Abstract
This paper discusses the semi-formal language of mathematics and presents the Naproche CNL, a controlled natural language for mathematical authoring. Proof Representation Structures, an adaptation of Discourse Representation Structures, are used to represent the semantics of texts written in the Naproche CNL. We discuss how the Naproche CNL can be used in formal mathematics, and present our prototypical Naproche system, a computer program for parsing texts in the Naproche CNL and checking the proofs in them for logical correctness.
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References
Asher, N.: Reference to Abstract Objects in Discourse (1993)
Blackburn, P., Bos, J.: Working with Discourse Representation Theory: An Advanced Course in Computational Linguistics (2003)
Coq Development Team: The Coq Proof Assistant Reference Manual: Version v8.1 (July 2007), http://coq.inria.fr
Carl, M., Cramer, M., Kühlwein, D.: Landau in Naproche, ch. 1, http://www.naproche.net/downloads/2009/landauChapter1.pdf
Cramer, M.: The Controlled Natural Language of Naproche in a nutshell, http://www.naproche.net/wiki/doku.php?id=dokumentation:language
Cramer, M.: Mathematisch-logische Aspekte von Beweisrepräsentationsstrukturen, Master’s thesis, University of Bonn (2008), http://naproche.net/downloads.shtml
Fuchs, N.E., Höfler, S., Kaljurand, K., Rinaldi, F., Schneider, G.: Attempto Controlled English: A Knowledge Representation Language Readable by Humans and Machines
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers, 4th edn. (1960)
Kamp, H., Reyle, U.: From Discourse to Logic: Introduction to Model-theoretic Semantics of Natural Language. Kluwer Academic Publisher, Dordrecht (1993)
Kolev, N.: Generating Proof Representation Structures for the Project Naproche, Magister thesis, University of Bonn (2008), http://naproche.net/downloads.shtml
Kühlwein, D.: A calculus for Proof Representation Structures, Diploma thesis, University of Bonn (2008), http://naproche.net/downloads.shtml
Landau, E.: Grundlagen der Analysis, 3rd edn. (1960)
Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. Mechanized Mathematics and Its Applications 4(2005) (2005)
Sutcliffe, G.: System Description: System on TPTP. In: CADE, pp. 406–410 (2000)
Texmacs Editor website: http://www.texmacs.org/
VeriMathDoc website: http://www.ags.uni-sb.de/~afiedler/verimathdoc/
Zinn, C.: Understanding Informal Mathematical Discourse, PhD thesis at the University of Erlangen (2004), http://citeseer.ist.psu.edu/233023.html
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Cramer, M., Fisseni, B., Koepke, P., Kühlwein, D., Schröder, B., Veldman, J. (2010). The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts. In: Fuchs, N.E. (eds) Controlled Natural Language. CNL 2009. Lecture Notes in Computer Science(), vol 5972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14418-9_11
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DOI: https://doi.org/10.1007/978-3-642-14418-9_11
Publisher Name: Springer, Berlin, Heidelberg
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