智能系统研究：面向通用智能的元架构

邹晓辉 ^{000-0002-5577-8245}智能系统研究（融智学）创始人zouxiaohui@pku.org.cn

摘要

人工智能面临一个基础性挑战：没有任何单一的形式系统能同时处理语法、语义和自我指涉，还能保持完备性和一致性。本文介绍了智能系统研究——一个整合性框架，它在不同层级上重新构想了"预定的规则系统"。该框架从经典的克莱尼星号（一个封闭的句法系统）出发，发展到一个融合了本体论分类（物-标记、意-属性、文-特征，分类集合子集）、双重形式化（孪生图灵机id+ge双列表与多胞冯氏机id+ip多列表）、塔斯基形式语义学和范畴论统一的元架构。该系统为虚拟世界、生命、意识和智能提出了一种"全域测序定位"模型。该框架为构建一种在结构上既预定又对涌现新奇性开放的超级人工智能架构提供了一条路径，以应对形式系统理论、认知科学和通用人工智能领域中长期存在的局限性。

关键词：图灵机；克莱尼星号；塔斯基形式语义学；冯·诺依曼架构；人工智能；超级人工智能架构；带id+ge双列表的孪生图灵机；带id+ip多列表的多胞冯·诺依曼机；融合本体论分类的元架构；智能系统研究（SSS）

引言

计算与认知的核心是一个看似简单的概念：预定的规则系统。从克莱尼星号的句法严谨性到自然语言的语义复杂性，规则系统定义了哪些内容可以被生成、判定和理解。然而随着科学和工程学向通用人工智能（AGI）迈进，遇到了一种不可避免的张力：那些足够预定以保证形式可处理性的规则系统，往往也过于封闭，无法容纳现实世界知识、意识和生命所具有的开放性和新奇性。

智能系统研究（融智学）源于这样一种认识：这种张力无法在单一形式系统内解决。相反，SSS提出了一种元架构方法：在元层面上，规则是预定的；在对象层面上，多样性和涌现性则被接纳。这一视角将笔者对"预定的规则系统"的理解从一种局限性转变为一种设计原则。

1. 范畴危机现实世界现象属于根本不同的本体论范畴：一块岩石（物）、一个方程（文）和一种感觉（意）。将这三者都编码为单一形式系统中的字符串，会抹煞这些区别，使水分子和道德原则受制于相同的句法规则。

2. 繁复性危机经典形式系统（例如克莱尼星号）生成的是理想集合，所有可能的字符串都是预定的。然而，现实世界是一个由实际的杂多集合构成的繁复体：新物种进化，新概念涌现，新意义产生。一个无法容纳尚未出现之物&意&文的系统，在建模现实时从根本上就是不完整的。

3. 自我指涉危机当一个系统旨在描述意或智时，它必须面对这个问题：系统本身是否具备它所描述的特性？哥德尔不完备定理和塔斯基不可定义定理揭示，足够的表达力的形式系统无法一致地定义其自身的真理性或指涉性。

