  In this paper we investigate an extended version of modal dependence logic by
allowing arbitrary Boolean connectives. Modal dependence logic was recently
introduced by Jouko V\"a\"an\"anen by extending modal logic by a the dependence
atom dep(.). In this paper we study the computational complexity of the model
checking problem. For a complete classification of arbitrary Boolean functions
we are using a Lattice approach introduced by Emil Post. This classification is
done for all fragments of the logical language allowing modalities $\Diamond$
and $\Box$, the dependence atom, and logical symbols for arbitrary Boolean
functions.
