Modal dependence logic was introduced very recently by Väänänen. It

enhances the basic modal language by an operator dep. For propositional

variables p_1,...,p_n, dep(p_1,...,p_(n-1);p_n) intuitively states that

the value of p_n only depends on those of p_1,...,p_(n-1). Sevenster (J.

Logic and Computation, 2009) showed that satisfiability for modal

dependence logic is complete for nondeterministic exponential time.

In this paper we consider fragments of modal dependence logic obtained

by restricting the set of allowed propositional connectives. We show

that satisfibility for poor man's dependence logic, the language

consisting of formulas built from literals and dependence atoms using

conjunction, necessity and possibility (i.e., disallowing disjunction),

remains NEXPTIME-complete. If we only allow monotone formulas (without

negation, but with disjunction), the complexity drops to

PSPACE-completeness. We also extend Väänänen's language by allowing

classical disjunction besides dependence disjunction and show that the

satisfiability problem remains NEXPTIME-complete. If we then disallow

both negation and dependence disjunction, satistiability is complete for

the second level of the polynomial hierarchy.

In this way we completely classify the computational complexity of the

satisfiability problem for all restrictions of propositional and

dependence operators considered by Väänänen and Sevenster.