# Semiotic Relations and Proof Methods: A Cross-Genre Study of Argument Structure with Large Language Models

arXiv: https://arxiv.org/abs/2609.15194 · HTML: https://mlsanity.com/paper/2609.15194/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 73 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Emergent Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2212.09196/) (2022)
- [ChatGPT-4 Outperforms Experts and Crowd Workers in Annotating Political Twitter Messages with Zero-Shot Learning](https://mlsanity.com/paper/2304.06588/) (2023)
- [NaturalProofs: Mathematical Theorem Proving in Natural Language](https://mlsanity.com/paper/2104.01112/) (2021)
- [The Alternative Annotator Test for LLM-as-a-Judge: How to Statistically Justify Replacing Human Annotators with LLMs](https://mlsanity.com/paper/2501.10970/) (2025)
- [NaturalProver: Grounded Mathematical Proof Generation with Language Models](https://mlsanity.com/paper/2205.12910/) (2022)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [Mining Legal Arguments in Court Decisions](https://mlsanity.com/paper/2208.06178/) (2022)
- [Evaluating the Robustness of Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2411.14215/) (2024)
- [Characterizing the Investigative Methods of Fictional Detectives with Large Language Models](https://mlsanity.com/paper/2505.07601/) (2025)
- [Towards Solving the Gilbert-Pollak Conjecture via Large Language Models](https://mlsanity.com/paper/2601.22365/) (2026)
- [Revisiting Northrop Frye's Four Myths Theory with Large Language Models](https://mlsanity.com/paper/2602.15678/) (2026)

## Abstract (arXiv)

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.