Digitisation, Representation and Formalisation: Digital Libraries of Mathematics
One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down.
[AA01] M. Athale and R. Athale. Exchange of mathematical information on the web: Present and Future. In Buchberger and Caprotti [BC01]. [AMS] AMS. Mathscinet. www.ams.org/mathscinet/. [APSC+01] A. Asperti, L. Padovani, C. Sacerdoti Coen, G. Ferruccio, , and I. Schena. Mathematical Knowledge Management in HELM. In Buchberger and Caprotti [BC01]. [APSCS01] A. Asperti, L. Padovani, C. Sacerdoti Coen, and I. Schena. HELM and the Semantic Math-Web. In Boulton and Jackson [BJ01]. [AS72] M. Abramowitz and I. A. Stegun. Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover, 1972. [AZ99] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer, 1999. [Bab23] C. Babbage. On the Theoretical Principles of the Machinery for Calculating Tables. Edin Phtl Jrl, 8:122â��128, 1823. [BB+96] B. Barras, S. Boutin, et al. The Coq Proof Assistant Reference Manual (Version 6.1). Technical report, INRIA, 1996. Available on-line with Coq distribution from ftp.inria.fr. [BB01] P. Baumgartner and A. Blohm. Automated Deduction Techniques for the Management of Personal Documents (Extended Abstract). In Buchberger and Caprotti [BC01]. [BC01] B. Buchberger and O. Caprotti, editors. MKM 2001 (First International Workshop on Mathematical Knowledge Management). www.risc.unilinz. ac.at/conferences/MKM2001/Proceedings, 2001. [Bel02] Research Review, 2002. www.lucent.com/news events/researchreview.html. [BJ01] R. J. Boulton and P. B. Jackson, editors. Theorem Proving in Higher Order Logics: 14th International Conference. Springer-Verlag LNCS 2152, 2001. [Bor01] J. M. Borwein. The International Math Unionâ��s Electronic Initiatives (Extended Abstract). In Buchberger and Caprotti [BC01]. [CA+86] R. L. Constable, S. F. Allen, et al. Implementing Mathematics with the NuPrl Proof Development System. Prentice-Hall, 1986. [Cit] Citeseer. www.citeseer.org. [CRL01] J. A. Campbell and E. Roanes-Lozano, editors. Artificial Intelligence and Symbolic Computation, International Conference AISC 2000. Revised Papers. Springer LNCS 1930, 2001. [Dav01] J. Davenport. Mathematical Knowledge Representation (Extended Abstract). In Buchberger and Caprotti [BC01]. [Dew00a] M. Dewar. OpenMath: An Overview. ACM SIGSAM Bulletin, 34(2):2â��5, June 2000. [Dew00b] M. Dewar. Special Issue on OPENMATH. ACM SIGSAM Bulletin, 34(2), June 2000. [DM97] M. Dauchet and Bidoit M., editors. Proc. Intl. Symp. on Theory and Practice of Software Development. Springer LNCS 1214, 1997. [Fro02] M. Froumentin. Mathematics on the Web with MathML. www.w3.org/People/maxf/papers/iamc.ps, 2002. [FTBM96] R. Fateman, T. Tokuyasu, B. P. Berman, and N. Mitchell. Optical Character Recognition and Parsing of Typeset Mathematics. Journal of Visual Communication and Image Representation, 7(1):2â��15, March 1996. [GM93] M. J. C. Gordon and T. F. Melham, editors. Introduction to HOL. CUP, 1993. [Har71] M. Hart. Project gutenberg, 1971. www.gutenberg.org. [Har00] J. Harrison. Formal verification of floating point trigonometric functions. In Hunt and Johnson [HJ00]. [HJ00] W. A. Hunt and S. D. Johnson, editors. Formal Methods in Computer-Aided Design: Third International Conference FMCAD 2000. Springer-Verlag LNCS 1954, 2000. [JB01] M. Jones and N. Beagrie. Preservation Management of Digital Materials (A Handbook). The British Library, 2001. [Kea00] T. Kealey. More is less. Nature, 405(279), May 2000. [Knu79] D. Knuth. TEX and METAFONT: New directions in Typesetting. AMS and Digital Press, 1979. [Koh01] M. Kohlhase. OMDoc: Towards an Internet Standard for the Administration, Distribution and Teaching of Mathematical Knowledge. In Campbell and Roanes-Lozano [CRL01], pages 32â��52. [Lam94] L. Lamport. LATEX: A Document Preparation System, 2/E. Addison Wesley, second edition, 1994. [Loz01] D. Lozier. The NIST Digital Library of Mathematical Functions Project. In Buchberger and Caprotti [BC01]. [McC62] J. et al. McCarthy. LISP 1.5 Programmerâ��s Manual. MIT Press, 1962. [Mic01] G. O. Michler. How to Build a Prototype for a Distributed Mathematics Archive Library. In Buchberger and Caprotti [BC01]. [ML84] P. Martin-L�¨of. Intuitionistic Type Theory. Bibliopolis, 1984. [Mos97] P. D. Mosses. CoFI: The Common Framework Initiative for Algebraic Specification and Development. In Dauchet and M. [DM97], pages 115â��137. [MY01] B. R. Miller and A. Youssef. Technical Aspects of the Digital Library of Mathematical Functions Dreams and Realities. In Buchberger and Caprotti [BC01]. [Pau88] L. C. Paulson. The Foundation of a Generic Theorem Prover. J. Automated Reasoning, 5:363â��396, 1988. [SOR] N. Shankar, S. Owre, and J. M. Rushby. The PVS Proof Checker: A Reference Manual. Computer Science Lab, SRI International. [Try80] A. Trybulec. The Mizar Logic Information Language, volume 1 of Studies in Logic, Grammar and Rhetoric. Bialystok, 1980. [Wol] www.wolfram.com.