Abstract
The Naproche system is a system for linguistically analysing and proof-checking mathematical texts written in a controlled natural language. The aim is to have an input language that is as close as possible to the language that mathematicians actually use when writing textbooks or papers.
Mathematical texts consist of a combination of natural language and symbolic mathematics, with symbolic mathematics obeying its own syntactic rules. We discuss the difficulties that a program for parsing and disambiguating symbolic mathematics must face and present how these difficulties have been tackled in the Naproche system. One of these difficulties is the fact that information provided in the preceding context – including information provided in natural language – can influence the way a symbolic expression has to be disambiguated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Avigad, J., Donnelly, K., Gray, D., Raff, P.: A formally verified proof of the prime number theorem. ACM Transactions on Computational Logic 9(1:2) (2007)
Brachman, R., Levesque, H.: Knowledge Representation and Reasoning. Morgan Kaufmann Publishers, Massachusetts (2004)
de Bruijn, R.G.: Reflections on Automath. In: Nederpelt, R.P., et al. (eds.) Selected Papers on Automath. Studies in Logic, vol. 133, pp. 201–228, 215. Elsevier, Amsterdam (1994)
Carl, M., Cramer, M., Kühlwein, D.: Chapter 1 from Landau in Naproche 0.5 (2011), http://naproche.net/downloads/2011/landauChapter1.pdf
Church, A.: A Formulation of the Simple Theory of Types. The Journal of Symbolic Logic 5(2), 56–68 (1940)
Cramer, M., Koepke, P., Kühlwein, D., Schröder, B.: The Naproche System. Calculemus, Emerging Trend Paper (2009)
Cramer, M., Fisseni, B., Koepke, P., Kühlwein, D., Schröder, B., Veldman, J.: The Naproche Project – Controlled Natural Language Proof Checking of Mathematical Texts. In: Fuchs, N.E. (ed.) CNL 2009. LNCS, vol. 5972, pp. 170–186. Springer, Heidelberg (2010)
Cramer, M., Kühlwein, D., Schröder, B.: Presupposition Projection and Accommodation in Mathematical Texts. In: Semantic Approaches in Natural Language Processing: Proceedings of the Conference on Natural Language Processing 2010 (KONVENS), pp. 29–36. Universaar (2010)
Ganesalingam, M.: The Language of Mathematics, PhD thesis, University of Cambridge (2009)
Hales, T.: Jordan’s proof of the Jordan Curve theorem. Studies in Logic, Grammar and Rhetoric 10(23) (2007)
Hales, T.: Introduction to the Flyspeck Project. Dagstuhl Seminar Proceedings (2006)
Heuser, H.: Lehrbuch der Analysis. In: Teil 2, 6th edn., B.G. Teubner, Stuttgart (1991)
Kadmon, N.: Formal Pragmatics. Wiley-Blackwell, Oxford, UK (2001)
Kamp, H., Reyle, U.: From Discourse to Logic: Introduction to Model-theoretic Semantics of Natural Language. Kluwer Academic Publishers, Dordrecht (1993)
Lackenby, M.: Topology and Groups. Lecture Notes (2008), http://people.maths.ox.ac.uk/lackenby/tg050908.pdf
Landau, E.: Grundlagen der Analysis, 3rd edn (1960)
Matuszewski, R., Rudnicki, P.: Mizar: The first 30 years. Mechanized Mathematics and Its Applications 4 (2005)
Ranta, A.: Structure grammaticales dans le français mathématique II (suite et fin). Mathématiques, Informatique et Sciences Humaines 139, 5–36 (1997)
Verchinine, K., Lyaletski, A., Paskevich, A.: System for Automated Deduction (SAD): a tool for proof verification. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 398–403. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cramer, M., Koepke, P., Schröder, B. (2011). Parsing and Disambiguation of Symbolic Mathematics in the Naproche System. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science(), vol 6824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22673-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-22673-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22672-4
Online ISBN: 978-3-642-22673-1
eBook Packages: Computer ScienceComputer Science (R0)