Importing the OEIS Library Into Omdoc
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A Framework for Semantic Publishing of Modular Content Objects
A Framework for Semantic Publishing of Modular Content Objects Catalin David, Deyan Ginev, Michael Kohlhase, Bogdan Matican, Stefan Mirea Computer Science, Jacobs University, Germany; http://kwarc.info/ Abstract. We present the Active Documents approach to semantic pub- lishing (semantically annotated documents associated with a content commons that holds the background ontologies) and the Planetary system (as an active document player). In this paper we explore the interaction of content object reuse and context sensitivity in the presentation process that transforms content modules to active documents. We propose a \separate compilation and dynamic linking" regime that makes semantic publishing of highly struc- tured content representations into active documents tractable and show how this is realized in the Planetary system. 1 Introduction Semantic publication can range from merely equipping published documents with RDFa annotations, expressing metadata or inter-paper links, to frame- works that support the provisioning of user-adapted documents from content representations and instrumenting them with interactions based on the seman- tic information embedded in the content forms. We want to propose an entry to the latter category in this paper. Our framework is based on semantically anno- tated documents together with semantic background ontologies (which we call the content commons). This information can then be used by user-visible, se- mantic services like program (fragment) execution, computation, visualization, navigation, information aggregation and information retrieval (see Figure 5). Finally a document player application can embed these services to make docu- ments executable. We call this framework the Active Documents Paradigm (ADP), since documents can also actively adapt to user preferences and envi- ronment rather than only executing services upon user request. -
Mathematical Document Representation and Processing1
Formats Format Usage in DML-CZ Delivery Summary and Conclusions Mathematical Document Representation and Processing1 Petr Sojka Faculty of Informatics, Masaryk University, Brno, CZ, EU Dec 1st, 2008 1Supported by the Academy of Sciences of Czech Republic grant #1ET200190513 Mathematical Document Representation and Processing Faculty of Informatics, Masaryk University, Brno, CZ, EU Formats Format Usage in DML-CZ Delivery Summary and Conclusions Purpose-driven format choices Purposes for storing mathematics I Format choice depends on application’s purpose. I Most applications have its own internal format anyway. I For exchange seems to win XML/MathML (but which one?). I As authoring tools seems to be prefered (La)TEX. I Quite different requirements have theorem proving systems. Mathematical Document Representation and Processing Faculty of Informatics, Masaryk University, Brno, CZ, EU Formats Format Usage in DML-CZ Delivery Summary and Conclusions Purpose-driven format choices Mathematical Document Representation and Processing Faculty of Informatics, Masaryk University, Brno, CZ, EU Formats Format Usage in DML-CZ Delivery Summary and Conclusions Purpose-driven format choices Math Author Tools: LATEX, AMSLATEX (pdfAMSLATEX) I Good for authors: authors may express as close as possible to their mental model in their brain (new macros, namespaces). I This author’s advantage make headaches to the editors and those wishing to convert to some standard formalism (to index, evaluate, . ). I Many different macropackages, and active development as possibilites grow (XeTeX, LuaTEX, pdfTEX), . Mathematical Document Representation and Processing Faculty of Informatics, Masaryk University, Brno, CZ, EU Formats Format Usage in DML-CZ Delivery Summary and Conclusions Purpose-driven format choices pdfTEX program (used in Infty) was born in Brno during studies of Vietnamese student Hàn Thê´ Thành (1990–2001). -
Arxiv:2005.03089V1 [Cs.LO] 5 May 2020 Abstract ??? Accepted: / ??? Received: Optrsine a Erlangen-N¨Urnberg E.G
