抽象、组合与合同：一种她af理论方法
Abstraction, Composition and Contracts: A Sheaf Theoretic Approach
AI总结：
本文提出基于她af理论、范畴论和拓扑学的框架，用于复杂系统组合的抽象与分析，通过sheaves建模系统行为，定义连接图并建立直觉逻辑语义。
摘要：
复杂系统-of-systems（SoS）由多个相互连接的子系统组成。通常，每个子系统使用特定的计算模型方法进行设计和分析，如Petri网、连续时间ODEs、非确定自动机等。在连接子系统时，设计师需根据子系统模型选择共同的抽象框架进行分析。本文引入一种新的框架，基于她af理论、范畴论和拓扑学的结果和方法，通过sheaves建模系统行为，利用范畴论方法定义连接图并形式化组合，并通过与拓扑学的联系，定义一种形式的（直觉/构造）逻辑，具有良好的sheaf语义。
英文摘要：
Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of computation considered --- Petri nets, continuous time ODEs, nondeterministic automata, to name a few. When interconnecting subsystems, a designer needs to choose, based on the specific subsystems models, a common abstraction framework to analyze the composition. In this paper we introduce a new framework for abstraction, composition and analysis of SoS that builds on results and methods developed in sheaf theory, category theory and topos theory. In particular, we will be modeling behaviors of systems using sheaves, leverage category theoretic methods to define wiring diagrams and formalize composition and, by establishing a connection with topos theory, define a formal (intuitionistic/constructive) logic with a sound sheaf semantics
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
