  Covariant-contravariant simulation and conformance simulation are two
generalizations of the simple notion of simulation which aim at capturing the
fact that it is not always the case that "the larger the number of behaviors,
the better". Therefore, they can be considered to be more adequate to express
the fact that a system is a correct implementation of some specification. We
have previously shown that these two more elaborated notions fit well within
the categorical framework developed to study the notion of simulation in a
generic way. Now we show that their behaviors have also simple and natural
logical characterizations, though more elaborated than those for the plain
simulation semantics.
