In this paper, we investigate the parameterized complexity of model checking for Dependence Logic which is a well studied logic 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.

中文翻译：

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依赖逻辑复杂性的参数化视图

在本文中，我们研究了依赖逻辑的模型检查的参数化复杂性，这是团队语义领域中一种经过充分研究的逻辑。我们从这个问题的九个直接参数化列表开始，即：析取（即分裂）/（自由）变量/通用量词的数量，公式大小，输入结构的盖夫曼图的树宽，宇宙/团队的大小，以及依赖原子的数量。我们全面展示了模型检查的参数化复杂性，并将问题划分为易处理和各种难处理的程度。此外，我们还通过固定部分输入来考虑模型检查问题的最重要变体（数据和表达式复杂性）的复杂性。