We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We also devise a game-theoretic semantics equivalent to the double team semantics. We make use of the double team semantics by defining a logic $$\hbox {DC}^2$$DC2 which canonically fuses together two-variable dependence logic$$\hbox {D}^2$$D2 and two-variable logic with counting quantifiers$$\hbox {FOC}^2$$FOC2. We establish that the satisfiability and finite satisfiability problems of $$\hbox {DC}^2$$DC2 are complete for $$\hbox {NEXPTIME}$$NEXPTIME.

中文翻译：

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广义量词的双重团队语义

我们用广义量词研究依赖逻辑的扩展。我们还介绍和研究了广义原子的概念。我们定义了一个语义系统，它可以适应依赖逻辑的变体，可能在同一个框架下扩展为广义量词和广义原子。语义基于成对的团队或双人团队。我们还设计了一种等效于双人组语义的博弈论语义。我们通过定义一个逻辑 $$\hbox {DC}^2$$DC2 来利用双组语义，该逻辑将二变量依赖逻辑$$\hbox {D}^2$$D2 和二变量逻辑规范地融合在一起带有计数量词$$\hbox {FOC}^2$$FOC2。我们确定$$\hbox {DC}^2$$DC2 的可满足性和有限可满足性问题对于$$\hbox {NEXPTIME}$$NEXPTIME 是完备的。