A CAP-like Trilemma for Large Language Models: Correctness, Non-bias, and Utility under Semantic Underdetermination

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.

BigText-QA: Question Answering over a Large-Scale Hybrid Knowledge Graph

Answering complex questions over textual resources remains a challenging problem$\unicode{x2013}$especially when interpreting the fine-grained relationships among multiple entities that occur within a natural-language question or clue. Curated knowledge bases (KBs), such as YAGO, DBpedia, Freebase and Wikidata, have been widely used in this context and gained great acceptance for question-answering (QA) applications in the past decade. While current KBs offer a concise representation of structured knowledge, they lack the variety of formulations and semantic nuances as well as the context of information provided by the natural-language sources. With BigText-QA, we aim to develop an integrated QA system which is able to answer questions based on a more redundant form of a knowledge graph (KG) that organizes both structured and unstructured (i.e., "hybrid") knowledge in a unified graphical representation. BigText-QA thereby is able to combine the best of both worlds$\unicode{x2013}$a canonical set of named entities, mapped to a structured background KB (such as YAGO or Wikidata), as well as an open set of textual clauses providing highly diversified relational paraphrases with rich context information.