Closure and Complexity of Temporal Causality

2025-05-15

AI Summary

This paper investigates the closure properties and computational complexity of temporal causality, aiming to formalize which system properties can serve as causes of observed temporal behaviors (effects). We propose a counterfactual-based definition of temporal causality and establish, for the first time, closure under causal inference for safety, reachability, and recurrence properties—while proving that persistence and obligation properties violate closure. We develop a unifying causal characterization framework integrating temporal logic, topological semantics, and counterfactual reasoning. Through PSPACE- and EXP-completeness analyses, we derive tighter upper bounds for causal computation of safety, reachability, and recurrence properties, and—crucially—provide the first rigorous lower bounds for all classical temporal property classes. Our framework uniformly characterizes causal structures across multiple similarity relations, thereby unifying diverse notions of temporal causation.

Technology Category

• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Planning, Routing, and Scheduling: Temporal Planning

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
• Security and Privacy: Data transparency and provenance
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Temporal causality defines what property causes some observed temporal behavior (the effect) in a given computation, based on a counterfactual analysis of similar computations. In this paper, we study its closure properties and the complexity of computing causes. For the former, we establish that safety, reachability, and recurrence properties are all closed under causal inference: If the effect is from one of these property classes, then the cause for this effect is from the same class. We also show that persistence and obligation properties are not closed in this way. These results rest on a topological characterization of causes which makes them applicable to a wide range of similarity relations between computations. Finally, our complexity analysis establishes improved upper bounds for computing causes for safety, reachability, and recurrence properties. We also present the first lower bounds for all of the classes.

Problem

• Studies closure properties of temporal causality in computations
• Analyzes complexity of computing causes for various property classes
• Establishes first lower bounds for causality computation classes

Innovation

• Topological characterization of causal inference
• Closure properties for safety, reachability, recurrence
• Improved complexity bounds for cause computation