On the Expressive Power of Modal Logics on Trees

Various logical languages are compared regarding their expressive power with respect to models consisting of nitely bounded branching in nite trees The basic multimodal logic with backward and forward necessity operators is equivalent to restricted rst order logic by adding the binary temporal operators since and until we get the expressive power of rst order logic on trees Hence restricted propositional quanti ers in temporal logic correspond to restricted set quanti ers in predicate logic Adding the CTL path modality E to temporal logic gives the expressive power of path logic Tree grammar operators give a logic as expressive as weak second order logic whereas adding xed point quanti ers in the so called propositional mu calculus results in a logic expressivly equivalent to monadic second order logic on trees