用动态系统建模认知过程，让思维逐步稳定在语义不变的状态。
A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence
- 基于反馈机制，用变换与语义等价推动认知状态演化。
- 通过不动点和压缩条件保证系统稳定，避免思维发散。
- 适用于语言理解等需上下文推理的场景，理论性强。
本文提出一种结构化且动态的认知过程建模框架，从控制论视角出发。认知状态被表示为状态空间中的元素，通过迭代更新规则 $ X_{t+1} = π\big(F(f(X_t))\big) $ 演化，其中 $f$ 描述内部变换，$F$ 表示解释映射，$π$ 强制语义等价。该模型被诠释为整合变换、观测与稳定化的反馈系统。引入范畴论形式以捕捉组合结构，通过不动点论证与压缩条件分析其动力学稳定性。通过计算实例与定性分析展示框架的操作性；具体语言应用表明，上下文依赖的解释可建模为趋于稳定语义类的轨迹。该方法融合动力系统、范畴论与认知建模，将认知统一为由反馈驱动、趋向不变解释的演化过程。
原文摘要 · Abstract (English)
This paper proposes a structural and dynamical framework for modeling cognitive processes within a cybernetic perspective. Cognitive states are represented as elements of a state space evolving through an iterative update rule of the form \[ X_{t+1} = π\big(F(f(X_t))\big), \] where $f$ describes internal transformations, $F$ represents interpretative mappings, and $π$ enforces semantic equivalence. The model is interpreted as a feedback system integrating transformation, observation, and stabilization. A categorical formulation is introduced to capture compositional structure, while the associated dynamics are analyzed through fixed-point arguments and contraction conditions ensuring stability. To demonstrate the operational character of the framework, a computational illustration is provided, together with a qualitative analysis of the induced dynamics. A concrete linguistic application shows how context-dependent interpretation can be modeled as a trajectory toward a stable semantic class. The proposed approach connects dynamical systems, category theory, and cognitive modeling, and provides a unified representation of cognition as a feedback-driven process evolving toward invariant interpretations.
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