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 we analyze the expressive power and proof theory of the causal-observational languages over this enriched semantics.
"Characterizing Counterfactuals and Dependencies over (Generalized) Causal Teams." Notre Dame J. Formal Logic 63 (3) 301 - 341, August 2022. https://doi.org/10.1215/00294527-2022-0017