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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.11672 |
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| _version_ | 1866911673341706240 |
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| author | Venugopal, Vinu Ellampallil |
| author_facet | Venugopal, Vinu Ellampallil |
| contents | 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. In such cases, a useful and decisive response requires the model to introduce a selection criterion, preference, prior, or value ordering. If this criterion is not supplied by the user or justified by the available premises, the response becomes biased in a broad selection-theoretic sense. Conversely, if the model avoids unsupported preferences, it may preserve correctness and non-bias but may reduce utility through refusal, hedging, or clarification. The paper formalizes this correctness--non-bias--utility trilemma, develops examples, and argues that certain LLM failures arise not merely from model limitations but from the structure of underdetermined decision requests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11672 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A CAP-like Trilemma for Large Language Models: Correctness, Non-bias, and Utility under Semantic Underdetermination Venugopal, Vinu Ellampallil Artificial Intelligence Databases 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. In such cases, a useful and decisive response requires the model to introduce a selection criterion, preference, prior, or value ordering. If this criterion is not supplied by the user or justified by the available premises, the response becomes biased in a broad selection-theoretic sense. Conversely, if the model avoids unsupported preferences, it may preserve correctness and non-bias but may reduce utility through refusal, hedging, or clarification. The paper formalizes this correctness--non-bias--utility trilemma, develops examples, and argues that certain LLM failures arise not merely from model limitations but from the structure of underdetermined decision requests. |
| title | A CAP-like Trilemma for Large Language Models: Correctness, Non-bias, and Utility under Semantic Underdetermination |
| topic | Artificial Intelligence Databases |
| url | https://arxiv.org/abs/2605.11672 |