Noname manuscript No. (will be inserted by the editor) Experiences from Exporting Major Proof Assistant Libraries Michael Kohlhase · Florian Rabe Received: ??? / Accepted: ??? Abstract The interoperability of proof assistants and the integration of their li- braries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc/MMT. Each translation presented tremendous theoretical, technical, and social chal- lenges, some universal and some system-specific, some solvable and some still open. In this paper, we survey these challenges and compare and evaluate the solutions we chose. We believe similar library translations will be an essential part of any future system interoperability solution and our experiences will prove valuable to others undertaking such efforts. 1 Introduction Motivation The hugely influential QED manifesto [2] of 1994 urged the automated reasoning community to work towards a universal, computer-based database of all mathematical knowledge, strictly formalized in logic and supported by proofs that can be checked mechanically. The QED database was intended as a communal re- source that would guide research and allow the evaluation of automated reasoning tools and systems. This database was never realized, but the interoperability of proof assistants and the integration of their libraries has remained a highly valued but elusive goal. This is despite the large and growing need for more integrated and easily reusable libraries of formalizations. For example, the Flyspeck project [20] build a formal proof of the Kepler conjecture in HOL Light. -
Languages of Mathematics1
Domain of Math Search Digital Libraries Document Similarity Conclusions Languages of Mathematics1 Petr Sojka Faculty of Informatics, Masaryk University, Brno, CZ, EU Dec 5th, 2009 1Supported by NPV II and AS CR grant #1ET200190513 Languages of Mathematics Faculty of Informatics, Masaryk University, Brno, CZ, EU Domain of Math Search Digital Libraries Document Similarity Conclusions Conveying the message Languages of mathematics different points of view random walking in mathematics of languages Languages of Mathematics Faculty of Informatics, Masaryk University, Brno, CZ, EU Domain of Math Search Digital Libraries Document Similarity Conclusions Conveying the message Languages of Mathematics Faculty of Informatics, Masaryk University, Brno, CZ, EU Domain of Math Search Digital Libraries Document Similarity Conclusions Conveying the message Q: Is elephant a wall (belly), hand fan (ear), solid pipe (tusk), pillar (leg), rope (tail) or tree branch (trunk)? Languages of Mathematics Faculty of Informatics, Masaryk University, Brno, CZ, EU Domain of Math Search Digital Libraries Document Similarity Conclusions Conveying the message E = mc2 ? ! E = mc2 E = mc2 Znacˇkova´nı´ Na´vrh Sazba Korektury Prˇedloha Tisk Distribuce Markup Design Typesetting Proofreading Preprint Print Distribution Languages of Mathematics Faculty of Informatics, Masaryk University, Brno, CZ, EU Domain of Math Search Digital Libraries Document Similarity Conclusions Conveying the message Levels of text/math understanding/processing 1.0 lexical { words, strings of characters/TeX's $ $. 2.0 syntactical { phrases, parsed formulas (trees/MathML). 3.0 semantical { meaning of parsed phrases (cloud tags/ontologies/OpenMath). Problem of message (content+form) representation (of math when transporting the message over the web). Google around 1.5 now (no semantics, but for the purpose are people happy). -
Experiences from Exporting Major Proof Assistant Libraries
Noname manuscript No. (will be inserted by the editor) Experiences from Exporting Major Proof Assistant Libraries Michael Kohlhase (corresponding author) · Florian Rabe Received: ??? / Accepted: ??? Abstract The interoperability of proof assistants and the integration of their li- braries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc/MMT. Each translation presented tremendous theoretical, technical, and social chal- lenges, some universal and some system-specific, some solvable and some still open. In this paper, we survey these challenges and compare and evaluate the solutions we chose. We believe similar library translations will be an essential part of any future system interoperability solution and our experiences will prove valuable to others undertaking such efforts. 1 Introduction Motivation The hugely influential QED manifesto [2] of 1994 urged the automated reasoning community to work towards a universal, computer-based database of all mathematical knowledge, strictly formalized in logic and supported by proofs that can be checked mechanically. The QED database was intended as a communal re- source that would guide research and allow the evaluation of automated reasoning tools and systems. This database was never realized, but the interoperability of proof assistants and the integration of their libraries has remained a highly valued but elusive goal. This is despite the large and growing need for more integrated and easily reusable libraries of formalizations. For example, the Flyspeck project [20] build a formal proof of the Kepler conjecture in HOL Light. -