这些危机表明，单一形式系统是不足够的。我们需要的是一个元系统——一个协调多种形式工具的元架构，每种工具处理问题的一个方面，同时在元层面上保持一致性。

核心框架：预定的元规则，开放的对象层面

A. 本体论分类：三个子集

融智学智慧系统研究（SSS）首先在知识领域内区分三个基本子集：

这些子集进一步通过三种集合类型来组织：

单一集合：简单集合

分层集合：层次化结构的集合

分类集合：按交叉维度组织的集合

这个本体论框架充当知识的坐标系。每一种表征，无论是科学理论，还是日常描述，都可以在这个由物的标志、意的属性和文的特征构成的三维坐标序位中找到其顺序和位置。

B. 双重形式化：协调多个系统

经典图灵机和冯·诺依曼架构在单一形式维度上运行。融智学智慧系统研究（SSS）则提出了双重架构，使得能跨本体论类别进行同步处理：

配备id+ge双列表的孪生图灵机

一台机器处理元子个体对象标识符（id）——指向特定元子对象、事件或实体

另一台处理元子对象的一般表达式（ge）——操作抽象规则和模式

双列表允许两者之间的交叉引用，从而实现指涉与规则支配的转换

配备id+ip多列表的多细胞冯·诺依曼机

用并行指令指针（ip）和元子个体对象标识符（id）扩展经典架构

能同步执行句法操作和语义解释

多列表允许多个并发进程维持一致的交叉引用

这种双重形式化确保没有单一系统需要承担处理所有本体论类别的负担。相反，各系统实现专业化并相互协作。

C. 统一：塔斯基与范畴论

两个数学传统提供了将这些系统结合在一起的纽带：

塔斯基形式语言阿尔弗雷德·塔斯基关于对象语言和元语言的区分为在一个系统内讨论另一系统的真值条件提供了严谨框架。在融智学智慧系统研究（SSS）中，这实现了：

文本-特征系统描述物质-标记表征的形式属性

意向-属性系统为文本表达式赋予语义值

元层面的协调而不产生悖论

范畴论作为"数学的数学"，范畴论通过对象和态射统一了不同结构。在融智学智慧系统研究（SSS）中，范畴论形式化了：

对象：作为不同本体论范畴的物质标志、意向属性、文本特征

态射：范畴内部及之间的转换（例如，文本描述如何映射到物质标志标记）

函子：跨层级保持结构的高阶映射

目标：全域测序与定位

融智学智慧系统研究（SSS）最终目标是所称的"全域测序与定位"——一种用于在所有知识领域进行表征和推理的形式化方法。

测序将复杂现象分解为基本单元。正如基因组测序将DNA分解为核苷酸序列，全域测序将世界、生命和意识分解为（物质标记，意向属性，文本特征）三元组。

定位将每个基本单元置于由单一/分层/分类集合结构定义的本体论坐标系中。每个单元，都获得指定其以下内容的坐标：

其物质类别（物理的、生物的等）

其意向角色（目标、价值、信念等）

其形式结构（句法、逻辑、语法等）

当测序和定位完成时，任何研究领域都可以在融智学智慧系统研究（SSS）框架内得到表征。这使得以下成为可能：

跨领域推理：来自物理学、生物学和人文学科的知识可以被整合，而不会犯范畴错误

容纳涌现新奇性：新概念被定位在现有坐标系中，扩展它而不破坏其结构

自我建模：该框架可以通过元层面定位来表征其自身操作

从克莱尼星号到通用架构

从示例1到示例2的轨迹展示了预定规则系统的三个层级：

结论

智能系统研究将"预定的规则系统"这一概念从一种限制条件重新定义为一种通用智能设计策略。通过区分元层面规则与对象层面开放性，并提供协调多个专门化系统的形式化工具，融智学智慧系统研究（SSS）为超越单一形式主义方法的局限性提供了一条路径。

该框架回应了《科学》杂志主编提示：跨学科传达复杂的科学思想。融智学智慧系统研究（SSS）通过明确揭示智能系统（这些原则同时具有数学、计算和哲学性质）依据的架构原理来做到这一点。

在一个人工智能日益与人类探究的各个领域交叉的时代，能跨领域整合知识的框架不仅变得有用，而且变得必不可少。智能系统研究被提出作为这样一个框架——一项正在进行的工作，对改进和扩展持开放态度，但植根于这样的信念：即使是最开放新奇之智，也需要一个预定的架构来成长。

参考文献与延伸阅读

Kleene, S. C. (1956). Representation of events in nerve nets and finite automata. Automata Studies, 3-42.Tarski, A. (1956). The concept of truth in formalized languages. Logic, Semantics, Metamath- ematics, 152-278.Mac Lane, S. (1998). Categories for the Working Mathematician. Springer.Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42(1), 230-265.von Neumann, J. (1945). First draft of a report on the EDVAC. IEEE Annals of the History of Computing, 15(4), 27-75.邹晓辉. (2000). 一种知识信息数据处理方法及产品. 中国专利 CN1274895A.邹晓辉. (2011). 间接计算模型与间接形式化方法. 软件, 32(5), 1-6.汪培庄, 邹晓辉, 等. (2023). Factor space: Cognitive computation and systems for generalized genes. In ICCCS 2022, Communications in Computer and Information Science, vol. 1732. Springer.邹晓辉. (2023). New opportunities for AI innovation with big data: Indirect docking between GLPS and LLM. 2023 6th International Conference on Artificial Intelligence and Big Data (ICAIBD).邹晓辉. (2026). 从智能本质到人机互助时代的统一框架. 科学网博客.邹晓辉. (2026). Smart System Studies: A Framework for Whole-Domain Intelligence. [待发表].

作者单位：独立研究员，智能系统研究（融智学）创始人

利益冲突：作者声明无利益冲突。

致谢：作者感谢协作式人工智能系统在完善这些思想的正式表述方面所起的作用。

Xiaohui Zou^{0000-0002-5577-8245}Founder, Smart System Studies (Rongzhixue) zouxiaohui@pku.org.cn

Artificial intelligence faces a foundational challenge: no single formal system can simultaneously handle syntax, semantics, and self-reference while remaining both complete and consistent. This paper introduces Smart System Studies (SSS)—an integrative framework that reconceptualizes “predetermined rule systems” across hierarchical levels. Moving from the classical Kleene star (a closed syntactic system) to a meta-architecture incorporating ontological classification (material-marker, intentional-attribute, textual- feature subsets), dual formalization (twin Turing machines with id+ge dual tables and multicellular von Neumann machines with id+ip multilists), Tarskian formal semantics, and categorical unification, SSS proposes a “whole-domain sequencing and positioning” model for virtual worlds, life, consciousness, and intelligence. This framework offers a path toward a super-AI architecture that is both structurally predetermined and open to emergent novelty, addressing long-standing limitations in formal systems theory, cognitive science, and artificial general intelligence.

