  Modal dependence logic (MDL) was introduced recently by V\"a\"an\"anen. It
enhances the basic modal language by an operator =(). For propositional
variables p_1,...,p_n the atomic formula =(p_1,...,p_(n-1),p_n) intuitively
states that the value of p_n is determined solely by those of p_1,...,p_(n-1).
We show that model checking for MDL formulae over Kripke structures is
NP-complete and further consider fragments of MDL obtained by restricting the
set of allowed propositional and modal connectives. It turns out that several
fragments, e.g., the one without modalities or the one without propositional
connectives, remain NP-complete. We also consider the restriction of MDL where
the length of each single dependence atom is bounded by a number that is fixed
for the whole logic. We show that the model checking problem for this bounded
MDL is still NP-complete. We additionally extend MDL by allowing classical
disjunction - introduced by Sevenster - besides dependence disjunction and show
that classical disjunction is always at least as computationally bad as bounded
arity dependence atoms and in some cases even worse, e.g., the fragment with
nothing but the two disjunctions is NP-complete. Furthermore we almost
completely classifiy the computational complexity of the model checking problem
for all restrictions of propositional and modal operators for both unbounded as
well as bounded MDL.
