We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under the Boolean negation. Our logics employ new probabilistic atoms that resemble so-called extended atoms from the team semantics literature. We also define counterparts of our logics over metafinite structures and show that all of our logics can be translated into functional fixed point logic implying a polynomial time upper bound for data complexity with respect to BSS-computations.

中文翻译：

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关于定量依赖性的基本逻辑

我们在概率团队语义的框架内和超元限制结构中定义和研究逻辑。我们的工作与最近在布尔语义下关闭的团队语义中的可公理化和易处理性逻辑的新发展并行。我们的逻辑采用了类似于团队语义学文献中所谓的扩展原子的新概率原子。我们还定义了与元有限结构相对应的逻辑，并表明我们所有的逻辑都可以转换为函数定点逻辑，这意味着相对于BSS计算，数据复杂度为多项式时间上限。