article

Ontologies and languages for representing mathematical knowledge on the Semantic Web

Author:

Christoph LangeAuthors Info & Claims

Semantic Web, Volume 4, Issue 2

Pages 119 - 158

Published: 01 April 2013 Publication History

Abstract

Mathematics is a ubiquitous foundation of science, technology, and engineering. Specific areas of mathematics, such as numeric and symbolic computation or logics, enjoy considerable software support. Working mathematicians have recently started to adopt Web 2.0 environments, such as blogs and wikis, but these systems lack machine support for knowledge organization and reuse, and they are disconnected from tools such as computer algebra systems or interactive proof assistants. We argue that such scenarios will benefit from Semantic Web technology.Conversely, mathematics is still underrepresented on the Web of [Linked] Data. There are mathematics-related Linked Data, for example statistical government data or scientific publication databases, but their mathematical semantics has not yet been modeled. We argue that the services for the Web of Data will benefit from a deeper representation of mathematical knowledge.Mathematical knowledge comprises structures given in a logical language --formulae, statements e.g. axioms, and theo-ries --, a mixture of rigorous natural language and symbolic notation in documents, application-specific metadata, and discussions about conceptualizations, formalizations, proofs, and counter-examples. Our review of vocabularies for representing these structures covers ontologies for mathematical problems, proofs, interlinked scientific publications, scientific discourse, as well as mathematical metadata vocabularies and domain knowledge from pure and applied mathematics.Many fields of mathematics have not yet been implemented as proper Semantic Web ontologies; however, we show that MathML and OpenMath, the standard XML-based exchange languages for mathematical knowledge, can be fully integrated with RDF representations in order to contribute existing mathematical knowledge to the Web of Data.We conclude with a roadmap for getting the mathematical Web of Data started: what datasets to publish, how to interlink them, and how to take advantage of these new connections.

References

[1]

acm.rkbexplorer.com, Advanced Knowledge Technologies (AKT), URL: http://acm.rkbexplorer.com.

[2]

ActiveMath, ACTIVEMATH, URL: http://www.activemath. org.

[3]

B. Adida, M. Birbeck, S. McCarron and I. Herman, RDFa Core 1.1. Syntax and processing rules for embedding RDF through attributes. W3C Working Draft, World Wide Web Consortium (W3C), March 2011, URL: http://www.w3.org/TR/2011/WD-rdfa-core-20110331/.

[4]

W. Akhtar, J. Kopecky, T. Krennwallner and A. Polleres, XSPARQL: Traveling between the XML and RDF worlds - And avoiding the XSLT pilgrimage, in Bechhofer et al. [26], pp. 432-447.

[5]

J. Alama, K. Brink, L. Mamane and J. Urban, Large formal wikis: Issues and solutions, in Davenport et al. [65], pp. 133- 148.

[6]

K. Alexander, R. Cyganiak, M. Hausenblas and J. Zhao, Describing linked datasets with the VoID vocabulary. W3C Interest Group Note. World Wide Web Consortium (W3C), March 2011, URL: http://www.w3.org/TR/2011/NOTE-void-20110303/.

[7]

American Mathematical Society, MathSciNet Mathematical Reviews on the Net, URL: http://www.ams.org/mathscinet/.

[8]

O. Andersson, R. Berjon, E. Dahlström, A. Emmons, J. Ferraiolo, A. Grasso, V. Hardy, S. Hayman, D. Jackson, C. Lilley, C. McCormack, A. Neumann, C. Northway, A. Quint, N. Ramani, D. Schepers and A. Shellshear. Scalable Vector Graphics (SVG) Tiny 1.2 specification. W3C Recommendation, World Wide Web Consortium (W3C), December 2008, URL: http://www.w3.org/TR/2008/REC-SVGTiny12-20081222/.

[9]

A. Ankolekar, M. Krötzsch, T. Tran and D. Vrande¿ic, The two cultures: Mashing up Web 2.0 and the Semantic Web, Web Semantics 6(1)(2008), 70-75.

Digital Library

[10]

I. Antoniou, C. Bratsas, A. Dimou, P. Ion, C. Lange and W. Sperber, Mathematics subject classification linked wiki. URL: http://sci-class.math.auth.gr/MSCLW/.

[11]

L. Aroyo, G. Antoniou, E. Hyvönen, A. ten Teije, H. Stuckenschmidt, L. Cabral and T. Tudorache, eds, The Semantic Web: Research and Applications (Part I), Lecture Notes in Computer Science, Vol. 6088, Springer Verlag, Berlin/Heidelberg, 2010.

[12]

ArXiv, arxiv.org e-Print archive, URL: http://www.arxiv.org.

[13]

A. Asperti, B. Buchberger and J.H. Davenport, eds, in: Proc. of Mathematical Knowledge Management, MKM'03, Lecture Notes in Computer Science, Vol. 2594, Springer Verlag, Berlin/Heidelberg, 2003.

[14]

A. Asperti, H. Geuvers and R. Natarajan, Social processes, program verification and all that, Mathematical Structures in Computer Science 19(5) (October 2009), 877-896.

Digital Library

[15]

A. Asperti, L. Padovani, C. Sacerdoti Coen, F. Guidi and I. Schena, Mathematical knowledge management in HELM, Annals of Mathematics and Artificial Intelligence, Special Issue on Mathematical Knowledge Management, Kluwer Academic Publishers 38(1-3) (May 2003), 27-46.

[16]

A. Asperti and C. Sacerdoti Coen, Some considerations on the usability of interactive provers, in Autexier et al. [19], pp. 147-156.

[17]

A. Asperti, C. Sacerdoti Coen, E. Tassi and S. Zacchiroli, User interaction with the Matita proof assistant, Journal of Automated Reasoning 39(2) (2007), 109-139.

Digital Library

[18]

R. Ausbrooks, S. Buswell, D. Carlisle, G. Chavchanidze, S. Dalmas, S. Devitt, A. Diaz, S. Dooley, R. Hunter, P. Ion, M. Kohlhase, A. Lazrek, P. Libbrecht, B. Miller, R. Miner, M. Sargent, B. Smith, N. Soiffer, R. Sutor and S. Watt, Mathematical Markup Language (MathML) version 3.0. W3C Recommendation, World Wide Web Consortium (W3C), 2010, URL: http://www.w3.org/TR/MathML3.

[19]

S. Autexier, J. Calmet, D. Delahaye, P.D.F. Ion, L. Rideau, R. Rioboo and A.P. Sexton, eds, in: Intelligent Computer Mathematics, Lecture Notes in Artificial Intelligence, Vol. 6167, Springer Verlag, Berlin/Heidelberg, 2010, ISBN 3642141277.

[20]

S. Autexier, D. Hutter, T. Mossakowski and A. Schairer, Maya: Maintaining structured documents, In OMDOC - An Open Markup Format for Mathematical Documents [Version 1.2] Kohlhase [118], Chapter 26.12, URL: http://omdoc.org/pubs/omdoc1.2.pdf.

