an:05817533
Zbl 1208.68145
D'agostino, Giovanna; Lenzi, Giacomo
On the \(\mu \)-calculus over transitive and finite transitive frames
EN
Theor. Comput. Sci. 411, No. 50, 4273-4290 (2010).
00270037
2010
j
68Q60 03B45
fixed points; modal \(\mu \)-calculus; alternation hierarchy; collapse; finite transitive frames; B??chi and co-B??chi definable
Summary: 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 B??chi and co-B??chi definable over the class of all models where, in a strongly connected component, vertexes are distinguishable by means of the propositions they satisfy.