发表机构
Academy for AI, Games and Media; Breda University of Applied Sciences; PUC-Rio（人工智能、游戏与媒体学院; 布雷达应用科学大学; 里约热内卢天主教大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出四种符号学关系（组合、聚合、对立、整体-部分）对应四种证明方法，并通过大语言模型对跨体裁语料库的实证研究发现，数学证明使用全部四种关系，而法律和日常推理几乎仅依赖推理。
AI 中文摘要
当对陈述$S$的直接证明似乎困难甚至不可能获得时，可能存在另一个（或一组）与$S$以某种方式相关的陈述$S^{*}$，基于$S^{*}$可以证明$S$。为了研究从$S$移动到$S^{*}$可用的选项，本文简要回顾了受符号学研究四种主修辞格启发的四种符号学关系。具体而言，我们的组合关系、聚合关系、对立关系和整体-部分关系分别对应于转喻、隐喻、反讽和提喻。我们提出，这四种符号学关系决定了从$S$移动到$S^{*}$的选项，从而分别导致推理证明、类比证明、反证法和分情况证明。为了考察这四种关系在不同类型论证中的实际使用情况，我们用一项实证研究补充了该框架。我们将这四种关系转化为明确的操作性定义，并使用一组大语言模型将其应用于包含数学、法律和日常论证的跨体裁语料库。我们发现这些关系在不同体裁中的使用极不均匀：数学证明使用了全部四种关系，而法律和日常推理几乎完全依赖推理。
英文摘要
When a direct proof of a statement $S$ seems hard or even impossible to obtain, there may exist another statement (or set of statements) $S^{*}$, somehow related to $S$, on the basis of which $S$ can be proved. In order to investigate what options can be used to move from $S$ to $S^{*}$, four kinds of semiotic relations inspired by the four master tropes of semiotic research are briefly reviewed. Specifically, our syntagmatic, paradigmatic, antithetic and meronymic relations correspond, respectively, to metonymy, metaphor, irony and synecdoche. It is suggested that these four semiotic relations determine the options to move from $S$ to $S^{*}$, leading to proof by inference, proof by analogy, proof by contradiction, and proof by case analysis. To examine how the four relations are actually used across different kinds of argument, we complement the framework with an empirical study. We turn the four relations into explicit operational definitions and apply them to a cross-genre corpus of mathematical, legal, and everyday argument using a panel of large language models. We find that the relations are used very unevenly across genres: mathematical proofs draw on all four, whereas legal and everyday reasoning rely almost entirely on inference.
