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Algebraic Modeling Systems pp 11–32Cite as

Towards a Self-Reflective, Context-Aware Semantic Representation of Mathematical Specifications

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Part of the book series: Applied Optimization ((APOP,volume 104))

Abstract

We discuss a framework for the representation and processing of mathematics developed within and for the MoSMathproject. The MoSMathproject aims to create a software system that is able to translate optimization problems from an almost natural language to the algebraic modeling language AMPL. As part of a greater vision (the FMathL project), this framework is designed both to serve the optimization-oriented MoSMathproject, and to provide a basis for the much more general FMathL project. We introduce the semantic memory, a data structure to represent semantic information, a type system to define and assign types to data, and the semantic virtual machine (SVM), a low level, Turing-complete programming system that processes data represented in the semantic memory. Two features that set our approach apart from other frameworks are the possibility to reflect every major part of the system within the system itself, and the emphasis on the context-awareness of mathematics. Arguments are given why this framework appears to be well suited for the representation and processing of arbitrary mathematics. It is discussed which mathematical content the framework is currently able to represent and interface.

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Notes

  1. 1.

    The FMathL web site is available at http://www.mat.univie.ac.at/~neum/FMathL.html

  2. 2.

    http://www.mat.univie.ac.at/~neum/FMathL.html

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Acknowledgements

Support by the Austrian Science Fund (FWF) under contract number P20631 is gratefully acknowledged.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, A-1090, Wien, Austria

    Peter Schodl, Arnold Neumaier, Kevin Kofler, Ferenc Domes & Hermann Schichl

Authors
  1. Peter Schodl
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  2. Arnold Neumaier
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  3. Kevin Kofler
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  4. Ferenc Domes
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  5. Hermann Schichl
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  1. Am Mahlstein 8, Weisenheim, 67273, Germany

    Josef Kallrath

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Schodl, P., Neumaier, A., Kofler, K., Domes, F., Schichl, H. (2012). Towards a Self-Reflective, Context-Aware Semantic Representation of Mathematical Specifications. In: Kallrath, J. (eds) Algebraic Modeling Systems. Applied Optimization, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23592-4_2

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