Abstract
Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are fixed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading time, taking reader preferences into account.
We present a representational infrastructure for notations in living mathematical documents. Mathematical notations can be defined declaratively. Author and reader can extensionally define the set of available notation definitions at arbitrary document levels, and they can guide the notation selection function via intensional annotations.
We give an abstract specification of notation definitions and the flexible rendering algorithms and show their coverage on paradigmatic examples. We show how to use this framework to render OpenMath and Content-MathML to Presentation-MathML, but the approach extends to arbitrary content and presentation formats. We discuss prototypical implementations of all aspects of the rendering pipeline.
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References
Ausbrooks, R., Buswell, S., Carlisle, D., Dalmas, S., Devitt, S., Diaz, A., Froumentin, M., Hunter, R., Ion, P., Kohlhase, M., Miner, R., Poppelier, N., Smith, B., Soiffer, N., Sutor, R., Watt, S.: Mathematical Markup Language (MathML) version 2.0, 2nd edn. W3C recommendation, World Wide Web Consortium (2003), http://www.w3.org/TR/MathML2
Buswell, S., Caprotti, O., Carlisle, D.P., Dewar, M.C., Gaetano, M., Kohlhase, M.: The Open Math standard, version 2.0. Technical report, The Open Math Society (2004), http://www.openmath.org/standard/om20
Cajori, F.: A History of Mathematical Notations. Courier Dover Publications(1993) (Originally published in 1929)
Cascading Style Sheets (1999), http://www.w3.org/Style/CSS/
Kay, M.: XSL Transformations (XSLT) Version 2.0. W3C Candidate Recommendation, World Wide Web Consortium (W3C) (June 2006), http://www.w3.org/TR/2006/CR-xslt20-20060608/
Kohlhase, M., Lange, C., Müller, C., Müller, N., Rabe, F.: Adaptation of notations in living mathematical documents. KWARC report, Jacobs University Bremen (2008)
Kohlhase, M., Lange, C., Rabe, F.: Presenting mathematical content with flexible elisions. In: Caprotti, O., Kohlhase, M., Libbrecht, P. (eds.) OpenMath/ JEM Workshop 2007 (2007)
Kohlhase, M., Müller, C., Müller, N.: Documents with flexible notation contexts as interfaces to mathematical knowledge. In: Libbrecht, P. (ed.) Mathematical User Interfaces Workshop 2007 (2007)
Kohlhase, M.: OMDoc – An open markup format for mathematical documents [Version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006)
Lange, C.: Mathematical Semantic Markup in a Wiki: The Roles of Symbols and Notations. In: Lange, C., Schaffert, S., Skaf-Molli, H., Völkel, M. (eds.) Proceedings of the 3rd Workshop on Semantic Wikis, European Semantic Web Conference 2008, Costa Adeje, Tenerife, Spain (June 2008)
Manzoor, S., Libbrecht, P., Ullrich, C., Melis, E.: Authoring Presentation for OpenMath. In: Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, pp. 33–48. Springer, Heidelberg (2006)
Müller, C., Müller, N., Kohlhase, M.: mmlkit - a toolkit for handling mathematical documents and MathML3 notation definitions. mmlkit v0.1 (November 2007) http://kwarc.info/projects/mmlkit
Müller, C., Rhei, P.: Project Home Page, http://kwarc.info/projects/panta-rhei/ (August 2007)
Naylor, B., Watt, S.M.: Meta-Stylesheets for the Conversion of Mathematical Documents into Multiple Forms. In: Proceedings of the International Workshop on Mathematical Knowledge Management (2001)
Naylor, B., Watt, S.M.: Meta-Stylesheets for the Conversion of Mathematical Documents into Multiple Forms. In: Proceedings of the International Workshop on Mathematical Knowledge Management [NW01a]
IEEE POSIX, ISO/IEC 9945 (1988)
Smirnova, E., Watt, S.M.: Generating TeX from Mathematical Content with Respect to Notational Settings. In: Proceedings International Conference on Digital Typography and Electronic Publishing: Localization and Internationalization (TUG 2006), Marrakech, Morocco, pp. 96–105 (2006)
Smirnova, E., Watt, S.M.: Notation Selection in Mathematical Computing Environments. In: Proceedings Transgressive Computing 2006: A conference in honor of Jean Della Dora (TC 2006), Granada, Spain, pp. 339–355 (2006)
Wolfram, S.: Mathematical notation: Past and future. In: MathML and Math on the Web: MathML International Conference, Urbana Champaign, USA (October 2000), http://www.stephenwolfram.com/publications/talks/mathml/
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Kohlhase, M., Müller, C., Rabe, F. (2008). Notations for Living Mathematical Documents. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_41
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DOI: https://doi.org/10.1007/978-3-540-85110-3_41
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