OMDoc - An Open Markup Format for Mathematical Documents [version 1.2]

In this report we present a content markup scheme for (collections of) mathematical documents including articles, textbooks, interactive books, and courses. It can serve as the content language for agent communication of mathematical services on a mathematical software bus. We motivate and describe the OMDoc language and present an Xml document type definition for it. Furthermore, we discuss applications and tool support. This document describes version 1.1 of the OMDoc format. This version is mainly a bug-fix release that has become necessary by the experiments of encoding legacy material and theorem prover interfaces in OMDoc. The changes are relatively minor, mostly adding optional fields. Version 1.1 of OMDoc freezes the development so that version 2.0 can be started off. In contrast to the OMDoc format which has not changed much, this report is a total re-write, it closes many documentation gaps, clarifies various remaining issues. and adds a multitude of new examples.

[1]  Andrea Kohlhase “Overcoming Proprietary Hurdles: CPoint as Invasive Editor” , 2005 .

[2]  William M. Farmer,et al.  IMPS: An Interactive Mathematical Proof System , 1990, CADE.

[3]  Dieter Hutter,et al.  Formal Software Development in MAYA , 2005, Mechanizing Mathematical Reasoning.

[4]  Volker Sorge,et al.  Agent-Oriented Integration of Distributed Mathematical Services , 1999, J. Univers. Comput. Sci..

[5]  G. Gentzen Untersuchungen über das logische Schließen. II , 1935 .

[6]  Michael Kohlhase OMDoc: an infrastructure for OpenMath content dictionary information , 2000, SIGS.

[7]  Michael Kohlhase,et al.  MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems , 2001, J. Symb. Comput..

[8]  Ian Green,et al.  System Description: Proof Planning in Higher-Order Logic with Lambda-Clam , 1998, CADE.

[9]  Frank van Harmelen,et al.  The Oyster-Clam System , 1990, CADE.

[10]  Michael Kohlhase,et al.  System Description: MBASE, an Open Mathematical Knowledge Base , 2000, CADE.

[11]  Dan Brickley,et al.  Resource Description Framework (RDF) Model and Syntax Specification , 2002 .

[12]  Frank Pfenning,et al.  System Description: Twelf - A Meta-Logical Framework for Deductive Systems , 1999, CADE.

[13]  Geoff Sutcliffe,et al.  TSTP Data-Exchange Formats for Automated Theorem Proving Tools , 2004 .

[14]  William M. Farmer,et al.  Theory Interpretation in Simple Type Theory , 1993, HOA.

[15]  Joël Ouaknine,et al.  System Description: Analytica 2 , 2003 .

[16]  Glenn C. Reid Postscript language - program design , 1988 .

[17]  Roy T. Fielding,et al.  Uniform Resource Identifiers (URI): Generic Syntax , 1998, RFC.

[18]  Stephen M. Watt,et al.  Mathematical Markup Language (MathML) Version 3.0 , 2001, WWW 2001.

[19]  Frank Pfenning,et al.  Logical Frameworks , 2001, Handbook of Automated Reasoning.

[20]  Armin Fiedler User-adaptive proof explanation , 2001 .

[21]  Carsten Ullrich,et al.  Description of an Instructional Ontology and its Application in Web Services for Education , 2004 .

[22]  Arvind Malhotra,et al.  Xml schema part 2: datatypes , 1999 .

[23]  Paul Libbrecht Authoring Web Content in ActiveMath: From Developer Tools and Further , 2004 .

[24]  Rance Cleaveland,et al.  Implementing mathematics with the Nuprl proof development system , 1986 .

[25]  Manolis Mavrikis,et al.  Mathematical, Interactive Exercise Generation from Static Documents , 2004, Electron. Notes Theor. Comput. Sci..

[26]  Richard J. Boulton,et al.  An Interface between Clam and HOL , 1998, TPHOLs.

[27]  Armin Fiedler,et al.  Towards a Proof Explainer , 1997 .

[28]  Armin Fiedler Using a Cognitive Architecture to Plan Dialogs for the Adaptive Explanation of Proofs , 1999, IJCAI.

[29]  Peter B. Andrews An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[30]  Arjeh M. Cohen,et al.  JAVA Phrasebooks for computer algebra and automated deduction , 2000, SIGS.

