Abstract
A major obstacle for bridging the gap between textbook mathematics and formalising it on a computer is the problem how to adequately capture the intuition inherent in the mathematical notation when formalising mathematical concepts. While logic is an excellent tool to represent certain mathematical concepts it often fails to retain all the information implicitly given in the representation of some mathematical objects. In this paper we concern ourselves with matrices, whose representation can be particularly rich in implicit information. We analyse different types of matrices and present a mechanism that can represent them very close to their textbook style appearance and captures the information contained in this representation but that nevertheless allows for their compilation into a formal logical framework. This firstly allows for a more human-oriented interface and secondly enables efficient reasoning with matrices.
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
Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, 2nd edn. Kluwer, Dordrecht (2002)
Bundy, A., Richardson, J.: Proofs about lists using ellipsis. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS (LNAI), vol. 1705, pp. 1–12. Springer, Heidelberg (1999)
de Bruijn, N.G.: The mathematical vernacular, a language for mathematics with typed sets. In: Selected Papers on Automath, pp. 865–935. Elsevier, Amsterdam (1994)
Elbers, H.: Connecting Informal and Formal Mathematics. PhD thesis. Eindhoven University of Technology (1998)
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)
Köcher, M.: Lineare Algebra und analytische Geometrie. Springer, Heidelberg (1992)
Kutsia, T.: Unification with sequence variables and flexible arity symbols and its extension with pattern-terms. In: Calmet, J., Benhamou, B., Caprotti, O., Hénocque, L., Sorge, V. (eds.) AISC 2002 and Calculemus 2002. LNCS (LNAI), vol. 2385. Springer, Heidelberg (2002)
Lang, S.: Algebra, 2nd edn. Addison-Wesley, Reading (1984)
NCAlgebra 3.7 - A Noncommutative Algebra Package for Mathematica, Available at: http://math.ucsd.edu/~ncalg/
Siekmann, J.H., Brezhnev, V., Cheikhrouhou, L., Fiedler, A., Horacek, H., Kohlhase, M., Meier, A., Melis, E., Moschner, M., Normann, I., Pollet, M., Sorge, V., Ullrich, C., Wirth, C.-P.: Proof development with OMEGA. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 144–148. Springer, Heidelberg (2002)
Pollet, M., Sorge, V.: Integrating computational properties at the term level. In: Proc. of Calculemus 2002, pp. 78–83 (2003)
Wenzel, M., Wiedijk, F.: A Comparison of Mizar and Isar. J. of Automated Reasoning 29(3-4), 389–411 (2002)
Wolfram, S.: The Mathematica book, 5th edn. Wolfram Media, Inc. (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pollet, M., Sorge, V., Kerber, M. (2004). Intuitive and Formal Representations: The Case of Matrices. In: Asperti, A., Bancerek, G., Trybulec, A. (eds) Mathematical Knowledge Management. MKM 2004. Lecture Notes in Computer Science, vol 3119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27818-4_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-27818-4_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23029-8
Online ISBN: 978-3-540-27818-4
eBook Packages: Springer Book Archive