Towards a Mizar Mathematical Library in Omdoc Format
STUDIES IN LOGIC, GRAMMAR AND RHETORIC 10 (23) 2007 Towards a Mizar Mathematical Library in OMDoc Format Grzegorz Bancereki and Michael Kohlhaseii i Technical University Bialystok, [email protected] ii Jacobs University Bremen, [email protected] Abstract. Mizar is one of largest libraries of formalized mathematics. The language of the library is highly optimized for authoring by humans. Like in natural languages, the meaning of an expression is influenced by its (mathematical) context in a way that is natural to humans, but hard to specify for machine manipulation. From this point of view, it may be considered as locked up in an arcane file format. Indeed, the Mizar system itself is currently the only system that can reliably operate on the Mizar library. This paper presents an experiment of using the Mizar system to trans- form the Mizar library into the OMDoc format (Open Mathematical Documents), an XML-based representation format for mathematical knowl- edge that is geared towards making formula structure and context depen- dencies explicit. We expect the result of this experiment: an OMDoc version of the Mizar library to enhance system support for formal mathematical libraries. 1 Introduction In the last years we have seen the birth of a new research area: “Mathemat- ical Knowledge Management” (MKM), which is concerned with representation formalisms for mathematical knowledge, such as MathML [2], OpenMath [9] or OMDoc [16], mathematical content management systems [12, 1, 5], search en- gines [24, 23, 19, 15, 10], as well as publication and education systems [18,20] for mathematics. The perceived interest in the domain of general knowledge manage- ment tools applied to mathematics is that mathematics is a very well-structured and well-conceptualized subject. -
Msetool: Management Strategy Evaluation Toolkit
Package ‘MSEtool’ August 13, 2021 Title Management Strategy Evaluation Toolkit Version 3.2.0 Description Development, simulation testing, and implementation of management procedures for fisheries (see Carruthers & Hordyk (2018) <doi:10.1111/2041-210X.13081>). License GPL-3 Encoding UTF-8 LazyData true RoxygenNote 7.1.1 Depends R (>= 3.5.0), snowfall Imports abind, dplyr, methods, grDevices, ggplot2, parallel, Rcpp, stats, utils Suggests boot, broom, covr, crayon, devtools, DT, fmsb, ggrepel, gridExtra, kableExtra, knitr, MASS, mvtnorm, openxlsx, purrr, r4ss, readxl, reshape2, rfishbase, rmarkdown, shiny, testthat, tidyr LinkingTo Rcpp, RcppArmadillo BugReports https://github.com/Blue-Matter/MSEtool/issues NeedsCompilation yes Author Adrian Hordyk [aut, cre], Quang Huynh [aut], Tom Carruthers [aut], Chris Grandin [ctb] (iSCAM functions) Maintainer Adrian Hordyk <[email protected]> Repository CRAN Date/Publication 2021-08-13 10:10:17 UTC 1 2 R topics documented: R topics documented: Albacore . .5 Albacore_TwoFleet . .6 applyMMP . .7 applyMP . .7 Atlantic_mackerel . .8 avail.............................................9 boxplot.Data . 10 calcRefYield . 10 CALsimp . 11 Can ............................................. 12 CheckDuplicate . 13 CheckMPs . 13 checkMSE . 14 Choose . 15 CombineMMP . 16 Converge . 16 Cos_thresh_tab . 18 cparscheck . 18 Cplot . 19 Data-class . 20 Data2csv . 24 DataDescription . 24 DataDir . 25 DataInit . 25 DataSlots . 26 Data_xl . 27 DecE_Dom . 28 DFO_bar . 29 DFO_hist . 30 DFO_plot . 30 DFO_plot2 . 31 DFO_proj . 31 DFO_quant . 32 DFO_report . 33 DFO_spider . 33 DFO_tab . 34 DFO_tab_formatted . 34 DLMDataDir . 35 dnormal . 36 Dom............................................. 36 expandHerm . 37 Fease . 38 Fleet-class . 39 FleetDescription . 41 FMSYref . 42 Generic_Obs . 43 R topics documented: 3 getclass . 44 getDataList . 45 getfirstlev . 45 getmov2 . 46 getsel . 47 Hist-class . 47 hist2 . 49 HistDescription . 50 Imp-class . 50 ImpDescription . -
Omdoc - an Open Markup Format for Mathematical Documents [Version 1.2]
