  This paper studies the relationships between three notions of behavioural
preorder that have been proposed in the literature: refinement over modal
transition systems, and the covariant-contravariant simulation and the partial
bisimulation preorders over labelled transition systems. It is shown that there
are mutual translations between modal transition systems and labelled
transition systems that preserve, and reflect, refinement and the
covariant-contravariant simulation preorder. The translations are also shown to
preserve the modal properties that can be expressed in the logics that
characterize those preorders. A translation from labelled transition systems
modulo the partial bisimulation preorder into the same model modulo the
covariant-contravariant simulation preorder is also offered, together with some
evidence that the former model is less expressive than the latter. In order to
gain more insight into the relationships between modal transition systems
modulo refinement and labelled transition systems modulo the
covariant-contravariant simulation preorder, their connections are also phrased
and studied in the context of institutions.
