AI RESEARCH
A CAP-like Trilemma for Large Language Models: Correctness, Non-bias, and Utility under Semantic Underdetermination
arXiv CS.AI
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ArXi:2605.11672v1 Announce Type: new The CAP theorem states that a distributed system cannot simultaneously guarantee consistency, availability, and partition tolerance under network partition. Inspired by this result, this paper formulates a CAP-like conjecture for Large Language Models (LLMs). The proposed trilemma states that, under semantic underdetermination, an LLM cannot always simultaneously guarantee strong correctness, strict non-bias, and high utility. A prompt is semantically underdetermined when the given premises do not determine a unique answer.