[31]  Michael Kohlhase,et al.  Notations for Living Mathematical Documents , 2008, AISC/MKM/Calculemus.

[32]  Natarajan Shankar,et al.  PVS: A Prototype Verification System , 1992, CADE.

[33]  Armin Fiedler Dialog-driven Adaptation of Explanations of Proofs , 2001, IJCAI.

[34]  William C. Mann,et al.  RHETORICAL STRUCTURE THEORY: A THEORY OF TEXT ORGANIZATION , 1987 .

[35]  Nathaniel S. Borenstein,et al.  Multipurpose Internet Mail Extensions (MIME) Part Two: Media Types , 1996, RFC.

[36]  Paul A. Cairns,et al.  Problems and Solutions for Markup for Mathematical Examples and Exercises , 2003, MKM.

[37]  Michael Kohlhase MDoc: An Open Markup Format for Mathematical Documents , 2000 .

[38]  Ricardo Conejo,et al.  SIETTE: A Web-Based Tool for Adaptive Testing , 2004, Int. J. Artif. Intell. Educ..

[39]  Geoff Sutcliffe,et al.  The TPTP Problem Library , 1994, Journal of Automated Reasoning.

[40]  Christine Paulin-Mohring,et al.  The coq proof assistant reference manual , 2000 .

[41]  Luca Padovani,et al.  HELM and the Semantic Math-Web , 2001, TPHOLs.

[42]  Volker Sorge,et al.  Proof Development with OMEGA , 2002, CADE.

[43]  Charles F. Goldfarb,et al.  SGML handbook , 1990 .

[44]  Volker Sorge,et al.  Integrating Tps and Omega , 1999, J. Univers. Comput. Sci..

[45]  Dieter Hutter,et al.  INKA: The Next Generation , 1996, CADE.

[46]  Andrew M. Odlyzko,et al.  Tragic Loss or Good Riddance? The Impending Demise of Traditional Scholary Journals , 1996, J. Univers. Comput. Sci..

[47]  F. Pfenning Logic programming in the LF logical framework , 1991 .

[48]  Dieter Hutter,et al.  Development graphs - Proof management for structured specifications , 2006, J. Log. Algebraic Methods Program..

[49]  Volker Sorge,et al.  LΩUI: Lovely ΩMEGA User Interface , 1999, Formal Aspects of Computing.

[50]  Jürgen Zimmer A Framework for Agent-Based Brokering of Reasoning Services , 2004, MICAI.

[51]  Xiaorong Huang,et al.  Presenting Machine-Found Proofs , 1996, CADE.

[52]  Benjamin S. Bloom,et al.  Taxonomy of Educational Objectives: The Classification of Educational Goals. , 1957 .

[53]  Bruno Buchberger,et al.  An Environment for Building Mathematical Knowledge Libraries , 2004 .

[54]  Markus Krötzsch,et al.  Semantic Wikipedia , 2006, WikiSym '06.

[55]  Till Mossakowski Heterogeneous Development Graphs and Heterogeneous Borrowing , 2002, FoSSaCS.

[56]  Nathan R. Yergler,et al.  ccREL : The Creative Commons Rights Expression Language , 2008 .

[57]  Dieter Hutter Management of change in structured verification , 2000, Proceedings ASE 2000. Fifteenth IEEE International Conference on Automated Software Engineering.

[58]  Helmut Horacek,et al.  Argumentation in Explanations to Logical Problems , 2001, International Conference on Computational Science.

[59]  de Ng Dick Bruijn,et al.  The Mathematical Vernacular, A Language for Mathematics with Typed Sets , 1994 .

[60]  Steven J. DeRose,et al.  Xml pointer language (xpointer) , 1998 .

[61]  Elena Paslaru Bontas Simperl,et al.  Towards Wikis as semantic hypermedia , 2006, WikiSym '06.

[62]  Christoph Benzmüller,et al.  Integrating Proof Assistants as Reasoning and Verification Tools into a Scientific WYSIWIG Editor , 2005 .

[63]  J. Siekmann,et al.  Computer supported mathematics with MEGA , 2005 .

