Argumentation Theory for Mathematical Argument

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, w...

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Vydáno v:Argumentation Ročník 33; číslo 2; s. 173 - 214
Hlavní autoři: Corneli, Joseph, Martin, Ursula, Murray-Rust, Dave, Rino Nesin, Gabriela, Pease, Alison
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.06.2019
Springer Nature B.V
Témata:
Argument structure
Argumentation
Communication Studies
Debates
Discourse
Education
Frame analysis
Legal History
Logic
Philosophy
Philosophy of Law
Political Communication
Property
Theories of Law
Inference Anchoring Theory
Mathematical practice
Mathematical argument
Structured proof
ISSN:0920-427X, 1572-8374
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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.
AbstractList 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.
Author Martin, Ursula
Pease, Alison
Murray-Rust, Dave
Rino Nesin, Gabriela
Corneli, Joseph
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  givenname: Dave
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  surname: Murray-Rust
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  organization: Edinburgh College of Art, University of Edinburgh
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  givenname: Gabriela
  surname: Rino Nesin
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  organization: Computing, Engineering and Mathematics, University of Brighton
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  givenname: Alison
  orcidid: 0000-0003-1856-9599
  surname: Pease
  fullname: Pease, Alison
  organization: Computing, School of Science and Engineering, University of Dundee
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Keywords Inference Anchoring Theory
Mathematical practice
Mathematical argument
Structured proof
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PublicationTitle Argumentation
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SubjectTerms Argument structure
Argumentation
Communication Studies
Debates
Discourse
Education
Frame analysis
Legal History
Logic
Philosophy
Philosophy of Law
Political Communication
Property
Theories of Law
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