[21]

J. Baez, Math blogs, Notices of the AMS (March 2010), 333, URL: http://www.ams.org/notices/201003/rtx100300333p. pdf.

[22]

G. Bancerek, Information retrieval and rendering with MML Query, in Borwein and Farmer [38], pp. 266-279.

[23]

R.S. Baraka, A framework for publishing and discovering mathematical web services, PhD thesis, Johannes Kepler Universität Linz, 2006, URL: http://www.risc.uni-linz.ac.at/publications/download/risc_2945/06-04.pdf.

[24]

M.J. Barany, '[b]ut this is blog maths and we're free to make up conventions as we go along: Polymath1 and the modalities of 'massively collaborative mathematics', in: Proc. of the 6th International Symposium on Wikis and Open Collaboration (WikiSym), P. Ayers and F. Ortega, eds, ACMPress, 2010, URL: http://www.wikisym.org/ws2010/Proceedings/.

[25]

S. Bechhofer, J. Ainsworth, J. Bhagat, I. Buchan, P. Couch, D. Cruickshank, D. De Roure, M. Delderfield, I. Dunlop, M. Gamble, C. Goble, D. Michaelides, P. Missier, S. Owen, D. Newman and S. Sufi, Why linked data is not enough for scientists, in: Proc. of 6th IEEE e-Science Conference, 2010, pp. 300-307.

Digital Library

[26]

S. Bechhofer, M. Hauswirth, J. Hoffmann and M. Koubarakis, eds, in: The Semantic Web: Research and Applications, Lecture Notes in Computer Science, Vol. 5021, Springer Verlag, Berlin/Heidelberg, 2008.

[27]

D. Beckett, RDF/XML syntax specification (revised). W3C Recommendation, World Wide Web Consortium (W3C), February 2004, URL: http://www.w3.org/TR/2004/REC-rdfsyntax-grammar-20040210/.

[28]

A. Berglund, S. Boag, D. Chamberlin, M.F. Fernández, M. Kay, J. Robie and J. Simeon, XML Path Language (XPath) 2.0. W3C Recommendation, World Wide Web Consortium (W3C), 2007, URL: http://www.w3.org/TR/2007/REC-xpath20-20070123/.

[29]

T. Berners-Lee, Cwm, 2009, URL: http://www.w3.org/2000/10/swap/doc/cwm.html.

[30]

T. Berners-Lee, Design issues: Linked data, Technical report, World Wide Web Consortium (W3C), 2006, URL: http://www.w3.org/DesignIssues/LinkedData.html.

[31]

T. Berners-Lee, Notation 3 (N3) - A readable RDF syntax, Technical report,WorldWideWeb Consortium (W3C), 2006, URL: http://www.w3.org/DesignIssues/Notation3.html.

[32]

T. Berners-Lee, R.T. Fielding and L. Masinter, Uniform resource identifier (URI): Generic syntax. RFC 3986, Internet Engineering Task Force (IETF), 2005, URL: http://www.ietf. org/rfc/rfc3986.txt.

[33]

D. Berrueta and J. Phipps, Best practice recipes for publishing RDF vocabularies. W3C Working Group Note, World Wide Web Consortium (W3C), August 2008, URL: http://www.w3. org/TR/2008/NOTE-swbp-vocab-pub-20080828/.

[34]

D. Berrueta, D. Brickley, S. Decker, S. Fernández, C. Görn, A. Harth, T. Heath, K. Idehen, K. Kjernsmo, A. Miles, A. Passant, A. Polleres and L. Polo, SIOC core ontology specification, March 2010, URL: http://rdfs.org/sioc/spec/.

[35]

C. Bizer, S. Auer and G.A. Grimnes, eds, in: Proc. of Scripting and Development for the Semantic Web (SFSW), CEUR Workshop Proceedings, Vol. 449, Aachen, May 2009, URL: http://CEUR-WS.org/Vol-449/.

[36]

U. Bojars and J.G. Breslin, SIOC core ontology specification. W3C Member Submission, World Wide Web Consortium (W3C), June 2007, URL: http://www.w3.org/Submission/2007/SUBM-sioc-spec-20070612/.

[37]

U. Bojars, J.G. Breslin, V. Peristeras, G. Tummarello, and S. Decker, Interlinking the social web with semantics. IEEE Intelligent Systems 23(3) (2008), 29-40.

Digital Library

[38]

J. Borwein and W.M. Farmer, eds, Mathematical Knowledge Management (MKM), Lecture Notes in Artificial Intelligence, Vol. 4108, Springer Verlag, Berlin/Heidelberg, 2006.

[39]

S. Bradner, Key words for use in RFCs to indicate requirement levels. RFC 2119, Internet Engineering Task Force (IETF), 1997, URL: http://www.ietf.org/rfc/rfc2119.txt.

[40]

D. Brickley, V.K. Chaudhri, H. Halpin and D.L. McGuinness, eds, in: Proc. of the AAAI Spring Symposium on Linked Data Meets Artificial Intelligence, 2010.

[41]

D. Brickley and L. Miller, FOAF vocabulary specification 0.98, Technical report, ILRT Bristol, URL: http://xmlns.com/foaf/spec/20100809.html.

[42]

M. Bröcheler, A mathematical semantic web, Bachelor's thesis, Computer Science, Jacobs University, Bremen, 2007, URL: http://www.eecs.jacobs-university.de/archive/bsc-2007/broecheler.pdf.

[43]

S. Buckingham Shum, T. Clark, A. de Waard, T. Groza, S. Handschuh and À. Sándor, Scientific discourse on the semantic web: A survey of models and enabling technologies. Accepted for publication in the Semantic Web Journal, 2011, URL: http://www.semantic-webjournal. net/content/scientific-discourse-semantic-websurvey-models-and-enabling-technologies.

[44]

L. Burnard and S. Bauman, TEI P5: Guidelines for electronic text encoding and interchange, Technical report, TEI Consor tium, URL: http://www.tei-c.org/release/doc/tei-p5-doc/en/html/.

[45]

S. Buswell, RDF/XML test cases for RDF logic, web ontology and maths content. Deliverable 5.3b, Semantic Web Advanced Development for Europe (SWAD-Europe), 2001, URL: http://www.w3.org/2001/sw/Europe/reports/xml_test_ cases/wp53.html.

[46]

S. Buswell, O. Caprotti, D.P. Carlisle, M.C. Dewar, M. Gaëtano and M. Kohlhase, The Open Math standard, version 2.0, Technical report, The OpenMath Society, 2004, URL: http://www.openmath.org/standard/om20.

[47]

O. Caprotti, M. Dewar and D. Turi, Mathematical service matching using description logic and OWL, Technical report, The MONET Consortium, 2004, URL: http://monet.nag.co. uk/monet/publicdocs/monet_onts.pdf.

[48]

O. Caprotti, M. Dewar and D. Turi, Mathematical service matching using description logic and OWL, in: Proc. of Mathematical Knowledge Management, MKM'04, A. Asperti, G. Bancerek and A. Trybulec, eds, Lecture Notes in Artificial Intelligence, Vol. 3119, Springer Verlag, Berlin/Heidelberg, 2004, pp. 73-87.

