Semiotic relations shape different proof methods across argument types
Semiotic Relations and Proof Methods: A Cross-Genre Study of Argument Structure with Large Language Models
Computation and Language
Summary
Sometimes proving a statement directly is very hard, so people try to prove related statements instead. The authors studied four types of relations—like using comparisons or opposites—that help move from one statement to another in proofs. They tested these ideas using large language models on math, legal, and everyday arguments. They found that math arguments use all four relation types, while legal and everyday arguments mainly rely on logical inference.
What this means in practice
- •For legal technology teams: Improve automated legal reasoning tools by focusing on inference-based argument structures common in legal texts.
- •For mathematics education platforms: Design interactive tools that teach different proof strategies by highlighting the four semiotic relations used in mathematical reasoning.
Authors
Edirlei Soares de Lima, Marco A. Casanova, Antonio L. Furtado
Abstract
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.