Embedding causal team languages into predicate logic

Causal team semantics ([2]) supports causal-observational languages, which enrich the languages for deterministic causation ([11,18]) with dependencies and other team-specific operators. Handling the causal aspects of these languages requires a richer semantics than propositional team semantics; nonetheless, in this paper we show that the causal-observational languages considered in [2] can be embedded into first-order dependence logic by means of a translation and a careful choice of models. We show that, in some significant cases, the translation can be refined to an embedding into the Bernays-Schonfinkel-Ramsey fragment of dependence logic or, in the restricted case of recursive causal models, into the existential fragment. As an application, we use the embeddings to show the decidability of a satisfiability problem for the causal-observational languages. Along the way, we question the correctness of the semantics for interventionist counterfactuals proposed by Halpern ([18]) and propose an alternative one which behaves as usual in the uncontroversial recursive case.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).