[49]

J. Carette, L. Dixon, C. Sacerdoti Coen and S.M. Watt, eds, Proc. of MKM/Calculemus, Lecture Notes in Artificial Intelligence, Vol. 5625, Springer Verlag, Berlin/Heidelberg, July 2009, ISBN 9783642026133.

[50]

P. Ciccarese and T. Groza, Ontology of rhetorical blocks (ORB). W3C Interest Group Note, World Wide Web Consortium (W3C), October 2011, URL: http://www.w3.org/TR/2011/NOTE-hcls-orb-20111020/.

[51]

T. Clark, J.S. Luciano, M. Scott Marshall, E. Prud'hommeaux and S. Stephens, eds, in: Proc. of Semantic Web Applications in Scientific Discourse (SWASD), CEUR Workshop Proceedings, Vol. 523, Aachen, 2009, URL: http://CEUR-WS.org/Vol-523/.

[52]

Connexions - XML languages, URL: http://cnx.org/help/authoring/xml.

[53]

CNX, Connexions, URL: http://cnx.org.

[54]

M. Codescu, F. Horozal, M. Kohlhase, T. Mossakowski and F. Rabe, Project Abstract: Logic Atlas and Integrator (LATIN), in: Davenport et al.[65], pages 289-291.

[55]

A.M. Cohen, H. Cuypers and R. Verrijzer, Mathematical context in interactive documents, Mathematics in Computer Science 3(3) (2010), 331-347.

[56]

S. Coppins and B. Hendricks, Content MathML (Connexions web site), URL: http://cnx.org/content/m9008/2.15/.

[57]

O. Corby, L. Kefi-Khelif, H. Cherfi, F. Gandon and K. Khelif, Querying the semantic web of data using SPARQL, RDF and XML, Technical Report 6847, INRIA Sophia Antipolis, February 2009, URL: http://hal.inria.fr/docs/00/36/23/81/PDF/RR-6847.pdf.

[58]

S. Corlosquet, R. Delbru, T. Clark, A. Polleres and S. Decker, Produce and consume linked data with Drupal! in: Proc. of the Semantic Web - ISWC 2009, A. Bernstein, D.R. Karger, T. Heath, L. Feigenbaum, D. Maynard, E. Motta and K. Thirunarayan, eds, Lecture Notes in Computer Science, Vol. 5823, Springer Verlag, Berlin/Heidelberg, October 2009, pp. 763-778.

[59]

H. Cuypers, A.M. Cohen, J.W. Knopper, R. Verrijzer and M. Spanbroek, MathDox, a system for interactive mathematics, in: Proc. of the World Conference on Educational Multimedia, Hypermedia & Telecommunications 2008 (ED-MEDIA'08), AACE, June 2008, pp. 5177-5182, URL: http://go.editlib.org/p/29092.

[60]

D2R server publishing the DBLP bibliography database, URL: http://dblp.l3s.de/d2r/.

[61]

W. Dalitz, W. Sperber and W. Neun, Math-Net, a model for information and communication systems in sciences, in: Proc. of EUNIS, J. von Knop, P. Schirmbacher and V. Mahnic, eds, Lecture Notes in Informatics, Vol. 13, GI, 2001, pp. 140-145, ISBN 3-88579-339-3.

[62]

R. Daniel Jr., Harvesting RDF statements from XLinks. W3C Note, World Wide Web Consortium (W3C), September 2000, URL: http://www.w3.org/TR/2000/NOTE-xlink2rdf- 20000929/.

[63]

J. Davenport, A small OpenMath type system, Bulletin of the ACM Special Interest Group on Symbolic and Automated Mathematics (SIGSAM) 34(2) (2000), 16-21.

[64]

J.H. Davenport and M. Kohlhase, Unifying math ontologies: A tale of two standards, in Carette et al. [49], pp. 263-278. ISBN 9783642026133, URL: http://kwarc.info/kohlhase/papers/mkm09-MMLOM3.pdf.

[65]

J. Davenport, W. Farmer, F. Rabe and J. Urban, eds, in: Intelligent Computer Mathematics, Lecture Notes in Artificial Intelligence, Vol. 6824, Springer Verlag, Berlin/Heidelberg, 2011.

[66]

C. David, M. Kohlhase, C. Lange, F. Rabe, N. Zhiltsov and V. Zholudev, Publishing math lecture notes as linked data, in: The Semantic Web: Research and Applications (Part II), L. Aroyo, G. Antoniou, E. Hyvönen, A. ten Teije, H. Stuckenschmidt, L. Cabral and T. Tudorache, eds, Lecture Notes in Computer Science, Vol. 6089, Springer Verlag, Berlin/Heidelberg, 2010, pp. 370-375.

[67]

DBpedia, URL: http://dbpedia.org.

[68]

DCMI Usage Board, DCMI metadata terms, DCMI recommendation, Dublin Core Metadata Initiative, 2008, URL: http://dublincore.org/documents/2008/01/14/dcmi-terms/.

[69]

J. De Roo, EulerSharp, URL: http://eulersharp.sourceforge. net/.

[70]

K. Dellschaft, H. Engelbrecht, J. Monte Barreto, S. Rutenbeck and S. Staab, Cicero: Tracking design rationale in collaborative ontology engineering, in Bechhofer et al. [26], pp. 782-786.

[71]

Deolalikar P vs NP paper, 2010, URL: http://michaelnielsen. org/polymath1/index.php?title=Deolalikar_P_vs_NP_ paper&oldid=3654.

[72]

Digital Library of Mathematical Functions, National Institute of Standards and Technology (NIST), 2010, URL: http://dlmf. nist.gov.

[73]

L. Ding, D. DiFranzo, A. Graves, J.R. Michaelis, X. Li, D.L. McGuinness and J. Hendler, Data-gov wiki: Towards linking government data, in Brickley et al. [40].

[74]

DITA, OASIS darwin information typing architecture (DITA), URL: http://www.oasis-open.org/committees/dita/.

[75]

L. Dodds and I. Davis, Linked Data Patterns. A pattern catalogue for modelling, publishing, and consuming Linked Data, August 2011, URL: http://patterns.dataincubator.org/book/.

[76]

P. Dolog, R. Gavrioloaie, W. Nejdl and J. Brase, Integrating adaptive hypermedia techniques and open RDF-based environments, in: Proc. of the 12th WWW Conference, ACM Press, 2003.

[77]

N. Drummond, A. Rector, R. Stevens, G. Moulton, M. Horridge, H. Wang and J. Sedenberg, Putting owl in order: Patterns for sequences in OWL. in: OWL: Experiences and Directions (OWLED), B. Cuenca Grau, P. Hitzler, C. Shankey and E. Wallace, eds, November 2006.

[78]

Dublin Core Metadata Element Set. Dublin Core metadata element set. DCMI recommendation, Dublin Core Metadata Initiative, 2008, URL: http://dublincore.org/documents/2008/01/04/dces/.

[79]

Dublin Core Metadata Initiative, URL: http://www. dublincore.org.

