Retrieval-based systems approximate access to a corpus by exposing only a truncated subset of available evidence. Even when relevant information exists in the corpus, truncation can prevent compatible evidence from co-occurring, leading to failures that are not captured by relevance-based evaluation. This paper studies retrieval from a structural perspective, modeling query answering as a feasibility problem under truncation. We formalize retrieval as a sequence of candidate evidence sets and characterize conditions under which feasibility in the limit implies feasibility at finite retrieval depth. We show that monotone truncation suffices to guarantee finite witnessability for individual queries. For classes of queries, we identify finite generation of witness certificates as the additional condition required to obtain a uniform retrieval bound, and we show that this condition is necessary. We further exhibit sharp counterexamples demonstrating failure under non-monotone truncation, non-finitely-generated query classes, and purely slotwise coverage. Together, these results isolate feasibility preservation as a correctness criterion for retrieval independent of relevance scoring or optimization, and clarify structural limitations inherent to truncation-based retrieval.

翻译：基于检索的系统通过仅暴露可用证据的截断子集来近似访问语料库。即使语料库中存在相关信息，截断也可能阻止兼容证据同时出现，导致基于相关性的评估无法捕捉的失败。本文从结构视角研究检索，将查询应答建模为截断下的可行性问题。我们形式化检索为候选证据序列，并刻画极限可行性蕴含有限检索深度可行性的条件。我们证明单调截断足以保证单个查询的有限可见证性。对于查询类，我们识别出有限生成见证证书作为获得一致检索边界所需的附加条件，并证明该条件是必要的。我们进一步展示尖锐反例，证明在非单调截断、非有限生成查询类和纯槽位覆盖下的失败。这些结果共同将可行性保持确立为独立于相关性评分或优化的检索正确性准则，并阐明了基于截断的检索固有的结构局限性。