Abstract
Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional Μ-calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the Μ-calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the Μ-calculus.
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