Narrative structure of mathematical texts

Fairouz Kamareddine, Manuel Maarek, Krzysztof Retel, J. B. Wells

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

There are many styles for the narrative structure of a mathematical document. Each mathematician has its own conventions and traditions about labeling portions of texts (e.g., chapter, section, theorem or proof) and identifying statements according to their logical importance (e.g., theorem is more important than lemma). Such narrative/structuring labels guide the reader's navigation of the text and form the key components in the reasoning structure of the theory reflected in the text. We present in this paper a method to computerise the narrative structure of a text which includes the relationships between labeled text entities. These labels and relations are input by the user on top of their natural language text. This narrative structure is then automatically analysed to check its consistency. This automatic analysis consists of two phases: (1) checking the correct usage of labels and relations (i.e., that a "proof" justifies a "theorem" but cannot justify an "axiom") and (2) checking that the logical precedences in the document are self-consistent. The development of this method was driven by the experience of computerising a number of mathematical documents (covering different authoring styles). We illustrate how such computerised narrative structure could be used for further manipulations, i.e. to build a skeleton of a formal document in a formal system like Mizar, Coq or Isabelle. © Springer-Verlag Berlin Heidelberg 2007.

Original languageEnglish
Title of host publicationTowards Mechanized Mathematical Assistants - 14th Symposium, Calculemus 2007 - 6th International Conference, MKM 2007, Proceedings
Pages296-312
Number of pages17
Volume4573 LNAI
Publication statusPublished - 2007
Event14th Symposium on Calculemus 2007 and 6th International Conference on Mathematical Knowledge Management - Hagenberg, Austria
Duration: 27 Jun 200730 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4573 LNAI
ISSN (Print)0302-9743

Conference

Conference14th Symposium on Calculemus 2007 and 6th International Conference on Mathematical Knowledge Management
Abbreviated title MKM 2007
CountryAustria
CityHagenberg
Period27/06/0730/06/07

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