Michael Kohlhase OMDoc - An Open Markup Format for Mathematical Documents [version 1.2] Foreword by Alan Bundy fyA Springer Table of Contents Part I Setting the Stage for Open Mathematical Documents 1 Document Markup for the Web 3 1.1 Structure vs. Appearance in Markup 3 1.2 Markup for the World Wide Web 5 1.3 XML, the extensible Markup Language 6 2 Markup for Mathematical Knowledge 13 2.1 Mathematical Objects and Formulae 14 2.2 Mathematical Texts and Statements 20 2.3 Large-Scale Structure and Context in Mathematics 21 3 Open Mathematical Documents 25 3.1 A Brief History of the OMDoc Format 25 3.2 Three Levels of Markup 28 3.3 Situating the OMDoc Format 29 , 3.4 The Future: An Active Web of (Mathematical) Knowledge . 31 Part II An OMDoc Primer 4 Textbooks and Articles 35 4.1 Minimal OMDoc Markup 36 4.2 Structure and Statements 39 4.3 Marking up the Formulae 41 4.4 Full Formalization 45 5 OpenMath Content Dictionaries 49 6 Structured and Parametrized Theories 55 7 A Development Graph for Elementary Algebra 59 XVI Table of Contents 8 Courseware and the Narrative/Content Distinction 65 8.1 A Knowledge-Centered View 67 8.2 A Narrative-Structured View 71 8.3 Choreographing Narrative and Content OMDoc 73 8.4 Summary 74 9 Communication Between Systems 75 Part III The OMDoc Document Format 10 OMDoc as a Modular Format 83 10.1 The OMDoc Namespaces 83 10.2 Common Attributes in OMDoc 85 11 Document Infrastructure 89 11.1 The Document Root 90 11.2 Metadata 91 11.3 Document Comments 92 11.4 Document Structure 93 11.5 Sharing Document Parts 94 12 Metadata 97 12.1 The Dublin Core Elements (Module DC) 98 12.2 Roles in Dublin Core Elements 101 12.3 Managing Rights 102 12.4 Inheritance of Metadata 104 13 Mathematical Objects 107 13.1 OpenMath 107 13.2 Content MathML 114 13.3 Representing Types in Content-MATHML and OPENMATH. -
An Open Markup Format for Mathematical Documents
Michael Kohlhase Computer Science Jacobs University Bremen [email protected] An Open Markup Format for Mathematical Documents OMDoc [Version 1.3] August 23, 2010 This Document is the OMDoc 1.3 Specification. Source Information revision 8755, last change August 23, 2010 by kohlhase https://svn.omdoc.org/repos/omdoc/branches/omdoc-1.3/doc/spec/spec.tex This work is licensed by the Creative Commons Share-Alike license http://creativecommons.org/licenses/by-sa/2.5/: the contents of this specification or fragments thereof may be copied and distributed freely, as long as they are attributed to the original author and source, derivative works (i.e. modified versions of the material) may be published as long as they are also licenced under the Creative Commons Share-Alike license. Springer spec.tex 8685 2010-08-23 08:55:17Z kohlhase To Andrea | my wife, collaborator, and best friend | for all her support dedication.tex 8685 2010-08-23 08:55:17Z kohlhase VII Abstract The OMDoc (Open Mathematical Documents) format is a content markup scheme for (collections of) mathematical documents including articles, text- books, interactive books, and courses. OMDoc also serves as the content language for agent communication of mathematical services on a mathemati- cal software bus. This document describes version 1.3 of the OMDoc format, the final and mature release of OMDoc1. The format features a modularized language design, OpenMath and MathML for representing mathematical objects, and has been employed and validated in various applications. This book contains the rigorous specification of the OMDoc document format, an OMDoc primer with paradigmatic examples for many kinds of mathematical documents. -
Wiki Authoring and Semantics of Mathematical Document Structure
Wiki Authoring and Semantics of Mathematical Document Structure Hiraku Kuroda∗ and Takao Namiki Department of Mathematics, Hokkaido University, 060-0810 Sapporo, Japan Abstract We are developing a CMS including document authoring feature based on wiki to publish struc- tural mathematical documents on the Web. Using this system, users can write documents including mathematical expressions written in LATEX notation and explicitly stated characteristic structures of mathematical articles such as definitions, theorems, and proofs. Documents input to the system is published on the Web as not only XHTML files to be browsed but also XML files complying with NLM-DTD, which is used to exchange articles electronically. Not only single wiki page document, users can build a document which consist of more than one pages and is described its structure se- mantically by the system. In order to do this, we also propose an application of OAI-ORE and RDF vocabularies to describe structures of documents consisting of several resources. 