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

arXiv: https://arxiv.org/abs/2501.10190 · HTML: https://mlsanity.com/paper/2501.10190/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Causal reasoning in LLMs, one of 17 directions in LLM reasoning.
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Placed in

- LLM reasoning / [Causal reasoning in LLMs](https://mlsanity.com/lr/causal-reasoning-in-llms/)

## Builds on (most cited first, 5 of 5)

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [Reasoning About Causal Models With Infinitely Many Variables](https://mlsanity.com/paper/2112.11362/) (2021)
- [Equivalent Causal Models](https://mlsanity.com/paper/2012.05603/) (2020)

## Abstract (arXiv)

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 textitrecursive 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.