[64]  Bruce W. Char,et al.  First Leaves: A Tutorial Introduction to Maple V , 1992 .

[65]  Steven J. DeRose,et al.  Xml linking language (xlink), version 1. 0 , 2000, WWW 2000.

[66]  Volker Sorge,et al.  Adaptive Course Generation and Presentation , 2000 .

[67]  Andreas Meier System Description: TRAMP: Transformation of Machine-Found Proofs into ND-Proofs at the Assertion Level , 2000, CADE.

[68]  F. Dick A survey of the project Automath , 1980 .

[69]  Fausto Giunchiglia,et al.  Reasoning Theories , 2001, Journal of Automated Reasoning.

[70]  not Cwi,et al.  CURIE Syntax 1.0, A syntax for expressing Compact URIs , 2007 .

[71]  Dieter Hutter,et al.  Towards an Evolutionary Formal Software-Development Using CASL , 1999, WADT.

[72]  Sebastian Schaffert,et al.  IkeWiki: A Semantic Wiki for Collaborative Knowledge Management , 2006, 15th IEEE International Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises (WETICE'06).

[73]  Tomek Strzalkowski,et al.  From Discourse to Logic , 1991 .

[74]  Michael Kohlhase,et al.  An Exploration in the Space of Mathematical Knowledge , 2005, MKM.

[75]  Richard J. Boulton,et al.  The PROSPER toolkit , 2003, International Journal on Software Tools for Technology Transfer.

[76]  Donald E. Knuth,et al.  The T E Xbook , 1987 .

[77]  Ian Green,et al.  System description : Proof planning in higher-order logic with λ Clam , 1998 .

[78]  Lawrence Charles Paulson,et al.  Isabelle: A Generic Theorem Prover , 1994 .

[79]  Joris Van der Hoeven GNU TeXmacs, A free, structured, wysiwyg and technical text editor , 2001 .

[80]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[81]  Piotr Rudnicki,et al.  An Overview of the MIZAR Project , 1992 .

[82]  Peter D. Mosses,et al.  Casl Reference Manual , 2004, Lecture Notes in Computer Science.

[83]  Klaus Schneider Verification of Reactive Systems , 2004, Texts in Theoretical Computer Science.

[84]  Simon Thompson,et al.  Type theory and functional programming , 1991, International computer science series.

[85]  Tobias Bürger,et al.  Learning with Semantic Wikis , 2006, SemWiki.

[86]  Michael Kohlhase,et al.  System Description: MathWeb, an Agent-Based Communication Layer for Distributed Automated Theorem Proving , 1999, CADE.

[87]  Klaus Schneider,et al.  Theorem Proving in Higher Order Logics - Emerging Trends , 2007 .

[88]  Michael Kohlhase,et al.  System Description: The MathWeb Software Bus for Distributed Mathematical Reasoning , 2002, CADE.

[89]  Andrea Kohlhase What if PowerPoint became emPowerPoint (through CPoint) , 2006 .

[90]  Gert Smolka,et al.  The Oz Programming Model , 1996, Computer Science Today.

[91]  Volker Sorge,et al.  ΩMEGA : Towards a mathematical assistant , 1997 .

[92]  Paul Libbrecht,et al.  Authoring Presentation for OpenMath , 2005, MKM.

[93]  Steven P. Abney Partial parsing via finite-state cascades , 1996, Natural Language Engineering.

[94]  Allen Newell,et al.  Computer science as empirical inquiry: symbols and search , 1976, CACM.

[95]  Erica Melis,et al.  Towards Adaptive Generation of Faded Examples , 2004, Intelligent Tutoring Systems.

[96]  Amy P. Felty,et al.  Hybrid Interactive Theorem Proving Using Nuprl and HOL , 1997, CADE.

[97]  Paul Libbrecht,et al.  Semantic-aware components and services of ActiveMath , 2006, Br. J. Educ. Technol..

[98]  Christoph Weidenbach SPASS - Version 0.49 , 2004, Journal of Automated Reasoning.

[99]  Stephen M. Watt,et al.  Reasoning about the Elementary Functions of Complex Analysis , 2000, Annals of Mathematics and Artificial Intelligence.

