Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define "Polyteam Semantics" in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatisation for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterise the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic (ESO). The analogous result is shown to hold for poly-independence logic and all ESO-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.

中文翻译：

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Polyteam 语义

团队语义是现代依赖和独立逻辑的数学框架，其中公式由一组分配（团队）而不是一阶逻辑中的单个分配来解释。为了深化团队语义和数据库依赖理论之间富有成效的相互作用，我们定义了“Polyteam Semantics”，其中对一系列团队评估公式。我们首先定义了一个新的依赖原子的 polyteam 变体，并给出了相关蕴涵问题的有限公理化。我们将 polyteam 语义与团队语义联系起来，并研究在哪些情况下前者的逻辑可以被后者的逻辑模拟。我们还通过在存在二阶逻辑 (ESO) 中向下封闭和可定义的 polyteams 的属性来表征 poly-dependence 逻辑的表达能力。类似的结果显示适用于多独立逻辑和所有 ESO 可定义的属性。我们还将多包含逻辑与最大定点逻辑联系起来。