Temporal Causal Models as a Model of Computation

2026-05-07

AI Summary

This work investigates the formal integration of causal reasoning into computational theory, with a focus on the relationship between causal models and classical computational frameworks in temporal settings. By treating Temporal Structural Equation Models (TSEMs) as a computational model, the study extends traditional causal frameworks to support reasoning over time and employs tools from formal language and automata theory for rigorous analysis. The primary contribution lies in establishing, for the first time, that TSEMs can encode linear bounded automata and, under countable variables, achieve Turing completeness. Furthermore, the paper demonstrates that TSEMs possess expressive power equivalent to context-sensitive languages, thereby laying a theoretical foundation for unifying counterfactual reasoning with computational theory.

Abstract

Causal models, also known as Structural Equation Models (SEM), are a well-known formalism for representing and reasoning about causal dependencies between events. In this paper, we show that Temporal SEMs (TSEMs), which extend SEMs to support causal reasoning in temporal settings, can be interpreted as a model of computation. We prove that TSEMs can encode Linear Bounded Automata, and thus causal settings representable in context sensitive languages. We also prove that TSEMs with countably many variables are Turing complete. These results establish a formal connection between causal reasoning and classical models of computation, enabling the integration of counterfactual reasoning techniques from causal inference into the theory of computation.

Problem

• Temporal Causal Models
• Structural Equation Models
• Model of Computation
• Turing Completeness
• Causal Reasoning

Innovation

• Temporal SEMs
• model of computation
• Turing completeness
• causal reasoning
• Linear Bounded Automata