At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is a~fundamental, often implicit, principle that structures the understanding, communication, and development of both scientific knowledge and everyday beliefs. Studies on abstraction have evolved from its origins in Ancient Greek philosophy through methodological approaches in psychological and philosophical theories to modern computational frameworks. This paper presents a novel logic-based framework for modeling abstraction processes in which all components are expressed within logic. The framework extends beyond the traditional focus on the entailment of necessary conditions by making sufficient conditions first-class citizens as well. We define approximate abstractions, study their tightest and exact forms, and extend the approach to layered abstractions, enabling hierarchical simplification of complex systems and models. The computational complexity of the related reasoning tasks is also discussed. For clarity, our framework is developed within classical logic, chosen for its simplicity, expressiveness, and computational friendliness.

翻译：抽象化的核心在于从具体实例归纳至更广泛概念或模型的过程，其主要目标是在保留预期目的所必需性质的同时降低复杂性。这是一个基础性且常隐含的原则，它构建了科学知识与日常认知的理解、交流和发展体系。关于抽象化的研究从古希腊哲学起源，历经心理学与哲学理论的方法论探索，已发展至现代计算框架。本文提出一种新颖的基于逻辑的抽象化过程建模框架，其中所有组件均通过逻辑语言表达。该框架突破传统对必要条件蕴涵的局限，将充分条件提升为同等重要的核心要素。我们定义了近似抽象化，研究其最紧致与精确形式，并将该方法扩展至分层抽象化，从而实现对复杂系统与模型的层级化简化。文中亦探讨了相关推理任务的计算复杂度。为保持清晰性，本框架基于经典逻辑构建——该逻辑体系因其简洁性、表达力与计算友好性而被选用。