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

Computer Science > Artificial Intelligence [Submitted on 3 Aug 2026] Predictive Set Theory: A Generative Framework for Cognitive Architecture with Operationalized Core Mechanisms Yiyang Yu 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. Comments: 103 pages. This preprint establishes the theoretical framework of Predictive Set Theory, providing a generative design specification for cognitive architecture. Comments welcome Subjects: Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO); Neurons and Cognition (q-bio.NC) MSC classes: 03B30, 03B70, 68T01, 92C20, 68T01, 91E10 ACM classes: F.4.1; I.2.0; I.2.6 Cite as: arXiv:2608.02704 [cs.AI]   (or arXiv:2608.02704v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2608.02704 Focus to learn more Submission history From: YiYang Yu [view email] [v1] Mon, 3 Aug 2026 15:28:32 UTC (80 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-08 Change to browse by: cs cs.LO q-bio q-bio.NC References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)