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

Structural Equation Models (SEM) are the standard approach to representing causal dependencies between variables in causal models. In this paper we propose a new interpretation of SEMs when reasoning about Actual Causality, in which SEMs 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 formalisms, and to introduce a temporal logic, CPLTL, for causal reasoning about such structures. We show that the standard restriction to socalled recursive models (with no cycles in the dependency graph) is not necessary in our approach, allowing us to reason about mutually dependent processes and feedback loops. Finally, introduce new notions of model equivalence for temporal causal models, and show that CPLTL has an efficient model-checking procedure. * This is an extended version of the same title paper published in the proceeding of AAAI-25 conference (Gladyshev et al. 2025). This version contains an additional section, in which we introduce TSEMs with arbitrary long temporal delays between causal dependencies and prove that these models are equivalent to TSEMs with 1-step delays only introduced in the original version of the paper.