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

TL;DR

This paper introduces a novel interpretation of Structural Equation Models for causal reasoning, enabling analysis of feedback loops and mutual dependencies through a new temporal logic, CPLTL, with an efficient model-checking process.

Contribution

It presents a new non-recursive SEM interpretation for causal reasoning, integrating counterfactuals with temporal logic, and introduces CPLTL for analyzing complex causal structures.

Findings

Allows reasoning about feedback loops in causal models

Develops an efficient model-checking procedure for CPLTL

Extends causal reasoning beyond recursive models

Abstract

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.