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On the Expressive Completeness of the Propositional Mu-Calculus With Respect to Monadic Second Order Logic (1996)
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@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...
Keyphrases
monadic second order logic expressive completeness propositional mu-calculus transition system expressive completeness result implies introduction transition system good framework binary relation nonempty set unary relation program scheme engineering system propositional calculus precise meaning many author bisimilar model propositional logic