[100]  Carsten Ullrich Tutorial Planning: Adapting Course Generation to Today's Needs , 2005, AIED.

[101]  Eyal Oren,et al.  Sindice.com: Weaving the Open Linked Data , 2007, ISWC/ASWC.

[102]  Dieter Hutter,et al.  Extending Development Graphs with Hiding , 2001, FASE.

[103]  Erica Melis,et al.  Interactivity of Exercises in ActiveMath , 2005, ICCE.

[104]  Olga Caprotti,et al.  Using OpenMath servers for distributing mathematical computations , 2000 .

[105]  Till Mossakowski,et al.  Heterogeneous Specification and the Heterogeneous Tool Set , 2004 .

[106]  David Orchard,et al.  XML Linking Language (XLink) , 2001 .

[107]  Steven Pemberton,et al.  RDFa in XHTML: Syntax and Processing , 2008 .

[108]  Christoph Benzmüller,et al.  Assertion-level Proof Representation with Under-Specification , 2004, Electron. Notes Theor. Comput. Sci..

[109]  Christoph Walther,et al.  The VeriFun tutorial , 2002 .

[110]  Christoph Weidenbach,et al.  Common Syntax of the DFG-Schwerpunktprogramm ''Deduktion'' , 1996 .

[111]  Michael Kohlhase,et al.  Towards Collaborative Content Management and Version Control for Structured Mathematical Knowledge , 2003, MKM.

[112]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[113]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[114]  Xiaorong Huang,et al.  Human oriented proof presentation - a reconstructive approach , 1996, DISKI.

[115]  Tobias Nipkow,et al.  Higher-Order Algebra, Logic, and Term Rewriting , 1993, Lecture Notes in Computer Science.

[116]  Bernd Krieg-Brückner,et al.  Literate Ontology Development , 2004, OTM Workshops.

[117]  Alessandro Armando,et al.  Towards Interoperable Mechanized Reasoning Systems: the Logic Broker Architecture , 2000, WOA.

[118]  Paul Libbrecht,et al.  Knowledge Representation and Management in ACTIVEMATH , 2004, Annals of Mathematics and Artificial Intelligence.

[119]  Arvind Malhotra,et al.  XML Schema Part 2: Datatypes Second Edition , 2004 .

[120]  Donald E. Knuth,et al.  The TeXbook , 1984 .

[121]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[122]  Steven J. DeRose,et al.  XML Path Language (XPath) Version 1.0 , 1999 .

[123]  Jörg H. Siekmann,et al.  Mi 3 — Page 1 Dialog: Natural Language-based Interaction with a Mathematics Assistance System , 2022 .

[124]  J. Pierce An introduction to information theory: symbols, signals & noise , 1980 .

[125]  Deepak Kapur,et al.  An Overview of Rewrite Rule Laboratory (RRL) , 1989, RTA.

[126]  Helmut Horacek,et al.  Generating Inference-Rich Discourse Through Revisions of RST-Trees , 1998, AAAI/IAAI.

[127]  Ian Jacobs,et al.  Cascading Style Sheets, level 2 CSS2 Specification , 2008 .

[128]  Xiaorong Huang,et al.  Proof Verbalization in PROVERB , 1999 .

[129]  Arjeh M. Cohen,et al.  Electronic Communication of Mathematics and the Interaction of Computer Algebra Systems and Proof Assistants , 2001, J. Symb. Comput..

[130]  Frank Pfenning,et al.  TPS: A theorem-proving system for classical type theory , 1996, Journal of Automated Reasoning.

[131]  G. Gentzen Untersuchungen über das logische Schließen. I , 1935 .

[132]  I. V. Ramakrishnan,et al.  Term Indexing , 1995, Lecture Notes in Computer Science.

[133]  Tobias Nipkow,et al.  Isabelle tutorial and user’s manual , 1990 .

[134]  Serge Autexier,et al.  Textbook Proofs Meet Formal Logic - The Problem of Underspecification and Granularity , 2005, MKM.

[135]  Peter Baumgartner,et al.  Automated Deduction Techniques for the Management of Personalized Documents , 2003, Annals of Mathematics and Artificial Intelligence.

[136]  J. Hintikka,et al.  What is Logic , 2007 .