  In this paper, we initiate a systematic study of the parametrised complexity
in the field of Dependence Logics which finds its origin in the Dependence
Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this
logic (PDL) and investigate a variety of parametrisations with respect to the
central decision problems. The model checking problem (MC) of PDL is
NP-complete. The subject of this research is to identify a list of
parametrisations (formula-size, treewidth, treedepth, team-size, number of
variables) under which MC becomes fixed-parameter tractable. Furthermore, we
show that the number of disjunctions or the arity of dependence atoms
(dep-arity) as a parameter both yield a paraNP-completeness result. Then, we
consider the satisfiability problem (SAT) showing a different picture: under
team-size, or dep-arity SAT is paraNP-complete whereas under all other
mentioned parameters the problem is in FPT. Finally, we introduce a variant of
the satisfiability problem, asking for teams of a given size, and show for this
problem an almost complete picture.
