On the logic of interventionist counterfactuals under indeterministic causal laws

TL;DR

The paper generalizes causal modeling to indeterministic laws by adopting relational causal teams, where laws are represented as relations rather than functions and interventions yield sets of possible outcomes. It develops a Halpern-style logic for interventionist counterfactuals, providing sound and complete axiomatizations for the full class of relational causal teams and for the recursive (acyclic) subclass. It identifies crucial differences from deterministic models, such as the emergence of uncertainty and the need to explicitly specify causal parents, and shows that traditional Composition may fail in the indeterministic setting while other principles adapt under recursion. The framework lays a rigorous foundation for reasoning about counterfactuals under indeterministic laws and opens paths toward deeper connections with determinism, totality, and classical counterfactual theories.

Abstract

We investigate the generalization of causal models to the case of indeterministic causal laws that was suggested in Halpern (2000). We give an overview of what differences in modeling are enforced by this more general perspective, and propose an implementation of generalized models in the style of the causal team semantics of Barbero & Sandu (2020). In these models, the laws are not represented by functions (as in the deterministic case), but more generally by relations. We analyze significant differences in the axiomatization of interventionist counterfactuals in the indeterministic vs. the deterministic case, and provide strongly complete axiomatizations over the full class of indeterministic models and over its recursive subclass.