Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current approaches often distill detailed probabilistic data into higher-level summaries to support tractable and interpretable analyses, though they typically struggle to fully represent the relational and probabilistic hierarchies through single-layered abstractions. We introduce a hierarchical probabilistic abstraction framework aimed at addressing these challenges by extending a measure-theoretic foundation for hierarchical abstraction. The framework enables modular problem-solving via layered mappings, facilitating both detailed layer-specific analysis and a cohesive system-wide understanding. This approach bridges high-level conceptualization with low-level perceptual data, enhancing interpretability and allowing layered analysis. Our framework provides a robust foundation for abstraction analysis across AI subfields, particularly in aligning System 1 and System 2 thinking, thereby supporting the development of diverse abstraction methodologies.

翻译：抽象是降低跨领域系统复杂性的关键手段，然而为概率模型设计有效的抽象方法因随机行为与不确定性的存在而具有内在挑战性。现有方法通常将详细的概率数据提炼为更高层次的摘要以支持可处理且可解释的分析，但这些方法往往难以通过单层抽象完整表征关系与概率的层次结构。本文提出一种层次化概率抽象框架，旨在通过扩展层次化抽象的测度论基础来解决这些挑战。该框架通过分层映射实现模块化问题求解，既支持针对特定层次的详细分析，也促进对系统整体的连贯理解。此方法衔接了高层次概念化与低层次感知数据，增强了可解释性并允许分层分析。我们的框架为人工智能各子领域的抽象分析提供了坚实基础，特别是在对齐系统1与系统2思维方面，从而支持多样化抽象方法的发展。