Abstract
Defining functions is a major topic when building mathematical repositories. Though relatively easy in mathematical vernacular, function definitions rise a number of questions and problems in fully formal languages (see [4]). This becomes even more important for repositories in which properties of the defined functions are not only stated, but also proved correct. In this paper we investigate function definitions in the Mizar system. Though most of them are straightforward and follow the intuition, we also found a number of examples differing from mathematical vernacular or where different solutions seem equally reasonable. Sometimes there even do not seem to exist solutions not somehow “ignoring mathematical vernacular”. So the question is: Should we seek for some kind of standard, that is a “formal mathematical vernacular”, or should we accept that different authors prefer different styles?
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bancerek, G.: Zermelo Theorem and Axiom of Choice. Formalized Mathematics 1(2), 265–267 (1990)
Becker, T., Weispfenning, V.: Gröbner Bases – A Computational Approach to Commutative Algebra. Springer, Heidelberg (1993)
de Bruijn, N.G.: The Mathematical Vernacular, a language for mathematics with typed sets. In: Dybjer, P., et al. (eds.) Proc. of the Workshop on Programming Languages, Marstrand, Sweden (1987)
Davenport, J.H.: MKM from book to computer: a case study. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 17–29. Springer, Heidelberg (2003)
Farmer, W.M.: Formalizing undefinedness arising in calculus. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 475–489. Springer, Heidelberg (2004)
Grabowski, A.: On the computer-assisted reasoning about rough sets. In: Dunin-Kȩplicz, B., et al. (eds.) Monitoring, Security, and Rescue Techniques in Multiagent Systems, Advances in Soft Computing, pp. 215–226. Springer, Heidelberg (2005)
Grabowski, A., Schwarzweller, C.: Rough Concept Analysis – theory development in the Mizar system. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 130–144. Springer, Heidelberg (2004)
Graham, R.E., Knuth, D.E., Patashnik, O.: Concrete Mathematics. Addison-Wesley, Reading (1994)
Kamareddine, F., Nederpelt, R.: A refinement of de Bruijn’s formal language of mathematics. Journal of Logic, Language and Information 13(3), 287–340 (2004)
Naumowicz, A., Byliński, C.: Improving Mizar texts with properties and requirements. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 190–301. Springer, Heidelberg (2004)
Retel, K., Zalewska, A.: Mizar as a tool for teaching mathematics. In: Proc. of Mizar 30 workshop, Białowieża, Poland (2004), available at, http://www.macs.hw.ac.uk/~retel/papers/KRetelAZalewska.pdf
Rudnicki, P., Trybulec, A.: Mathematical Knowledge Management in Mizar. In: Buchberger, B., Caprotti, O. (eds.) Proc. of MKM 2001, Linz, Austria (2001)
Rudnicki, P., Trybulec, A.: On the integrity of a repository of formalized mathematics. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 162–174. Springer, Heidelberg (2003)
Sacerdoti Coen, C.: From proof-asistants to distributed knowledge repositories: tips and pitfalls. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 30–44. Springer, Heidelberg (2003)
Urban, J.: Basic facts about inaccessible and measurable cardinals. Formalized Mathematics 9(2), 323–329 (2001)
Wiedijk, F.: The Mathematical Vernacular. unpublished note, available at, http://www.cs.ru.nl/~freek/notes/mv.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grabowski, A., Schwarzweller, C. (2006). Translating Mathematical Vernacular into Knowledge Repositories. In: Kohlhase, M. (eds) Mathematical Knowledge Management. MKM 2005. Lecture Notes in Computer Science(), vol 3863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618027_4
Download citation
DOI: https://doi.org/10.1007/11618027_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31430-1
Online ISBN: 978-3-540-31431-8
eBook Packages: Computer ScienceComputer Science (R0)