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

2025-01-17

AI Summary

This paper addresses the challenges of causal temporal modeling and cyclic dependency analysis in non-recursive structural equation models (SEMs). Methodologically, it transcends the limitations of traditional recursive SEMs by interpreting an SEM as a dynamical system wherein exogenous variables drive the temporal evolution of endogenous variables; it introduces the temporal causal logic CPLTL, defines equivalence of non-recursive causal models under counterfactual semantics, and establishes a formal verification framework supporting feedback loops and mutual dependencies. Key contributions include: (i) the first temporal causal logic framework tailored to non-recursive SEMs; (ii) a proof that CPLTL model checking is polynomial-time decidable; and (iii) practical causal identification and efficient formal verification for systems exhibiting cyclic dependencies.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

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 extit{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.

Problem

• Causal Relationships
• Non-recursive Structural Equation Models
• Model Similarity

Innovation

• Non-recursive Structural Equation Modeling
• CPLTL Temporal Logic
• Model Similarity Judgment