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
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