[80]

E. Dubmill, DOAP - Description of a project, URL: http://trac.usefulinc.com/doap.

[81]

B. DuCharme, Using RDFa with DITA and DocBook, 2009, URL: http://www.devx.com/semantic/Article/42543/.

[82]

T. Eiter, G. Ianni, T. Krennwallner and A. Polleres, Rules and ontologies for the semantic web. in: Proc. of Reasoning Web, C. Baroglio, P.A. Bonatti, J. Maluszynski, M. Marchiori, A. Polleres and S. Schaffert, eds, Lecture Notes in Computer Science, Vol. 5224, Springer, 2008, pp. 1-53, URL: http://axel.deri.ie/publications/eite-etal-2008.pdf.

[83]

H.M. Enzensberger, Drawbridge up, A K PETERS, LTD., 1999, German original: Zugbrücke außer Betrieb. Die Mathematik im Jenseits der Kultur, English translation by Tom Artin.

[84]

W.M. Farmer, MKM: A new interdisciplinary field of research, Bulletin of the ACM Special Interest Group on Symbolic and Automated Mathematics (SIGSAM) 38(2) (2004), 47-52.

[85]

W. Farmer, J. Guttman and X. Thayer, Little theories, in: Proc. of the 11th Conference on Automated Deduction, Saratoga Springs, NY, USA, D. Kapur, ed., Lecture Notes in Computer Science, Vol. 607, Springer Verlag, Berlin/Heidelberg, 1992, pp. 467-581.

[86]

A. Fiedler, P.rex: An interactive proof explainer. in: Proc. of Automated Reasoning - 1st International Joint Conference, IJCAR 2001, Siena, Italy, R. Goré, A. Leitsch and T. Nipkow, eds, Lecture Notes in Artificial Intelligence, Vol. 2083, Springer Verlag, Berlin/Heidelberg, 2001, pp. 416-420.

[87]

GAMS: Guide to available mathematical software, National Institute of Standards and Technology (NIST), URL: http://gams.nist.gov.

[88]

J. Giceva, C. Lange and F. Rabe, Integrating web services into active mathematical documents, in: Carette et al.[49], pp. 279-293, ISBN 9783642026133, URL: https://svn.omdoc. org/repos/jomdoc/doc/pubs/mkm09/jobad/jobad-server.pdf.

[89]

D. Ginev, C. Jucovschi, S. Anca, M. Grigore, C. David and M. Kohlhase, An architecture for linguistic and semantic analysis on the arXMLiv corpus. in: Applications of Semantic Technologies (AST) Workshop at Informatik 2009, 2009, URL: http://www.kwarc.info/projects/lamapun/pubs/AST09_LaMaPUn+appendix.pdf.

[90]

B. Glimm and C. Ogbuji, SPARQL 1.1 entailment regimes, W3C Working Draft, World Wide Web Consortium (W3C), October 2010, URL: http://www.w3.org/TR/2010/WD-sparql11-entailment-20101014/.

[91]

G. Goguadze, Metadata for mathematical libraries, Deliverable D3.a, MoWGLI, 2003, URL: http://mowgli.cs.unibo.it/misc/deliverables/metadata/D3a_ metadata_for_math/math_metadata.pdf.

[92]

G. Goguadze, Metadata model, Deliverable D3.b, MoWGLI, 2003, URL: http://mowgli.cs.unibo.it/misc/deliverables/metadata/D3bmetadata_model/metadata_model.pdf.

[93]

T. Gowers and M. Nielsen, Massively collaborative mathematics, Nature 461(15) (2009), 879-881.

[94]

P. Grosso, E. Maler, J. Marsh and N. Walsh, W3C XPointer framework. W3C Recommendation, World Wide Web Consortium (W3C), March 2003, URL: http://www.w3.org/TR/2003/REC-xptr-framework-20030325/.

[95]

T. Groza and S. Handschuh, SALT document ontology, Technical report, Digital Enterprise Research Institute (DERI), 2009, URL: http://salt.semanticauthoring.org/ontologies/sdo.

[96]

T. Groza and S. Handschuh, SALT annotation ontology, Technical report, Digital Enterprise Research Institute (DERI), 2009, URL: http://salt.semanticauthoring.org/ontologies/sao.

[97]

T. Groza and S. Handschuh, SALT rhetorical ontology, Technical report, Digital Enterprise Research Institute (DERI), 2009, URL: http://salt.semanticauthoring.org/ontologies/sro.

[98]

T. Groza, S. Handschuh, T. Clark, S. Buckingham Shum and A. deWaard, A short survey of discourse representation models, in: Clark et al.[51], URL: http://CEUR-WS.org/Vol-523/.

[99]

T. Groza, S. Handschuh, K. Möller and S. Decker, SALT - Semantically annotated LATEX for scientific publications, in: The Semantic Web: Research and Applications, E. Franconi, M. Kifer and W. May, eds, Lecture Notes in Computer Science, Vol. 4519, Springer Verlag, Berlin/Heidelberg, 2007, pp. 518-532, ISBN 978-3-540-72666-1.

[100]

T. Groza, K. Möller, S. Handschuh, D. Trif and S. Decker, SALT: Weaving the claim web, in: Proc. of ISWC/ASWC, K. Aberer, K.-S. Choi, N. Fridman Noy, D. Allemang, K.- I. Lee, L.J.B. Nixon, J. Golbeck, P. Mika, D. Maynard, R. Mizoguchi, G. Schreiber and P. Cudré-Mauroux, eds, Lecture Notes in Computer Science, Vol. 4825, Springer Verlag, Berlin/Heidelberg, 2007, pp. 197-210, ISBN 978-3-540- 76297-3.

[101]

F. Guidi, Searching and retrieving in content-based repositories of formal mathematical knowledge, PhD thesis, Università di Bologna, 2003.

[102]

F. Guidi and C. Sacerdoti Coen, Querying distributed digital libraries of mathematics, in: Proc. of the 11th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning (Calculemus 2003), T. Hardin and R. Rioboo, eds, Rome, Italy, September 2003, pp. 17-30. URL: http://www. calculemus.net/meetings/rome03/Proceedings/final.pdf.

[103]

F. Guidi and I. Schena, A query language for a metadata framework about mathematical resources, in Asperti et al. [13], pp. 105-118.

[104]

T.C. Hales, J. Harrison, S. McLaughlin, T. Nipkow, S. Obua and R. Zumkeller, A revision of the proof of the Kepler conjecture. Discrete and Computational Geometry (2010), 1-34.

[105]

K. Hammond, P. Horn, A. Konovalov, S. Linton, D. Roozemond, A. Al Zain and P. Trinder, Easy composition of symbolic computation software: A new lingua franca for symbolic computation, in: Proc. of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC), ACM Press, 2010, pp. 339-346.

[106]

S. Harris and A. Seaborne, SPARQL 1.1 query language. W3C Working Draft, World Wide Web Consortium (W3C), October 2010, URL: http://www.w3.org/TR/2010/WD-sparql11-query-20101014/.

[107]

O. Hartig, H. Muhleisen and J.-C. Freytag, Linked data for building a map of researchers, in Bizer et al. [35], URL: http://CEUR-WS.org/Vol-449/.

[108]

T. Heath and C. Bizer, Linked Data: Evolving the Web into a Global Data Space. Morgan & Claypool, San Rafael, CA, 2011, URL: http://linkeddatabook.com.

