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.
On leave from: Institute of Informatics, Warsaw University, Banacha 2, 02-097 Warsaw, POLAND
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Janin, D., Walukiewicz, I. (1996). On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic. In: Montanari, U., Sassone, V. (eds) CONCUR '96: Concurrency Theory. CONCUR 1996. Lecture Notes in Computer Science, vol 1119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61604-7_60
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