Temporal Causal Reasoning with (Non-Recursive) Structural Equation Models

Structural equation models (SEM) are a standard approach to representing causal dependencies between variables. In this paper we propose a new interpretation of existing formalisms in the field of Actual Causality in which SEM's are viewed as mechanisms transforming the dynamics of exogenous variables into the dynamics of endogenous variables. This allows us to combine counterfactual causal reasoning with existing temporal logic formalizms, and to introduce a temporal logic, CPLTL, for causal reasoning about such structures. Then, we demonstrate that the standard restriction to so-called recursive models (with no cycles in the dependency graphs) is not necessary in our approach. This fact provides us extra tools for reasoning about mutually dependent processes and feedback loops. Finally, we introduce the notions of model equivalence for temporal causal models and show that CPLTL has an efficient model-checking procedure.