Presentation Information
[3L2-GS-5f-05]Limits of Certainty in Agentic AI Systems: An Information-Theoretic and Categorical Analysis
〇Yiyang Jia1, Jun Mitani2 (1. Tokyo City University, 2. University of Tsukuba)
Keywords:
Certainty–Scope Trade-off,Markov category,Agentic AI
Recent agentic AI systems, especially those based on large language models, exhibit a fundamental tension between reliability and generality. Floridi’s Certainty–Scope Conjecture informally states that, for mechanisms with finite informational resources, increasing operational scope necessarily degrades certainty. In this work, we provide a formal information-theoretic proof of this trade-off. Modeling an AI mechanism as a stochastic channel with finite capacity, we operationalize scope as the number of semantic classes and certainty as optimal classification accuracy. Using Fano’s inequality and data-processing arguments, we derive an explicit upper bound relating certainty, scope, and channel capacity, independent of architectural or learning details. We further show that the bound is essentially tight, extend the analysis to continuous semantic domains via rate–distortion theory, and reformulate the results categorically in the language of Markov categories. These results establish the certainty–scope tension as a structural limitation of finite-capacity agentic systems.