Of the Hennessy-Milner property and Other Demons
Raul Leal, Clemens Kupke

Abstract:
We relate three different, but equivalent, ways to characterise
behavioural equivalence for set coalgebras. These are: using final
coalgebras, using coalgebraic languages that have the Hennessy- Milner
property and using coalgebraic languages that have ``logical
congruences''. On the technical side the main result of our paper is a
straightforward construction of the final $T$-coalgebra of a set
functor using a given logical language that has the Hennessy-Milner
property with respect to the class of $T$-coalgebras.