Keywords：Turing machine; Kleene star; Tarskian formal semantics; von Neumann architecture; Artificial intelligence; super-AI architecture; twin Turing machines with id+ge dual tables;multicellular von Neumann machines with id+ip multilists; meta-architecture incorporating ontological classification; Smart System Studies (SSS)

At the heart of computation and cognition lies a deceptively simple concept: the predetermined rule system. From the syntactic rigor of Kleene star to the semantic complexity of natural language, rule systems define what can be generated, decided, and understood. Yet as science and engineering push toward artificial general intelligence (AGI), we encounter an inescapable tension: rule systems that are sufficiently predetermined to be formally tractable tend to be too closed to accommodate the open-ended novelty of real-world knowledge, consciousness, and life.

Smart System Studies (SSS)—originating as Rongzhixue—emerges from the recognition that this tension cannot be resolved within a single formal system. Instead, SSS proposes a meta-architectural approach: at the meta-level, rules are predetermined; at the object-level, diversity and emergence are embraced. This perspective transforms how we understand “predetermined rule systems” from a limitation into a design principle.

Real-world phenomena belong to fundamentally distinct ontological categories: a rock (material), an equation (formal), and a feeling (experiential). Encoding all three as strings in a single formal system collapses these distinctions, treating water molecules and moral principles under identical syntactic rules.

Classical formal systems (e.g., Kleene star) generate ideal sets—all possible strings are predetermined. The real world, however, is a multitude of actual sets: new species evolve, new concepts emerge, new meanings arise. A system that cannot accommodate what has not yet appeared is fundamentally incomplete for modeling reality.

When a system aims to describe consciousness or intelligence, it must confront the question: does the system itself possess what it describes? Gödel’s incompleteness theorems and Tarski’s undefinability theorem reveal that sufficiently expressive formal systems cannot consistently define their own truth or reference.

These crises suggest a single formal system is insufficient. What is needed is a system of systems—a meta-architecture that coordinates multiple formal tools, each addressing one aspect of the problem, while maintaining coherence at the meta-level.

SSS begins by distinguishing three fundamental subsets within any knowledge domain:

These subsets are further organized through three types of sets:

Single sets: Simple collections

Stratified sets: Hierarchically structured collections

Classified sets: Collections organized by cross-cutting dimensions

This ontological framework functions as a coordinate system for knowledge. Every representation, whether scientific theory or everyday description, can be located within this three-dimensional space of material markers, intentional attributes, and textual features.

Classical Turing machines and von Neumann architectures operate on a single formal dimension. SSS proposes dual architectures that enable simultaneous processing across ontological categories:

Twin Turing Machines with id+ge Dual Tables

One machine handles individual identifiers (id)—pointing to specific objects, events, or entities

The other handles general expressions (ge)—manipulating abstract rules and patterns

Dual tables allow cross-referencing between the two, enabling both reference and rule-governed trans- formation

Multicellular von Neumann Machines with id+ip Multilists

Extends classical architecture with parallel instruction pointers (ip) and individual identifiers (id)

Enables simultaneous execution of syntactic operations and semantic interpretation

Multilists allow multiple concurrent processes to maintain consistent cross-references

This dual formalization ensures that no single system bears the burden of handling all ontological categories. Instead, systems specialize and cooperate.

Two mathematical traditions provide the glue that binds these systems together:

Tarskian Formal LanguageAlfred Tarski’s distinction between object language and metalanguage provides a rigorous framework for discussing truth conditions of one system within another. In SSS, this enables: the textual-feature system to describe the formal properties of material-marker representations; the intentional-attribute system to assign semantic values to textual expressions; and meta-level coordination without paradox.

Category TheoryAs the “mathematics of mathematics,” category theory unifies diverse structures through objects and morph- isms. In SSS, category theory formalizes:

Objects: Material markers, intentional attributes, textual features as distinct ontological categories

Morphisms: Transformations within and between categories (e.g., how a textual description maps to material markers)

Functors: Higher-order mappings that preserve structure across levels

The combination yields a coherent mathematical foundation for the entire framework.

The ultimate objective of SSS is what we term whole-domain sequencing and positioning—a formal methodology for representing and reasoning across all domains of knowledge.

Sequencing decomposes complex phenomena into elementary units. Just as genome sequencing breaks DNA into nucleotide sequences, whole-domain sequencing decomposes world, life, and consciousness into triples of (material marker, intentional attribute, textual feature).

