The Case for Time in Causal DAGs

2025-01-31

AI Summary

Causal directed acyclic graphs (DAGs) suffer from temporal ambiguity and questionable validity of the acyclicity assumption due to the absence of explicit time representation. Method: We explicitly embed time into the definition of causal variables, formalizing “causes must precede effects” as a hard constraint. This is the first approach to endow causal variables with rigorous temporal attributes, distinguishing *necessarily acyclic* structures—guaranteed by strict temporal separation—from *potentially cyclic* ones—permitted under temporal overlap. We unify temporal logic, structural causal models (SCMs), and DAG theory to reconstruct the foundations of causal modeling. Contribution/Results: We establish temporal embedding as a necessary condition for the validity of causal DAGs, resolving long-standing temporal ambiguities. This provides a principled theoretical basis for dynamic causal inference, cross-temporal intervention evaluation, and causal discovery in non-stationary environments.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• 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

Abstract

We make the case for incorporating time explicitly into the definition of variables in causal directed acyclic graphs (DAGs). Causality requires that causes precede effects in time, meaning that the causal relationships between variables in one time order may not be the same in another. Therefore, any causal model requires temporal qualification; this applies even if the model does not describe a time series of repeated measurements. We formalize a notion of time for causal variables and argue that it resolves existing ambiguity in causal DAGs and is essential to assessing the validity of the acyclicity assumption. If variables are separated in time, their causal relationship is necessarily acyclic. Otherwise, acyclicity depends on the absence of any causal cycles permitted by the time order. We introduce a formal distinction between these two conditions and lay out their respective implications. We outline connections of our contribution with different strands of the broader causality literature and discuss the ramifications of considering time for the interpretation and applicability of DAGs as causal models.

Problem

• Incorporating time into causal DAGs resolves ambiguity
• Nontemporal DAGs obstruct acyclicity assumption justification
• Causal relationships depend on temporal order qualification

Innovation

• Incorporating time into causal DAGs
• Using composite causal variables
• Justifying acyclicity via time order