AI身份的类型论解释
A Category Theory Account of AI Identity
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中文总结 AI 辅助
本文用范畴论形式化AI系统身份，通过弱解释（信任度相等）和强解释（互保信任可达性）刻画历时与共时身份，为负责任AI主张的跨版本转移提供结构化前提。
中文摘要 AI 辅助
人工智能系统在部署后经常通过再训练和环境变化进行修改。这些转变引发了一个形而上学问题：在什么条件下，AI系统在时间或跨部署中保持同一系统？早期工作通过将固定AI系统类型内的身份与信任度水平的相等性相关联，以命题形式阐述了共时和历时身份。这些标准指定了身份陈述何时为真，但隐含了所比较状态的结构、连接它们的变换以及持久性的时间组织。我们开发了AI身份的范畴论形式化。AI系统类型由包含技术功能、信任度概况和信任度水平函数的数据指定。轮廓相对状态通过可允许的生命周期路径连接，这些路径限于保持信任度水平的变换，并商化以获得可达性范畴。时间可允许函子表示AI系统历史，而时间同步自然变换比较实现的历史。该形式化产生了早期AI身份标准的两种范畴论解释。弱解释将身份恢复为信任度水平的相等性。强解释要求互保信任可达性，通过状态同构或实现历史的自然同构表达。因此，范畴论用历时和共时标准的结构化层次取代了单一的AI身份关系。由此产生的框架确定了将负责任AI的主张、证据和治理程序跨版本或部署转移的身份相关前提，而不将范畴身份本身视为此类转移的充分条件。
英文摘要
Artificial intelligence (AI) systems are routinely modified after deployment through retraining and changes in their environments. These transformations raise a metaphysical question: under what conditions does an AI system remain the same system over time or across deployments? Earlier work formulates synchronic and diachronic identity propositionally, by relating identity within a fixed AI system type to equality of trustworthiness levels. Such criteria specify when identity statements are true, but leave implicit the structure of the states compared, the transformations connecting them, and the temporal organization of persistence. We develop a category-theoretic formalization of AI identity. An AI system type is specified by a datum consisting of a techno-function, a trustworthiness profile, and a trustworthiness-level function. Profile-relative states are connected by admissible lifecycle paths, which are restricted to trustworthiness-level-preserving transformations and quotiented to obtain a reachability category. Temporally admissible functors represent AI system histories, while time-synchronous natural transformations compare realized histories. The formalization yields two categorical interpretations of the earlier AI identity criteria. A weak interpretation recovers identity as equality of trustworthiness level. A strong interpretation requires mutual trustworthiness-preserving reachability, expressed through state isomorphism or natural isomorphism of realized histories. Category theory therefore replaces a single AI identity relation with a structured hierarchy of diachronic and synchronic criteria. The resulting framework identifies identity-related preconditions for transferring responsible-AI claims, evidence, and governance procedures across versions or deployments, without treating categorical identity as sufficient by itself for such transfer.