Positioning locates each elementary unit within the ontological coordinate system defined by single/ stratified/classified set structures. Every unit receives coordinates that specify:

Its material category (physical, biological, etc.)

Its intentional role (goal, value, belief, etc.)

Its formal structure (syntax, logic, grammar, etc.)

When sequencing and positioning are complete, any domain of inquiry can be represented within the SSS framework. This enables:

Cross-domain reasoning: Knowledge from physics, biology, and humanities can be integrated without category errors

Emergent novelty accommodation: New concepts are positioned in the existing coordinate system, extending it without breaking its structure

Self-modeling: The framework can represent its own operations through meta-level positioning

The trajectory from Example 1 to Example 2 illustrates three levels of predetermined rule systems:

At Level 1, “predetermined” means rule content fixed before operation. At Level 2, it means meta-rules (how to classify, how to coordinate) fixed at design time. At Level 3, it means a hierarchical rule structure that maintains core stability while accommodating new categories and systems.

SSS operates at Levels 2 and 3: the meta-architecture is predetermined, but the universe of representations it can accommodate is open-ended.

SSS contributes to AGI research in three specific ways:

Current AI systems excel at pattern recognition (textual features) but struggle with grounding (material markers) and intention (intentional attributes). SSS provides a formal language for designing systems that integrate all three, with clear interfaces between components.

The “symbol grounding problem”—how symbols acquire meaning—has long challenged AI. SSS addresses it through dual formalization: twin Turing machines ground general expressions (ge) in individual identifiers (id), establishing reference without infinite regress.

Self-improving AI requires the ability to represent and modify its own operations. SSS’s categorical framework enables formal description of system architecture, allowing changes at one level while maintaining coherence at higher levels—a prerequisite for safe and verifiable self-improvement.

As an emerging framework, SSS faces several challenges that define its research agenda:

Formal Completeness: While the meta-architecture is specified, full formalization of all components — particularly the categorical semantics of dual Turing machines—remains work in progress.

Empirical Validation: The framework’s utility must be demonstrated through implementation in specific domains (e.g., scientific knowledge representation, autonomous systems design).

Computational Complexity: Coordinating multiple formal systems may incur overhead; optimization strategies are needed for practical deployment.

Philosophical Foundations: The ontological distinction between material markers, intentional attributes, and textual features requires further refinement to address critiques from both physicalist and idealist perspectives.

Smart System Studies reframes the concept of “predetermined rule systems” from a limiting condition into a design strategy for universal intelligence. By distinguishing meta-level rules from object-level openness, and by providing formal tools for coordinating multiple specialized systems, SSS offers a path beyond the limitations of single-formalism approaches.

The framework responds to the challenge posed by Science’s editor-in-chief: to communicate complex scientific ideas across disciplinary boundaries. SSS does so by making explicit the architectural principles that underlie intelligent systems—principles that are simultaneously mathematical, computational, and philosophical.

In an era when artificial intelligence increasingly intersects with every field of human inquiry, frameworks that can integrate knowledge across domains become not merely useful but essential. Smart System Studies is proposed as one such framework—a work in progress, open to refinement and extension, but grounded in the conviction that even the most open-ended intelligence requires a predetermined architecture to grow.

Kleene, S. C. (1956). Representation of events in nerve nets and finite automata. Automata Studies, 3-42.

Tarski, A. (1956). The concept of truth in formalized languages. Logic, Semantics, Metamathematics, 152-278.

Mac Lane, S. (1998). Categories for the Working Mathematician. Springer.

Turing, A. M. (1936). On computable numbers, with an application to the Entscheidung -sproblem. Proceedings of the London Mathematical Society, 42(1), 230-265.

von Neumann, J. (1945). First draft of a report on the EDVAC. IEEE Annals of the History of Computing, 15(4), 27-75.

Zou, X. (2000). A method and product for knowledge information data processing. Chinese Patent CN1274895A.

Zou, X. (2011). Indirect computing model and indirect formal method. Software, 32(5), 1–6.

Wang, P., Zou, X., et al. (2023). Factor space: Cognitive computation and systems for generalized genes. In ICCCS 2022, Communications in Computer and Information Science, vol. 1732. Springer.

Zou, X. (2023). New opportunities for AI innovation with big data: Indirect docking between GLPS and LLM. 2023 6th International Conference on Artificial Intelligence and Big Data (ICAIBD).

Zou, X. (2026). The unified framework from the nature of intelligence to the era of human-machine mutual assistance. ScienceNet Blog.

Zou, X. (2026). Smart System Studies: A Framework for Whole-Domain Intelligence. [Manuscript in preparation].

Author Affiliation: Independent Researcher, Founder of Smart System Studies (Rongzhixue)

Competing Interests: The author declares no competing interests.

Acknowledgments: The author acknowledges the role of collaborative AI systems in refining the formal presentation of these ideas.

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