  In the setting of the modal logic that characterizes modal refinement over
modal transition systems, Boudol and Larsen showed that the formulae for which
model checking can be reduced to preorder checking, that is, the characteristic
formulae, are exactly the consistent and prime ones. This paper presents
general, sufficient conditions guaranteeing that characteristic formulae are
exactly the consistent and prime ones. It is shown that the given conditions
apply to various behavioural relations in the literature. In particular,
characteristic formulae are exactly the prime and consistent ones for all the
semantics in van Glabbeek's linear time-branching time spectrum.
