Characterizing Counterfactuals and Dependencies over (Generalized) Causal Teams

Abstract

This is a repository copy of Characterizing counterfactuals and dependencies over (generalized) causal teams.

Team Semantics for Interventionist Counterfactuals: Observations vs. Interventions

“…Proof. The paper (Barbero and Yang, 2022) proves the strong completeness of a (finitary) system of axioms and (natural deduction style) rules for CO formulas. 5 We will show that the axioms and rules of said system are derivable in finitely many steps in our system, from which the statement immediately follows.…”

“…The validity of C3-4-4b was pointed out in (Barbero and Sandu, 2021), and the importance of C5 in (Barbero and Yang, 2022).…”

“…Axioms C6, C7 and C11 take the same roles as the principles of Effectiveness, Composition and Recursivity from (Galles and Pearl, 1998). The current, more intuitive form of axiom C7 was introduced in (Barbero and Yang, 2022). Halpern (Halpern, 2000) noticed that distributes over boolean operators, and formulated analogues of C1 and C2.…”

“…The axioms ValDef and ValUnq of ( Barbero and Yang, 2022) are special cases of our axioms A3 and A1, respectively.…”

“…The three operators can be studied in a shared semantic framework called causal multiteam semantics. The framework is meaningful already in a non-probabilistic context, where it has been studied both from a semantic and a proof-theoretic perspective (Barbero and Sandu, 2021;Barbero and Yang, 2022;Barbero and Galliani, 2022). The proof-theoretical results rely on a body of earlier work ((Galles and Pearl, 1998;Halpern, 2000;Briggs, 2012)) on proof systems for (non-probabilistic) counterfactuals evaluated on structural equation models (of which the causal multiteams are a generalization).…”