Digital Library

[109]

P. Heim, S. Lohmann and T. Stegemann, Interactive relationship discovery via the semantic web, in: Aroyo et al.[11], pp. 303-317.

[110]

B. Heintz, Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin. Springer Verlag, Wien, 2000.

[111]

HELM. Hypertextual Electronic Library of Mathematics, URL: http://helm.cs.unibo.it.

[112]

I. Hickson, HTML5. A vocabulary and associated APIs for HTML and XHTML. W3C Working Draft, World Wide Web Consortium (W3C), May 2011, URL: http://www.w3.org/TR/2011/WD-html5-20110525/.

[113]

IEEE Learning Technology Standards Committee, Standard for learning object metadata, Technical Report 1484.12.1, IEEE, 2002a.

[114]

IEEE Learning Technology Standards Committee, Standard for resource description framework (RDF) binding for learning object metadata data model, Technical Report 1484.12.4, IEEE, 2002.

[115]

P. Jain, P. Hitzler, P.Z. Yeh, K. Verma and A.P. Sheh, Linked data is merely more data, in Brickley et al.[40].

[116]

F. Kamareddine, M. Maarek, K. Retel and J.B. Wells, Narrative structure of mathematical texts, in: Proc. of Towards Mechanized Mathematical Assistants. MKM/Calculemus, M. Kauers, M. Kerber, R. Miner and W. Windsteiger, eds, Lecture Notes in Artificial Intelligence, Vol. 4573, Springer Verlag, Berlin/Heidelberg, 2007, pp. 296-312, ISBN 978-3-540- 73083-5.

[117]

F. Kamareddine, J.B. Wells and C. Zengler, Computerising mathematical text with MathLang, Electron. Notes Theor. Comput. Sci. 205 (2008), 5-30, ISSN 1571- 0661, URL: http://www.cedar-forest.org/forest/papers/drafts/mathlang-coq-short.pdf.

Digital Library

[118]

M. Kohlhase, OMDOC - An open markup format for mathematical documents [Version 1.2], Lecture Notes in Artificial Intelligence, Vol. 4180, Springer Verlag, Berlin/Heidelberg, August 2006, URL: http://omdoc.org/pubs/omdoc1.2.pdf.

[119]

M. Kohlhase, Towards bootstrapping the pragmatic to strict mapping in OMDoc, August 2009, URL: https://svn.omdoc. org/repos/omdoc/trunk/doc/blue/p2s-bootstrap/note.pdf.

[120]

M. Kohlhase, Using LATEX as a semantic markup format. Mathematics in Computer Science 2(2) (2008), 279-304, URL: https://svn.kwarc.info/repos/stex/doc/mcs08/stex.pdf.

[121]

M. Kohlhase, J. Corneli, C. David, D. Ginev, C. Jucovschi, A. Kohlhase, C. Lange, B. Matican, S. Mirea, and V. Zholudev, The Planetary system: Web 3.0 & active documents for STEM, Procedia Computer Science 4 (2011), 598-607, URL: https://svn.mathweb.org/repos/planetary/doc/epc11/paper.pdf, Finalist at the Executable Papers Challenge.

[122]

A. Kohlhase and M. Kohlhase, Spreadsheet interaction with frames: Exploring a mathematical practice, in Carette et al. [49], pp. 341-356, ISBN 9783642026133, URL: http://kwarc. info/kohlhase/papers/mkm09-framing.pdf.

[123]

A. Kohlhase and M. Kohlhase, Semantic knowledge management for education, Proc. of the IEEE; Special Issue on Educational Technology 96(6) (June 2008), 970-989. URL: http://kwarc.info/kohlhase/papers/semkm4ed.pdf.

[124]

M. Kohlhase, T. Mossakowski and F. Rabe, Latin: Logic atlas and integrator, URL: http://latin.omdoc.org.

[125]

M. Kohlhase and I. Sucan, A search engine for mathematical formulae, in: Proc. of Artificial Intelligence and Symbolic Computation, AISC'2006, T. Ida, J. Calmet and D. Wang, eds, Lecture Notes in Artificial Intelligence, Vol. 4120, Springer Verlag, Berlin/Heidelberg, 2006, pp. 241-253, URL: http://kwarc.info/kohlhase/papers/aisc06.pdf.

Digital Library

[126]

W. Kunz and H.W.J. Rittel, Issues as elements of information systems, Working paper 131, Institute of Urban and Regional Development, University of California, Berkeley, July 1970.

[127]

I. Lakatos, Proofs and Refutations, Cambridge University Press, 1976.

[128]

C. Lange, Enabling collaboration on semiformal mathematical knowledge by Semantic Web integration. PhD thesis, Jacobs University Bremen, 2011, number 11 in Studies on the Semantic Web., AKA Verlag and IOS Press, Heidelberg and Amsterdam, 2011.

[129]

C. Lange, Krextor - An extensible XML? RDF extraction framework, in Bizer et al.[35], URL: http://ceur-ws.org/Vol- 449/ShortPaper2.pdf.

[130]

C. Lange, Krextor - An extensible framework for contributing content math to the web of data, in Davenport et al. [65], pp. 304-306, URL: http://kwarc.info/clange/pubs/krextor-system.pdf.

[131]

C. Lange, The OMDoc ontology, 2010, URL: http://kwarc. info/projects/docOnto/omdoc.html.

[132]

C. Lange, Towards OpenMath content dictionaries as linked data, in: 23rd OpenMath Workshop, M. Kohlhase and C. Lange, eds, July 2010, URL: http://cicm2010.cnam.fr/om/.

[133]

C. Lange, wiki.openmath.org - How it works, how you can participate, in: Proc. of 22nd OpenMath Workshop J.H. Davenport, ed., July 2009, URL: http://staff.bath.ac.uk/masjhd/OM2009.html.

[134]

C. Lange, U. Bojars, T. Groza, J. Breslin and S. Handschuh, Expressing argumentative discussions in social media sites, in: Social Data on the Web (SDoW), Workshop at the 7th International Semantic Web Conference, J. Breslin, U. Bojars, A. Passant and S. Fernández, eds, CEUR Workshop Proceedings, Vol. 405, Aachen, 2008, URL: http://ceur-ws.org/Vol- 405/paper4.pdf.

[135]

C. Lange et al., Krextor - The KWARC RDF extractor, URL: http://kwarc.info/projects/krextor/.

[136]

C. Lange, T. Hastrup and S. Corlosquet, Arguing on issues with mathematical knowledge items in a semantic wiki, in: Wissens- und Erfahrungsmanagement LWA (Lernen, Wissensentdeckung und Adaptivität) Conference Proceedings, J. Baumeister and M. Atzmüller, eds, October 2008, Vol. 448.

[137]

C. Lange, P. Ion, A. Dimou, C. Bratsas, W. Sperber, M. Kohlhase and I. Antoniou, Getting mathematics towards the web of data: The case of the Mathematics Subject Classification, Submitted to Extended Semantic Web Conference 2012, URL: http://kwarc.info/clange/pubs/eswc2012- msc-skos.pdf.

