  We introduce an extension of team semantics which provides a framework for
the logic of manipulationist theories of causation based on structural equation
models, such as Woodward's and Pearl's; our causal teams incorporate (partial
or total) information about functional dependencies that are invariant under
interventions. We give a unified treatment of observational and causal aspects
of causal models by isolating two operators on causal teams which correspond,
respectively, to conditioning and to interventionist counterfactual
implication. We then introduce formal languages for deterministic and
probabilistic causal discourse, and show how various notions of cause (e.g.
direct and total causes) may be defined in them.
  Through the tuning of various constraints on structural equations
(recursivity, existence and uniqueness of solutions, full or partial definition
of the functions), our framework can capture different causal models. We give
an overview of the inferential aspects of the recursive, fully defined case;
and we dedicate some attention to the recursive, partially defined case, which
involves a shift of attention towards nonclassical truth values.
