Model Checking for Modal Dependence Logic: An Approach Through Post's Lattice

Abstract: 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.