[138]

C. Lange and M. Kohlhase, A mathematical approach to ontology authoring and documentation, in Carette et al. [49], pp. 389-404, ISBN 9783642026133, URL: http://kwarc.info/kohlhase/papers/mkm09-omdoc4onto.pdf.

[139]

P. Libbrecht, Cross curriculum search through the geoskills ontology, in: Proc. of the 2nd International Workshop on Search and Exchange of e-le@rning Material (SE@M), lo cated at EC-TEL-2008, D. Massart, J.-N. Colin, F. Van Asche and M. Wolpers, eds, CEUR Workshop Proceedings, Aachen, 2008, CEUR-WS.org, URL: http://ceur-ws.org/Vol-385/.

[140]

P. Libbrecht, Notations around the world: Census and exploitation, in: Autexier et al. [19], pp. 398-410, ISBN 3642141277.

[141]

P. Libbrecht and E. Melis, Methods for access and retrieval of mathematical content in ActiveMath, in: Proc. of ICMS-2006, N. Takayama and A. Iglesias, eds, Lecture Notes in Artificial Intelligence, Vol. 4151, Springer Verlag, Berlin/Heidelberg, 2006, pp. 331-342, URL: http://www.activemath.org/publications/Libbrecht-Melis-Access-and-Retrieval-ActiveMath-ICMS-2006.pdf.

[142]

W.C. Mann and M. Taboada, Rhetorical structure theory, URL: http://www.sfu.ca/rst/.

[143]

M. Marchiori, The mathematical semantic web, in: Asperti et al. [13], pp. 216-223, Keynote.

[144]

J. Marsh, D. Veillard and N. Walsh, xml:id version 1.0. W3C Recommendation, World Wide Web Consortium (W3C), September 2005, URL: http://www.w3.org/TR/2005/REC-xml-id-20050909/.

[145]

V. Mascardi, V. Cordì and P. Rosso, A comparison of upper ontologies, in: Proc. of WOA, M. Baldoni, A. Boccalatte, F. De Paoli, M. Martelli and V. Mascardi, eds, Seneca Edizioni Torino, 2007, pp. 55-64, ISBN 978-88-6122-061-4.

[146]

MathDox, MathDox - Interactive mathematics, URL: http://www.mathdox.org.

[147]

C. Masolo, S. Borgo, A. Gangemi, N. Guarino, A. Oltramari and L. Schneider, The wonderweb library of foundational ontologies, Wonder Web Deliverable 17, Laboratory for Applied Ontology - ISTC-CNR, May 2003, URL: http://wonderweb. semanticweb.org/deliverables/documents/D17.pdf.

[148]

Math-Net, An international information and communication system. International Mathematical Union (IMU), URL: http://www.math-net.org.

[149]

Mathematics Subject Classification MSC2010, 2010, URL: http://msc2010.org.

[150]

MathOverflow, URL: http://mathoverflow.net.

[151]

D.L. McGuinness, L. Ding, P. Pinheiro da Silva and C. Chang, PML 2: A modular explanation interlingua, in: Proc. of the AAAI Workshop on Explanation-Aware Computing (ExaCt), T. Roth-Berghofer, S. Schulz and D.B. Leake, eds, 2007, URL: http://www.aaai.org/Papers/Workshops/2007/WS-07- 06/WS07-06-008.pdf.

[152]

E. Melis, G. Goguadze, P. Libbrecht and C. Ullrich, Culturally adapted mathematics education with ActiveMath, AI & Society 24(3) (2009), 251-265.

Digital Library

[153]

P. Missier, S.S. Sahoo, J. Zhao, C. Goble and A. Sheth, Janus: From workflows to semantic provenance and linked open data, in: Proc. of the 3rd Provenance and Annotation Workshop, 2010.

[154]

Mizar mathematical library, URL: http://www.mizar.org/library.

[155]

Mizar system, URL: http://mizar.org/system/.

[156]

MKMNET, MKMNET (Mathematical knowledge management network), URL: http://monet.nag.co.uk/mkm/.

[157]

Monet, MONET - Mathematics on the net, web page at http://monet.nag.co.uk, URL: http://monet.nag.co.uk.

[158]

T. Mossakowski, Hets: The Heterogeneous tool set, URL: http://www.dfki.de/sks/hets.

[159]

T. Mossakowski, C. Maeder and K. Lüttich, The heterogeneous tool set, in: Proc. of the 13th International Conference on Tools and Algorithms for the Construction and Analysis of Systems TACAS-2007, O. Grumberg and M. Huth, eds, Lecture Notes in Computer Science, Vol. 4424, Springer Verlag, Berlin, Germany, 2007, pp. 519-522.

[160]

C. Müller, Adaptation of mathematical documents, PhD thesis, Jacobs University Bremen, 2010, URL: http://kwarc.info/cmueller/papers/thesis.pdf.

[161]

H. Naja-Jazzar, N. de Silva, H. Skaf-Molli, C. Rahhal and P. Molli, OntoReST: A RST-based ontology for enhancing documents content quality in collaborative writing, INFOCOMP Journal of Computer Science 8(3) (September 2009), 1-10.

[162]

M. Nilsson, M. Palmér and J. Brase, The LOM RDF binding - Principles and implementation, in: Proc. of 3rd Annual Ariadne Conference, 2003.

[163]

M. Nilsson, A. Powell, P. Johnston and A. Naeve, Expressing Dublin core metadata using the resource description framework (RDF), DCMI recommendation, Dublin Core Metadata Initiative, URL: http://dublincore.org/documents/2008/01/14/dc-rdf/.

[164]

nLab, URL: http://ncatlab.org/.

[165]

OEBPS Container Format (OCF), Recommended specification, International Digital Publishing Forum, 2006, URL: http://www.idpf.org/ocf/ocf1.0/download/ocf10.htm.

[166]

OMDoc, URL: http://omdoc.org.

[167]

T. Omitola, C.L. Koumenides, I.O. Popov, Y. Yang, M. Salvadores, M. Szomszor, T. Berners-Lee, N. Gibbins, W. Hall, M.C. Schraefel and N. Shadbolt, Put in your postcode, out comes the data: A case study, in Aroyo et al.[11], pp. 318- 332.

[168]

Open Packaging Format (OPF), version 2.0 v1.0. Recommended specification, International Digital Publishing Forum, 2007, URL: http://www.idpf.org/2007/opf/OPF_2.0_ final_spec.html.

[169]

OpenLink Software, OpenLink universal integration middleware - Virtuoso product family, URL: http://virtuoso. openlinksw.com.

[170]

OPENMATH content dictionaries, URL: http://www. openmath.org/cd/.

[171]

C.-E. Ore and Ø. Eide, TEI and cultural heritage ontologies: Exchange of information? Literary and Linguistic Computing 24(2) (2009), 161-172.

[172]

L. Padovani, GtkMathView, URL: http://helm.cs.unibo.it/mml-widget/.

[173]

L. Padovani and S. Zacchiroli, From notation to semantics: There and back again, in Borwein and Farmer[38], pp. 194- 207.

[174]

A. Passant, P. Ciccarese, J.G. Breslin and T. Clark. SWAN/ SIOC: Aligning scientific discourse representation and social semantics, in Clark et al.[51].

