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

Julian-Steffen Müller, Heribert Vollmer

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 Väänänen 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 \(\lozenge\) and □, the dependence atom, and logical symbols for arbitrary Boolean functions.