Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic systems, the case for abstracting probabilistic models is not yet fully understood. In this paper, we provide a semantical framework for analyzing such abstractions from first principles. We develop the framework in a general way, allowing for expressive languages, including logic-based ones that admit relational and hierarchical constructs with stochastic primitives. We motivate a definition of consistency between a high-level model and its low-level counterpart, but also treat the case when the high-level model is missing critical information present in the low-level model. We prove properties of abstractions, both at the level of the parameter as well as the structure of the models. We conclude with some observations about how abstractions can be derived automatically.

中文翻译：

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抽象概率模型：逻辑视角

摘要是科学中广泛使用的强大思想，通过省略不相关的细节，在更易于处理的搜索空间中对系统的行为进行建模、推理和解释。尽管确定性系统的抽象概念已经成熟，但对概率模型进行抽象的情况尚未完全理解。在本文中，我们提供了一个语义框架，用于从第一原理分析此类抽象。我们以通用方式开发框架，允许表达语言，包括基于逻辑的语言，这些语言允许具有随机原语的关系和层次结构。我们提出了高级模型与其低级对应物之间一致性的定义，但也会处理高级模型缺少低级模型中存在的关键信息的情况。我们证明抽象的性质，无论是在参数层面还是在模型结构层面。我们总结了一些关于如何自动导出抽象的观察结果。