  We analyze the causal-observational languages that were introduced in Barbero
and Sandu (2018), which allow discussing interventionist counterfactuals and
functional dependencies in a unified framework. In particular, we
systematically investigate the expressive power of these languages in causal
team semantics, and we provide complete natural deduction calculi for each
language. Furthermore, we introduce a generalized semantics which allows
representing uncertainty about the causal laws, and analyze the expressive
power and proof theory of the causal-observational languages over this enriched
semantics.