[175]

PlanetMath.org, PlanetMath.org - Math for the people, by the people, URL: http://planetmath.org.

[176]

J. Plümer, Erinnerungen an Prof. Dr. Schwanzl, 2004. URL: http://d-mathnet.preprints.org/research/wissinfo/NachrufRS. html.

[177]

G. Pólya, How to Solve It, Princeton University Press, 1973.

[178]

Programmable Web, Mashups, APIs, and the Web as Platform, URL: http://www.programmableweb.com.

[179]

ProofWiki, URL: http://www.proofwiki.org.

[180]

F. Rabe, Representing logics and logic translations, PhD thesis, Jacobs University Bremen, 2008, URL: http://kwarc.info/frabe/Research/phdthesis.pdf.

[181]

F. Rabe and M. Kohlhase, A scalable module system, Manuscript, submitted to Information & Computation (2011), URL: http://kwarc.info/frabe/Research/mmt.pdf.

[182]

R. Radaelli-Sanchez and Connexions, The intermediate CNXML (Connexions web site), URL: http://cnx.org/content/m9006/2.22/.

[183]

R.G. Raskin and M.J. Pan, Knowledge representation in the semantic web for earth environmental terminology (SWEET), Computers & Geosciences 31 (2005), 1119-1125.

Digital Library

[184]

K. Retel, Gradual computerisation and verification of mathematics, PhD thesis, Heriot-Watt University, Edinburgh, April 2009.

[185]

Rhaptos Trac: Collection structure redesign / inception, 2009, URL: https://trac.rhaptos.org/trac/rhaptos/wiki/CollectionStructureRedesign/Inception?version=54.

[186]

A. Robbins, Semantic MathML, 2009, URL: http://straymindcough.blogspot.com/2009/06/semanticmathml. html.

[187]

L. Sauermann and R. Cyganiak, Cool URIs for the semantic web, W3C Interest Group Note, World Wide Web Consortium (W3C), December 2008, URL: http://www.w3.org/TR/2008/NOTE-cooluris-20081203/.

[188]

I. Schena, Towards a semantic web for formal mathematics, PhD thesis, University of Bologna, March 2002, Technical Report UBLCS-2002-6.

[189]

SCIEnce, The SCIEnce project - Symbolic computation infrastructure for Europe, URL: http://www.symboliccomputation. org/.

[190]

Semantic MediaWiki, URL: http://semantic-mediawiki.org.

[191]

Semantic web for earth and environmental terminology (SWEET), NASA, 2011, URL: http://sweet.jpl.nasa.gov/.

[192]

F.-P. Servant, Linking enterprise data, in: Proc. of Linked Data on the Web (LDOW), C. Bizer, T. Heath, K. Idehen and T. Berners-Lee, eds, CEUR Workshop Proceedings, Vol. 369, Aachen, April 2008, URL: http://CEUR-WS.org/Vol-369/.

[193]

J. Sheridan and J. Tennison, Linking UK government data, in: Proc. of Linked Data on the Web (LDOW), C. Bizer, T. Heath, T. Berners-Lee and M. Hausenblas, eds, CEUR Workshop Proceedings, Vol. 628, Aachen, April 2010, URL: http://CEUR-WS.org/Vol-628/.

[194]

D. Shotton and S. Peroni, DoCo, the Document Components Ontology, May 2011, URL: http://purl.org/spar/doco.

[195]

SKOS Simple Knowledge Organization System, World Wide Web Consortium (W3C), URL: http://www.w3.org/2004/02/skos/.

[196]

N.J.A. Sloane, The on-line encyclopedia of integer sequences, Notices of the AMS 50(8) (2003), 912.

[197]

SPAR - Semantic publishing and referencing, 2011, URL: http://purl.org/spar.

[198]

Specifications for the digital talking book. Technical report, DAISY Consortium, 2005, URL: http://www.daisy.org/z3986/2005/Z3986-2005.html, ANSI/NISO Z39.86-2005. ISSN 1041-5653.

[199]

W. Sperber, Math-Net international and the Math-Net page, in: Proc. of Electronic Information and Communication in Mathematics, F. Bai and B. Wegner, eds, Lecture Notes in Computer Science, Vol. 2730, Springer, 2003, pp. 169-177.

[200]

M. Sporny, B. Adrian, N. Rixham, M. Birbeck and I. Herman, RDFa API, W3C Working Draft, World Wide Web Consortium (W3C), April 2011, URL: http://www.w3.org/TR/2011/WD-rdfa-api-20110419/.

[201]

H. Stamerjohanns, M. Kohlhase, D. Ginev, C. David and B. Miller, Transforming large collections of scientific publications to XML, Mathematics in Computer Science 3(3) (2010), 299-307, URL: http://kwarc.info/kohlhase/papers/mcs10.pdf.

[202]

P. Suresh, S.-H. Hsu, P. Akkisetty, G.V. Reklaitis and V. Venkatasubramanian, OntoMODEL: Ontological mathematical modeling knowledge management in pharmaceutical product development, 1: Conceptual framework, Industrial & Engineering Chemistry Research 49(17) (2010), 7758- 7767.

[203]

SysMO-DB SEEK, URL: http://www.sysmo-db.org/seek/.

[204]

TEI - Ontologies SIG, URL: http://www.tei-c.org/Activities/SIG/Ontologies/.

[205]

C. Tejo-Alonso, S. Fernández, D. Berrueta, L. Polo, M.J. Fernández and V. Morlán, eZaragoza, a tourist promotional mashup, in: Proc. of AI Mashup Challenge at ESWC, A. Giurca, B. Endres-Niggemeyer, C. Lange, L. Maicher and P. Hitzler, eds, June 2010, URL: http://sites.google.com/a/fhhannover. de/aimashup/home/ezaragoza.

[206]

C. Tempich, H.S. Pinto, Y. Sure and S. Staab, An argumentation ontology for DIstributed, Loosely-controlled and evolv-InG Engineering processes of oNTologies (DILIGENT), in: The Semantic Web: Research and Applications, A. Gómez-Pérez and J. Euzenat, eds, Lecture Notes in Computer Science, Vol. 3532, Springer Verlag, Berlin/Heidelberg, 2005, pp. 241-256, ISBN 3-540-26124-9.

[207]

C. Tempich, E. Simperl, M. Luczak, R. Studer and H.S. Pinto, Argumentation-based ontology engineering, IEEE Intelligent Systems 22(6) (2007), 52-59, ISSN 1541-1672.

Digital Library

[208]

The Coq proof assistant, URL: http://coq.inria.fr/.

[209]

The n-Category Café, A group blog on math, physics and philosophy, URL: http://golem.ph.utexas.edu/category/.

[210]

The polymath blog, URL: http://polymathprojects.org/.

[211]

Tricki, A repository of mathematical know-how, URL: http://www.tricki.org.

[212]

J. Trzeciak, Writing Mathematical Papers in English, Gdánskie Wydawnictwo óswiatowe, 1995.

[213]

J. Urban, Content-based encoding of mathematical and code libraries, in: ITP Workshop on Mathematical Wikis (Math-Wikis) , C. Lange and J. Urban, eds, CEUR Workshop Proceedings, Vol. 767, Aachen, 2011, pp. 49-53, URL: http://ceur-ws.org/Vol-767/paper-09.pdf.

