Lecture Notes in Computer Science 2594 Edited by G. Goos, J. Hartmanis, and J. van Leeuwen 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo Andrea Asperti Bruno Buchberger James H. Davenport (Eds.) Mathematical Knowledge Management Second International Conference, MKM 2003 Bertinoro, Italy, February 16-18, 2003 Proceedings 13 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Andrea Asperti University of Bologna, Department of Computer Science Mura Anteo Zamboni, 7, 40127 Bologna, Italy E-mail: [email protected] Bruno Buchberger Johannes Kepler University Research Institute for Symbolic Computation 4232 Castle of Hagenberg, Austria E-mail: [email protected] James Harold Davenport University of Bath Departments of Mathematical Sciences and Computer Science Bath BA2 7AY, England E-mail: [email protected] Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. CR Subject Classification (1998): H.3, I.2, H.2.8, F.4.1, H.4, C.2.4, G.4, I.1 ISSN 0302-9743 ISBN 3-540-00568-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Printed in Germany Typesetting: Camera-ready by author, data conversion by PTP-Berlin S. Sossna e.K. Printed on acid-free paper SPIN 10872514 06/3142 543210 Preface This volume contains the proceedings of the Second International Conference on Mathematical Knowledge Management (MKM 2003), held 16–18 February 2003 in Bertinoro, Italy. Mathematical Knowledge Management is an exciting new field at the inter- section between mathematics and computer science. We need efficient, new tech- niques, based on sophisticated formal mathematics and software technology, to exploit the enormous knowledge available in current mathematical sources and to organize mathematical knowledge in a new way. On the other side, due to its very nature, the realm of mathematical information looks like the best candidate for testing innovative theoretical and technological solutions for content-based systems, interoperability, management of machine-understandable information, and the Semantic Web. The organizers are grateful to Dana Scott and Massimo Marchiori for agree- ing to give invited talks at MKM 2003. November 2002 Andrea Asperti Bruno Buchberger James Davenport Conference Organization Andrea Asperti (Program Chair) Luca Padovani (Organizing Chair) Program Commitee A. Asperti (Bologna) P. D. F. Ion (Michigan) B. Buchberger (RISC Linz) Z. Luo (Durham) J. Caldwell (Wyoming) R. Nederpelt (Eindhoven) O. Caprotti (RISC Linz) M. Sofroniou (Wolfram Research Inc.) J. Davenport (Bath) N. Soiffer (Wolfram Research Inc.) W. M. Farmer (McMaster Univ.) M. Suzuki (Kyushu) H. Geuvers (Nijmegen) N. Takayama (Kobe) T. Hardin (Paris 6) A. Trybulec (Bialystok) M. Hazewinkel (CWI Amsterdam) S. M. Watt (UWO) M. Kohlhase (CMU) B. Wegner (Berlin) Invited Speakers Massimo Marchiori (W3C, University of Venezia) Dana Scott (CMU) Additional Referees G. Bancerek R. Gamboa G. Jojgov P. Callaghan B. Han V. Prevosto D. Doligez Table of Contents Regular Contributions Digitisation, Representation, and Formalisation (Digital Libraries of Mathematics) .................................. 1 Andrew A. Adams MKM from Book to Computer: A Case Study ....................... 17 James H. Davenport From Proof-Assistants to Distributed Libraries of Mathematics: Tips and Pitfalls .................................................. 30 Claudio Sacerdoti Coen Managing Digital Mathematical Discourse............................ 45 Jonathan Borwein, Terry Stanway NAG Library Documentation ....................................... 56 David Carlisle, Mike Dewar On the Roles of LATEX and MathML in Encoding and Processing Mathematical Expressions .......................................... 66 Luca Padovani Problems and Solutions for Markup for Mathematical Examples and Exercises .................................................... 80 Georgi Goguadze, Erica Melis, Carsten Ullrich, Paul Cairns An Annotated Corpus and a Grammar Model of Theorem Description ... 93 Yusuke Baba, Masakazu Suzuki A Query Language for a Metadata Framework about Mathematical Resources .......................................... 105 Ferruccio Guidi, Irene Schena Information Retrieval in MML ..................................... 119 Grzegorz Bancerek, Piotr Rudnicki An Expert System for the Flexible Processing of Xml–Based Mathematical Knowledge in a Prolog–Environment .................. 133 Bernd D. Heumesser, Dietmar A. Seipel, Ulrich G¨untzer Towards Collaborative Content Management and Version Control for Structured Mathematical Knowledge ................................ 147 Michael Kohlhase, Romeo Anghelache X Table of Contents On the Integrity of a Repository of Formalized Mathematics ........... 162 Piotr Rudnicki, Andrzej Trybulec A Theoretical Analysis of Hierarchical Proofs ........................ 175 Paul Cairns, Jeremy Gow Comparing Mathematical Provers ................................... 188 Freek Wiedijk Translating Mizar for First Order Theorem Provers ................... 203 Josef Urban Invited Talk The Mathematical Semantic Web ................................... 216 Massimo Marchiori Author Index ................................................... 225 Author Index Adams, Andrew A. 1 Kohlhase, Michael 147 Anghelache, Romeo 147 Marchiori, Massimo 216 Baba, Yusuke 93 Melis, Erica 80 Bancerek, Grzegorz 119 Borwein, Jonathan 45 Padovani, Luca 66 Cairns, Paul 80, 175 Rudnicki, Piotr 119, 162 Carlisle, David 56 Coen, Claudio Sacerdoti 30 Schena, Irene 105 Seipel, Dietmar A. 133 Davenport, James H. 17 Stanway, Terry 45 Dewar, Mike 56 Suzuki, Masakazu 93 Goguadze, Georgi 80 Trybulec, Andrzej 162 Gow, Jeremy 175 G¨untzer, Ulrich 133 Ullrich, Carsten 80 Guidi, Ferruccio 105 Urban, Josef 203 Heumesser, Bernd D. 133 Wiedijk, Freek 188 Digitisation, Representation, and Formalisation Digital Libraries of Mathematics Andrew A. Adams School of Systems Engineering, The University of Reading. [email protected] Abstract. One of the main tasks of the mathematical knowledge man- agement 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 rep- resented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digi- tised 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 ma- terial 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 avail- able 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 ben- efit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks. 1 Introduction In this paper we present an overview of the use of information technology in mathematics. Some of the earliest uses of computers was the automation of math- ematics. Babbage’s Difference and Analytical Engines [Bab23] were designed to engineer tedious, error-prone, mathematical calculations. Some of the first dig- ital computers were designed for the purpose of breaking encryption codes. In the early days of digital computing, much was expected of this mechanical revo- lution in computation, and yet so little appeared for decades. As with the Strong AI and Ubiquitous Formal Methods communities, early over-selling of the idea of mechanised mathematical assistants led to a dismissal of the whole idea by many in the mathematics community. This work is supported by EU Grant MKMNet IST-2001-37057 and UK EPSRC Grant GR/S10919 A. Asperti, B. Buchberger, J.H. Davenport (Eds.): MKM 2003, LNCS 2594, pp. 1–16, 2003. c Springer-Verlag Berlin Heidelberg 2003 2 A.A. Adams This raises a side question as to who is part of this “mathematical commu- nity”. Athale and Athale presented a modest categorisation