Toward an object-oriented structure for mathematical text

Fairouz Kamareddirie, Manuel Maarek, J. B. Wells

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

3 Citations (Scopus)

Abstract

Computerizing mathematical texts to allow software access to some or all of the texts' semantic content is a long and tedious process that currently requires much expertise. We believe it is useful to support computerization that adds some structural and semantic information, but does not require jumping directly from the word-processing level (e.g., LATEX) to full formalization (e.g., Mizar, Coq, etc.). Although some existing mathematical languages are aimed at this middle ground (e.g., MathML, OpenMath, OMDoc), we believe they miss features needed to capture some important aspects of mathematical texts, especially the portion written with natural language. For this reason, we have been developing MathLang, a language for representing mathematical texts that has weak type checking and support for the special mathematical use of natural language. MathLang is currently aimed at only capturing the essential grammatical and binding structure of mathematical text without requiring full formalization. The development of MathLang is directly driven by experience encoding real mathematical texts. Based on this experience, this paper presents the changes that yield our latest version of MathLang. We have restructured and simplified the core of the language, replaced our old notion of "context" by a new system of blocks and local scoping, and made other changes. Furthermore, we have enhanced our support for the mathematical use of nouns and adjectives with object-oriented features so that nouns now correspond to classes, and adjectives to mixins. © Springer-Verlag Berlin Heidelberg 2006.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages217-233
Number of pages17
Volume3863 LNAI
Publication statusPublished - 2006
EventMathematical Knowledge Management - 4th International Conference - International University Bremen, Bremen, Germany
Duration: 15 Jul 200517 Jul 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3863 LNAI
ISSN (Print)0302-9743

Conference

ConferenceMathematical Knowledge Management - 4th International Conference
Abbreviated titleMKM 2005
CountryGermany
CityBremen
Period15/07/0517/07/05

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  • Cite this

    Kamareddirie, F., Maarek, M., & Wells, J. B. (2006). Toward an object-oriented structure for mathematical text. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3863 LNAI, pp. 217-233). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3863 LNAI).