## On the Expressive Completeness of the Propositional Mu-Calculus With Respect to Monadic Second Order Logic (1996)

Citations: | 65 - 3 self |

### BibTeX

@MISC{Janin96onthe,

author = {David Janin and Igor Walukiewicz},

title = {On the Expressive Completeness of the Propositional Mu-Calculus With Respect to Monadic Second Order Logic},

year = {1996}

}

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### 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 -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 -calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the -calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...