Complexity through Translations for Modal Logic with Recursion

This paper studies the complexity of classical modal logics , of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complex-ity results for multi-agent logics via translations to and from the & mu;-calculus and modal logic, which allow us to transfer known upper and lower bounds. We also use these translations to introduce a terminating tableau system for the logics we study, based on Kozen's tableau for the & mu;-calculus , the one of Fitting and Massacci for modal logic.