We prove that the modal mu-calculus collapses to first order logic over the class of finite transitive frames. The proof is obtained by using some byproducts of a new proof of the collapse of the mu-calculus to the alternation free fragment over the class of transitive frames. Moreover, we prove that the modal mu-calculus is Buechi and co-Buechi definable over the class of all models where, in a strongly connected component, vertexes are distinguishable by means of the propositions they satisfy.

On the Mu-calculus over transitive and finite transitive frames

LENZI, Giacomo;
2010-01-01

Abstract

We prove that the modal mu-calculus collapses to first order logic over the class of finite transitive frames. The proof is obtained by using some byproducts of a new proof of the collapse of the mu-calculus to the alternation free fragment over the class of transitive frames. Moreover, we prove that the modal mu-calculus is Buechi and co-Buechi definable over the class of all models where, in a strongly connected component, vertexes are distinguishable by means of the propositions they satisfy.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/3012429
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