Causality Without Causal Models
This work addresses a foundational problem in causality theory for researchers and practitioners by extending causal definitions beyond structural equation models, though it is incremental as it builds on existing definitions.
The paper tackles the limitation of the Halpern-Pearl causality definition by abstracting it to work with any model that defines counterfactuals, enabling application to a wider range of models and formulas, including those with disjunctions, negations, beliefs, and nested counterfactuals.
Perhaps the most prominent current definition of (actual) causality is due to Halpern and Pearl. It is defined using causal models (also known as structural equations models). We abstract the definition, extracting its key features, so that it can be applied to any other model where counterfactuals are defined. By abstracting the definition, we gain a number of benefits. Not only can we apply the definition in a wider range of models, including ones that allow, for example, backtracking, but we can apply the definition to determine if A is a cause of B even if A and B are formulas involving disjunctions, negations, beliefs, and nested counterfactuals (none of which can be handled by the Halpern-Pearl definition). Moreover, we can extend the ideas to getting an abstract definition of explanation that can be applied beyond causal models. Finally, we gain a deeper understanding of features of the definition even in causal models.