We study the expressivity and the complexity of various logics in probabilistic team semantics with the Boolean negation. In particular, we study the extension of probabilistic independence logic with the Boolean negation, and a recently introduced logic FOPT. We give a comprehensive picture of the relative expressivity of these logics together with the most studied logics in probabilistic team semantics setting, as well as relating their expressivity to a numerical variant of second-order logic. In addition, we introduce novel entropy atoms and show that the extension of first-order logic by entropy atoms subsumes probabilistic independence logic. Finally, we obtain some results on the complexity of model checking, validity, and satisfiability of our logics.

翻译：本研究探讨了在概率团队语义框架下，带有布尔否定的各类逻辑的表达能力与计算复杂性。我们重点研究了概率独立逻辑在加入布尔否定后的扩展形式，以及近期提出的逻辑FOPT。本文全面刻画了这些逻辑与概率团队语义中最常研究的逻辑之间的相对表达能力，并将它们的表达能力与一种数值化的二阶逻辑变体联系起来。此外，我们引入了新的熵原子，并证明了通过熵原子扩展的一阶逻辑能够涵盖概率独立逻辑。最后，我们获得了关于这些逻辑的模型检测、有效性与可满足性问题的若干复杂性结果。