  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.
