In [4], we introduced an extension of team semantics (causal teams) which assigns an interpretation to interventionist counterfactuals and causal notions based on them (as e.g. in Pearl's and Woodward's manipulationist approaches to causation). We now present a further extension of this framework (causal multiteams) which allows us to talk about probabilistic causal statements. We analyze the expressivity resources of two causal-probabilistic languages, one finitary and one infinitary. We show that many causal-probabilistic notions from the field of causal inference can be expressed already in the finitary language, and we prove a normal form theorem that throws new light on Pearl's ``ladder of causation''. On the other hand, we provide an exact semantic characterization of the infinitary language, which shows that this language captures precisely those causal-probabilistic statements that do not commit us to any specific interpretation of probability; and we prove that no usual, countable language is apt for this task.

翻译：在文献[4]中，我们引入了团体语义学的一种扩展（因果团体），该扩展为基于干预主义的反事实及其因果关系概念提供了解释（例如珀尔和伍德沃德关于因果关系的操控主义方法）。我们现在提出该框架的进一步扩展（因果多团体），它使我们能够讨论概率因果陈述。我们分析了两种因果概率语言（一种有限语言和一种无限语言）的表达力资源。我们证明，因果推断领域的许多因果概率概念已经可以在有限语言中得到表达，并且我们证明了一个范式定理，为珀尔的“因果关系阶梯”提供了新的视角。另一方面，我们提供了无限语言的精确语义刻画，表明这种语言恰好捕获了那些不使我们承诺任何特定概率解释的因果概率陈述；我们还证明，没有通常的可数语言适用于这一任务。