预测集合论：具有可操作核心机制的认知架构生成框架
Predictive Set Theory: A Generative Framework for Cognitive Architecture with Operationalized Core Mechanisms
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中文总结 AI 辅助
本文提出预测集合论（PST）这一形式生成框架，从第一性原理重构认知架构，解决经典认知问题，并确立其原创性与完整性。
中文摘要 AI 辅助
预测加工理论将大脑描绘为最小化预测误差的分层预测引擎，但它们缺乏对“预测”的结构、对预测误差的标准化响应以及维持连续更新间一致性的机制的可操作定义。贝叶斯认知科学试图将所有不确定性归入概率信念更新之下，但它预设了一个封闭的假设空间，且未提供关于概率所分布的对象最初如何成为离散、可识别指称的生成性解释。本文介绍预测集合论（Predictive Set Theory，PST），这是一个从第一性原理重构认知架构的形式生成框架。PST将认知锚定在一组最小操作上——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指称链形式（指称、反指称和半指称），并严格推导核心认知功能，包括状态序列、需求、比较、效率和有限 horizon 概率规划。PST不模拟神经机制，而是为任何必须在不完全信息和不可逆风险下行动同时维持内部一致性的系统提供设计规范。该框架为经典问题提供了新颖的解决方案，如罗素悖论、哥德尔不完备性的认知地位、负反馈的基础以及电影剪辑的理解。本文的主要目的是通过公开学术记录确立预测集合论框架的原创性和完整性。
英文摘要
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. 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. This paper introduces Predictive Set Theory (PST), a formal generative framework that reconstructs cognitive architecture from first principles. 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. 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. 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. The primary purpose of this paper is to establish, through the public academic record, the originality and completeness of the Predictive Set Theory framework.
