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

Summary

This partial ingest is based on the extracted full PDF text. Gladyshev et al. reinterpret Structural Equation Models as mechanisms that transform time series of exogenous values into time series of endogenous values. The resulting temporal causal framework combines interventions with past/future temporal logic in CPLTL, supports non-recursive SEMs without solving simultaneous equations at a single time, defines temporal and rescalable model equivalence, and gives an efficient model-checking story for temporal causal claims.

Key Claims

• Many causal claims are temporally extended: they ask not only whether A causes B, but whether A at one time causes B at another.
• Static SEMs are not designed for temporal behavior; treating equations as one-step mechanisms lets SEMs generate computations over time.
• Non-recursive dependency graphs become well-behaved under temporal interpretation because current values depend on previous-step values rather than simultaneous fixed points.
• CPLTL combines time-indexed interventions with LTL-style past and future modalities.
• Temporal equivalence and rescalable equivalence compare causal models by their observable trajectories under interventions, including models that run on different time scales.

Methods / Formalism

• A temporal context is an infinite sequence of exogenous assignments:

$$\vec{u}:\mathbb{N}\to \prod _{U\in \mathcal{U}}R(U).$$

• Given a causal model M, temporal context u, and default endogenous assignment v, the computation C satisfies C(0)=v and for i>0 applies each structural equation to the previous time step.
• A time-sensitive intervention such as Y(n) <- y fixes the value of endogenous variable Y at step n.
• CPLTL formulas have the form [Y(n)<-y]psi, where psi is a past/future LTL formula over endogenous assignments.
• Temporal model equivalence requires agreement on observables under all observable interventions; rescalable equivalence allows one model’s tick to correspond to k ticks of another.
• Temporal Structural Equation Models collects the TSEM/CPLTL construction and its connection to the follow-up computation paper.

Evidence / Experiments

• The paper is theoretical and example-driven.
• Treatment/recovery examples show why feedback loops can be represented cleanly as non-recursive temporal SEMs.
• Firing-squad and deadline examples illustrate delayed causal effects, chain-free model representations, and time-scale dependence.
• The paper reports an efficient model-checking procedure for CPLTL over the represented temporal causal scenarios.

Connections

• Extends Structural Equation Models with temporal contexts, time-indexed interventions, and LTL-style properties.
• Bridges Causality and Temporal Logic by making temporal formulas the language of causal effects.
• Connects to Actual Causality because it supports questions about temporally located causes and outcomes.
• Prepares the ground for Gladyshev2026 - Temporal Causal Models as a Model of Computation, where TSEMs are used as computational devices.

Open Questions

• The framework assumes discrete time and requires the modeler to specify what one tick means.
• The equivalence notions depend on choosing observable variables and intervention classes.
• Extending the logic to richer intervention types, learned temporal abstractions, or stochastic/noisy temporal SEMs remains open.

Citation

Gladyshev, M., Alechina, N., Dastani, M., Doder, D., and Logan, B. (2025). Temporal Causal Reasoning with (Non-Recursive) Structural Equation Models. AAAI 2025 extended version, arXiv:2501.10190v2.