Argumentation theory for mathematical argument

TL;DR

This paper introduces a new framework for modeling mathematical arguments that captures objects, relationships, and inferences, facilitating analysis of dialogues and texts, and supporting computational reasoning.

Contribution

The paper presents a novel argumentation framework tailored for mathematical discourse, improving upon existing methods like Lamport's structured proofs.

Findings

Framework effectively analyzes mathematical dialogues and texts

Can recover key discourse elements at sentence level

Supports computational reasoning in mathematical argumentation

Abstract

To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. We show how the framework might be used to support computational reasoning, and argue that it provides a more natural way to examine the process of proving theorems than do Lamport's structured proofs.