics with a facility for the
recursive definition of formulae. It is shown how several examples of
characteristic-formula constructions from the literature can be recovered as
instances of the proposed general framework, and how the framework can be used
to yield novel constructions.
