Theoretical Framework for Completeness and Consistency of Knowledge in Generative AI Large Language Models

Abstract

Generative AI Large Language Models (LLMs) such as GPT-4, Claude, and Gemini are reshaping knowledge work across disciplines. Yet these systems exhibit a puzzling paradox: they can pass rigorous professional examinations while simultaneously failing elementary reasoning tasks. This paper presents a condensed theoretical framework explaining how knowledge is created, stored, and retrieved in LLMs through Stochastic Knowledge Aggregation (SKA) – a process fundamentally different from the Systematic Knowledge Scaffolding (SKS) that characterizes human learning. We introduce 19 foundational concepts, three formal theories, and a set of propositions collectively forming the Jagged Knowledge Frontier (JKF) framework. Empirical cases validate the framework and illuminate implications for Knowledge Management (KM). The paper argues that understanding AI knowledge creation is essential for bridging traditional human KM with the emerging discipline of AI Knowledge Management, and for designing governance structures that account for the inherent incompleteness and inconsistency of LLM knowledge.