Predictive Set Theory: A Generative Framework for Cognitive Architecture with Operationalized Core Mechanisms

预测集合论：一种具有可操作核心机制的认知架构生成框架

Abstract: Predictive processing theories portray the brain as a hierarchical prediction engine that minimizes prediction error, yet they lack operational definitions for the structure of a “prediction,” the standardized response to a prediction error, and the mechanism that maintains consistency across successive updates.

摘要： 预测处理理论将大脑描述为一种旨在最小化预测误差的分层预测引擎，然而，这些理论缺乏对“预测”结构、针对预测误差的标准化响应，以及在连续更新中维持一致性的机制的定义。

Bayesian cognitive science attempts to subsume all uncertainty under probabilistic belief updating, but it presupposes a closed hypothesis space and provides no generative account of how the objects over which probabilities are distributed become discrete, identifiable referents in the first place.

贝叶斯认知科学试图将所有不确定性归纳为概率信念更新，但它预设了一个封闭的假设空间，且未能提供关于概率分布的对象最初是如何成为离散、可识别的指称对象的生成性解释。

This paper introduces Predictive Set Theory (PST), a formal generative framework that reconstructs cognitive architecture from first principles.

本文引入了预测集合论（Predictive Set Theory, PST），这是一个从第一性原理出发重构认知架构的形式化生成框架。

PST anchors cognition in a minimal set of operations---a sensor formalized as an identity function, set-theoretic state refresh, and three fundamental forms of reference chains (reference, counter-reference, and semi-reference)---and rigorously derives core cognitive functions including state sequences, demand, comparison, efficiency, and finite-horizon probabilistic planning.

PST 将认知锚定在一组最小化操作上——即形式化为恒等函数的传感器、集合论状态刷新，以及三种基本形式的引用链（引用、反引用和半引用）——并严格推导出了核心认知功能，包括状态序列、需求、比较、效率以及有限视界的概率规划。

Rather than modeling neural mechanisms, PST constitutes a design specification for any system that must maintain internal consistency while acting under incomplete information and irreversible risk.

PST 并非旨在模拟神经机制，而是为任何需要在不完全信息和不可逆风险下行动且必须保持内部一致性的系统提供了一套设计规范。

The framework offers novel resolutions to classical problems such as Russell’s paradox, the cognitive status of Gödelian incompleteness, the grounding of negative feedback, and the comprehension of film editing.

该框架为罗素悖论、哥德尔不完备性的认知地位、负反馈的奠基以及电影剪辑的理解等经典问题提供了新颖的解决方案。

The primary purpose of this paper is to establish, through the public academic record, the originality and completeness of the Predictive Set Theory framework.