提出统一的'状态'形式框架，支撑智能与跨领域理论构建。
A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation
- 构建分层状态网格，统一数学、物理与语言中的状态描述。
- 引入中间元宇宙模型，避免自指矛盾并支持元认知操作。
- 打通宏观与微观跨宇宙操作，适用于智能定义与理论建模。
本研究旨在通过引入数学严谨且统一的形式结构，强化各类系统（包括智能的公理化定义）的理论基础，解决长期缺乏共识与形式清晰度的'状态'概念问题。首先，提出由'状态深度'与'映射层级'构成的'分层状态网格'，建立跨数学、物理和语言领域的统一记号系统。其次，引入'中间元宇宙（IMU）'，明确描述定义者（我们自身）及所用语言，实现意识层面的元操作，同时规避自指与逻辑不一致。在此元理论基础上，将跨宇宙理论从数学拓展至语言翻译与智能体整合，提出宏观跨宇宙与微观跨宇宙操作的概念区分，以增强表达力。本文最终构建了一个以'定义=状态'为原则的元形式逻辑框架，贯穿时间、语言、智能体与操作，为智能定义、形式逻辑及科学理论提供坚实的数学基础。
原文摘要 · Abstract (English)
This study aims to reinforce the theoretical foundation for diverse systems--including the axiomatic definition of intelligence--by introducing a mathematically rigorous and unified formal structure for the concept of 'state,' which has long been used without consensus or formal clarity. First, a 'hierarchical state grid' composed of two axes--state depth and mapping hierarchy--is proposed to provide a unified notational system applicable across mathematical, physical, and linguistic domains. Next, the 'Intermediate Meta-Universe (IMU)' is introduced to enable explicit descriptions of definers (ourselves) and the languages we use, thereby allowing conscious meta-level operations while avoiding self-reference and logical inconsistency. Building on this meta-theoretical foundation, this study expands inter-universal theory beyond mathematics to include linguistic translation and agent integration, introducing the conceptual division between macrocosm-inter-universal and microcosm-inter-universal operations for broader expressivity. Through these contributions, this paper presents a meta-formal logical framework--grounded in the principle of definition = state--that spans time, language, agents, and operations, providing a mathematically robust foundation applicable to the definition of intelligence, formal logic, and scientific theory at large.
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