Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based on potentially many different documents, conflicting data sources, and using reasoning. But, different kinds of questions have different answers, and different answers have different complexities. In this paper, we introduce a novel framework for analyzing the complexity of a question answer based on the natural deduction calculus as presented in Prawitz (1965). Our framework is novel both in that no one to our knowledge has used this logic as a basis for complexity classes, and also in that no other existing complexity classes to these have been delineated using any analogous methods either. We identify three decidable fragments in particular called the forward, query and planning fragments, and we compare this to what would be needed to do proofs for the complete first-order calculus, for which theorem-proving is long known to be undecidable.

翻译：鉴于大规模语言模型新兴的推理能力，信息检索正变得日益复杂。现代信息检索系统不仅能够检索文档，更宣称可以基于可能存在差异的多个文档、冲突的数据源进行推理并综合生成答案。然而，不同问题对应不同答案，不同答案亦具有不同复杂度。本文提出了一种创新框架，基于Prawitz（1965）提出的自然演绎演算来分析问题的答案复杂度。该框架的独创性体现在两方面：其一，据我们所知，此前尚未有人采用此类逻辑作为复杂度类别的划分基础；其二，现有复杂度类别中亦未有任何类比方法进行过类似界定。我们特别识别出三个可判定片段，分别称为前向片段、查询片段和规划片段，并将其与完整一阶演算所需的证明过程进行比较——众所周知，一阶演算的定理证明长期以来被证实是不可判定的。