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：我们研究了在带有布尔否定的概率团队语义下各种逻辑的表达力与复杂性。特别地，我们考察了概率独立逻辑添加布尔否定后的扩展，以及近期引入的逻辑FOPT。我们完整刻画了这些逻辑与概率团队语义框架中最常研究的逻辑之间的相对表达力，并将其表达力与二阶逻辑的数值变体相联系。此外，我们引入了新颖的熵原子，并证明通过熵原子扩展的一阶逻辑可涵盖概率独立逻辑。最后，我们获得了关于这些逻辑的模型检测、有效性和可满足性复杂性方面的一些结果。