A new proof of completeness for a relative modal logic with composition and intersection

This paper is devoted to the completeness issue of RMLCI | the relative modal logic with composition and intersection | a restriction of the propositional dynamic logic with intersection. The trouble with RMLCI is that the operation of intersection is not modally deenable. Using the notion of mosaics, we give a new proof of a theorem considered in a previous paper \Complete axiomatization of a relative modal logic with composition and intersection". The theorem asserts that the proof theory of RMLCI is complete for the standard Kripke semantics of RMLCI.