Cut–Free Axiomatizations for Stratified Modal Fixed Point Logic

We present an infinitary and a finitary cut–free axiomatization for a fragment of the modal μ–calculus in which nesting of fixed points is restricted to non–interleaving occurrences. In this study we prove soundness and completeness of both axiomatizations. Completeness is established by constructing a canonical countermodel to any non– provable formula using an extension of the method of saturated sequents. Soundness of the finitary axiomatization is a consequence of the small model property and well–known results about monotone operators while completeness follows from the corresponding result for the infinitary case.