A parameterized view on the complexity of dependence and dependence logic

In this paper, we investigate the parameterized complexity of model checking for Dependence and Independence logic, which are well studied logics in the area of Team Semantics. We start with a list of nine immediate parameterizations for this problem, namely the number of disjunctions (i.e. splits)/(free) variables/universal quantifiers, formula-size, the tree-width of the Gaifman graph of the input structure, the size of the universe/team and the arity of dependence atoms. We present a comprehensive picture of the parameterized complexity of model checking and obtain a division of the problem into tractable and various intractable degrees. Furthermore, we also consider the complexity of the most important variants (data and expression complexity) of the model checking problem by fixing parts of the input.