1 Introduction Today, many documents are published on the Web. The term “documents” here includes articles of news or blog, wiki pages, journal articles, and any other web pages. These documents are published as HTML or XHTML to be browsed, or as PDF or PS file to be printed out. Sometimes one document is published as several formats. Some documents consist of several resources. One of examples is a document including a graphic image. Here, we assume that body text of the document is written in a HTML file and the image is a JPG file. On the Web, each of them is independent resource and given unique URI. -
A Semantic Wiki for Mathematical Knowledge Management
SWiM – A Semantic Wiki for Mathematical Knowledge Management Christoph Lange Computer Science, Jacobs University Bremen, [email protected] Abstract. SWiM is a semantic wiki for collaboratively building, edit- ing and browsing mathematical knowledge represented in the domain- specific structural semantic markup language OMDoc. It motivates users to contribute to collections of mathematical knowledge by instantly shar- ing the benefits of knowledge-powered services with them. SWiM is cur- rently being used for authoring content dictionaries, i. e. collections of uniquely identified mathematical symbols, and prepared for managing a large-scale proof formalisation effort. 1 Research Background and Application Context: Mathematical Knowledge Management A great deal of scientific work consists of collaboratively authoring documents— taking down first hypotheses, commenting on results of experiments, circulating informal drafts inside a working group, and structuring, annotating, or reor- ganising existing items of knowledge, finally leading to the publication of a well-structured article or book. Here, we particularly focus on the domain of mathematics and on tools that support collaborative authoring by utilising the knowledge contained in the documents. In recent years, several semantic markup languages have been developed to represent the clearly defined and hi- erarchical structures of mathematics. The XML languages MathML [9], Open- Math [11], and OMDoc [3] particularly aim at exchanging mathematical knowl- edge on the web. OMDoc, employing Content MathML or OpenMath repre- senting the functional structure of mathematical formulæ—as opposed to their visual appearance—and adding support for mathematical statements (like sym- arXiv:1003.5196v1 [cs.DL] 26 Mar 2010 bol declarations or axioms) and theories, has many applications in publishing, education, research, and data exchange [3, chap. -
The Planetary System: Active Documents and a Web3.0 for Math
The Planetary System: Active Documents and a Web3.0 for Math. Michael Kohlhase http://kwarc.info/kohlhase Center for Advanced Systems Engineering Jacobs University Bremen, Germany May 30. 2012, NIST Kohlhase: Planetary: Web3.0 for Math 1 NIST, May 2012 Introduction Kohlhase: Planetary: Web3.0 for Math 2 NIST, May 2012 The way we do math will change dramatically Publication Application Compute/ Experiment Prove The Creativity Spiral Mathematical Creativity Visualize Specify/ Formalize Spiral [Buchberger 1995] Conjecture Com− Teaching munication • Every step will be supported by mathematical software systems • Towards an infrastructure for web-based mathematics! Kohlhase: Planetary: Web3.0 for Math 3 NIST, May 2012 • Recent Improvements of the Math-on-the Web Environment: • MathML3 is out • MathML enabled in WebKit (in Safari 5.1, on the road for Chrome, Konquerer) • MathML is in HTML5 (without Namespaces though) • MathJax has reached 1.0 (Display MathML by JavaScript in many Browsers) • Recent Improvements of the Semantic Web: • RDF can be embedded into XML via RDFa (linked data export) • RDF querying via SPARQL (modulo OWL Ontologies) (semantic search) • OMDoc as a mathematical Ontology format (modularity, documentation, full Math) • Overview over the talk: • MathML3 brings more semantics (strict content Math, elementary Math) • integrating MathML/LATEX into the Web 2.0 • ALATEX-based Semantic Web for Mathematics eMath 3.0: The Time is Ripe • Background: • Web 2.0 is the term used for the \social Web" (tagging, blogs, wikis, facebook, . .) • The \Semantic Web" is a version of the Web, where humans & machines cooperate • Web 3.0 is the term used for the \social Semantic Web".