A Metalinguistic Axiomatic Theory of Intelligent Systems: Formal Structures of Cognition, Knowledge, and Theoretical Systems

English abstractThis work develops a metalinguistic axiomatic framework for cognition, knowledge, theories, intelligent systems, and AI. At the cognitive level, the framework distinguishes objectified items, registered meta-level interfaces, and residual metalanguage, retaining failure and unevaluability. Evaluation, object admission, name binding, and state writeback each have separate conditions. At the knowledge level, knowledge-base membership is distinct from verified or assertable status. Provenance, composite status, four-valued judgment, argumentation, tracing, and safe introduction serve distinct roles. At the theory level, theory objects comprise object and relation sets under co-rootedness and well-founded dependency conditions. Theory evaluation, transformation, and positioning have separate conditional interfaces. At the intelligent-system level, maintenance constrains optimization. Boundary, stable, and higher-order intelligence depend on stated criteria; AI generation and model scale alone do not establish these qualifications. Behavioral interfaces conditionally connect complete action, interaction goals and evaluations, and traceable joint descriptions. A six-step metatheoretical workflow organizes the deconstruction, reconnection, and reconstruction of existing theories. Task-relative textual and geometric representations organize theoretical expression and retrieval without replacing the underlying theory texts. The contribution combines theory-internal axiomatic or quasi-axiomatic reconstruction with cross-level interface organization. It makes domains, dependencies, admissibility, failures, and theoretical effects explicit. Empirical scales, engineering realizations, and system effectiveness require independent implementation and testing.中文摘要认知、知识、理论、智能系统与人工智能研究常使用相互分离的概念语言。产生结果与引入对象、保存信息与接受知识、改善输出与维持系统等不同任务,也因此容易混淆。本文建立一套元语言公理化框架,通过对象层与元层接口连接这些研究层次。框架区分已对象化项目、已登记元语言接口,以及当前对象语言不能吸收的元语言余项,并保留失败与不可评价。 在认知与知识方面,框架分别规定求值、对象引入、名称绑定与状态写回的资格。知识库成员不等于已验证或可断言知识。来源、复合知识标签、主显示、四值判断、论证、回溯和安全引入各有职责;它们不构成所有候选必经的流水线。 在理论层,理论由对象集及其中的关系对象集构成,对象集须满足共根与依赖良基条件。原始对象与基本原理由内部前驱读取,理论品质、变换和结构位置则通过各自的条件接口处理。 在系统层,维持约束优化,边界、稳定和高阶智能按明示判据区分。AI的生成与规模本身不证明这些资格成立。行为附录通过条件接口接入完整行为结构、互动目标与评估,以及可追溯的联合描述。行为分类不等同于趋人化或主体资格。 前四章的部分接口被组织为六步流程,并由四组异质方法示例说明。收束命题仅在各步资格与输入输出条件成立时连接环节;示例本身不独立证明这些条件。第8章规定任务相关的文本与几何表示,并区分假设与待定承接位。索引调用受答案覆盖、局部正确性和完整成本约束。 本文结合选定概念的理论内重建与跨层接口组织,明确各项内容的对象域或元层角色、资格、依赖、失败值与理论效力。工程实现、经验量尺和系统效果仍需独立实现与检验。 Full texts and supplementary materialThis record provides the full text in English and Chinese, together with separate English and bilingual Chinese-English theory-framework diagrams to support reading and cross-referencing of the main text. Companion website: yipenggu.com (planned to go online before manuscript submission). 全文与补充材料本记录提供本理论的中英文全文,以及英文版和中英版理论框架图补充材料,供读者辅助理解、定位和对照正文。配套网站域名为yipenggu.com,计划于提交论文前上线。