Temporal Causal Reasoning with (Non-Recursive) Structural Equation Models
This work addresses causal reasoning in AI and formal methods, offering a novel framework for handling non-recursive models and temporal aspects, which is incremental in extending existing SEM and logic approaches.
The paper tackles the problem of causal reasoning with Structural Equation Models (SEMs) by proposing a new interpretation that views SEMs as mechanisms transforming exogenous to endogenous variable dynamics, enabling combination with temporal logic and introduction of CPLTL for causal reasoning, and shows that recursive restrictions are unnecessary, allowing reasoning about feedback loops, with results including efficient model-checking for CPLTL.
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 so-called \textit{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, we introduce new notions of model equivalence for temporal causal models, and show that CPLTL has an efficient model-checking procedure.