[214]

J. Urban, J. Alama, P. Rudnicki and H. Geuvers, A wiki for Mizar: Motivation, considerations, and initial prototype, in Autexier et al.[19], pp 455-469, ISBN 3642141277.

[215]

D. Vrande¿ic, M. Krötzsch, S. Rudolph and U. Lösch, Leveraging non-lexical knowledge for the linked open data web, in: The Fifth RAFT, the Yearly Bilingual Publication on Nonchalant Research, R. Héliot and A. Zimmermann, eds, 2010, URL: http://km.aifb.kit.edu/projects/numbers/linked_ open_numbers.pdf.

[216]

D. Vrande¿ic, C. Lange, M. Hausenblas, J. Bao and L. Ding, Semantics of governmental statistics data, in: Proc. of Web-Sci'10: Extending the Frontiers of Society On-Line, Web Science Trust, 2010, URL: http://journal.webscience.org/400/.

[217]

N. Walsh, The DocBook schema, Committee specification, OASIS, August 2008, URL: http://www.docbook.org/specs/docbook-5.0-spec-cs-01.html.

[218]

N. Walsh and L. Muellner, DocBook 5.0: The Definitive Guide, O'Reilly, 2008.

[219]

E.W. Weisstein, ed., Wolfram Math World, the web's most extensive mathematics resource, URL: http://mathworld. wolfram.com.

[220]

M. Wenzel, C. Ballarin, S. Berghofer, T. Bourke, L. Dixon, F. Haftmann, G. Klein, A. Krauss, T. Nipkow, D. von Oheimb, L. Paulson and S. Skalberg, The Isabelle/Isar Reference Manual, URL: http://isabelle.in.tum.de/doc/isar-ref.pdf.

[221]

F.Wiedijk, Statistics on digital libraries of mathematics, Studies in Logic, Grammar and Rhetoric 18(31) (2009).

[222]

Wikipedia: Knowledge management, Knowledge management, December 2009, URL: http://en.wikipedia. org/w/index.php?title=Knowledge_management&oldid= 329227520.

[223]

Wikipedia: Linus' Law, Linus' Law, March 2011, URL: http://en.wikipedia.org/w/index.php?title=Linus

[224]

Wikipedia: Mathematics, Portal: Mathematics, December 2009, URL: http://en.wikipedia.org/w/index.php?title= Portal:Mathematics&oldid=329137789.

[225]

Wikipedia: Open notebook science, Open Notebook Science, July 2010, URL: http://en.wikipedia.org/w/index.php?title= Open_Notebook_Science&oldid=372235042.

[226]

Wikipedia: Pythagorean theorem, Pythagorean theorem, November 2009, URL: http://en.wikipedia.org/w/index.php? title=Pythagorean_theorem&oldid=328597679.

[227]

Wikipedia, Wikipedia, the free encyclopedia, URL: http://www.wikipedia.org.

[228]

G.T. Williams, SPARQL 1.1 Service Description, W3C Working Draft, World Wide Web Consortium (W3C), May 2011, URL: http://www.w3.org/TR/2010/WD-sparql11- service-description-20110512/.

[229]

Wolfram|Alpha widgets, URL: http://developer. wolframalpha.com/widgets/.

[230]

S. Zacchiroli, User Interaction widgets for interactive theorem proving, PhD thesis, Università di Bologna, 2007.

[231]

Zentralblatt MATH, URL: http://www.zentralblatt-math.org.

[232]

J. Zimmer, MathServe - A framework for semantic reasoning services, PhD thesis, Universität des Saarlandes, July 2008.

[233]

A. Zimmermann, Ontology recommendations for the data publishers, in: Proc. of 1st Workshop on Ontology Repositories and Editors, M. d'Aquin, A. García Castro, C. Lange and K. Viljanen, eds, CEUR Workshop Proceedings, Vol. 596, Aachen, 2010, URL: http://ceur-ws.org/Vol-596/.

[234]

C. Zinn, Understanding informal mathematical discourse, PhD thesis, Technischen Fakultät der Universität Erlangen-Nürnberg, 2004.

Cited By

D'Aquin MBunoiu RCirstea HLenczner MLieber JZamkotsian F(2023)Combining representation formalisms for reasoning upon mathematical knowledgeProceedings of the 12th Knowledge Capture Conference 202310.1145/3587259.3627549(180-187)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3587259.3627549
McDaniel MStorey V(2019)Evaluating Domain OntologiesACM Computing Surveys10.1145/332912452:4(1-44)Online publication date: 11-Sep-2019
https://dl.acm.org/doi/10.1145/3329124
Sargolzaei Javan MAkbari M(2019)SmartData 4.0The Journal of Supercomputing10.1007/s11227-018-2705-y75:7(3585-3620)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s11227-018-2705-y
Show More Cited By

Index Terms

Ontologies and languages for representing mathematical knowledge on the Semantic Web
1. Information systems
  1. Information retrieval
2. Theory of computation
  1. Logic

Index terms have been assigned to the content through auto-classification.

Recommendations

Description logic programs: combining logic programs with description logic
WWW '03: Proceedings of the 12th international conference on World Wide Web

We show how to interoperate, semantically and inferentially, between the leading Semantic Web approaches to rules (RuleML Logic Programs) and ontologies (OWL/DAML+OIL Description Logic) via analyzing their expressive intersection. To do so, we define a ...
Using SPARQL to query bioportal ontologies and metadata
ISWC'12: Proceedings of the 11th international conference on The Semantic Web - Volume Part II

BioPortal is a repository of biomedical ontologies--the largest such repository, with more than 300 ontologies to date. This set includes ontologies that were developed in OWL, OBO and other languages, as well as a large number of medical terminologies ...
Interchanging lexical resources on the Semantic Web

Lexica and terminology databases play a vital role in many NLP applications, but currently most such resources are published in application-specific formats, or with custom access interfaces, leading to the problem that much of this data is in "data ...

Comments

Information & Contributors

Information

Published In

cover image Semantic Web

Semantic Web Volume 4, Issue 2

April 2013

114 pages

ISSN:1570-0844

EISSN:2210-4968

Issue’s Table of Contents

Publisher

IOS Press

Netherlands

Publication History

Published: 01 April 2013

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

11
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 11 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

D'Aquin MBunoiu RCirstea HLenczner MLieber JZamkotsian F(2023)Combining representation formalisms for reasoning upon mathematical knowledgeProceedings of the 12th Knowledge Capture Conference 202310.1145/3587259.3627549(180-187)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3587259.3627549
McDaniel MStorey V(2019)Evaluating Domain OntologiesACM Computing Surveys10.1145/332912452:4(1-44)Online publication date: 11-Sep-2019
https://dl.acm.org/doi/10.1145/3329124
Sargolzaei Javan MAkbari M(2019)SmartData 4.0The Journal of Supercomputing10.1007/s11227-018-2705-y75:7(3585-3620)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s11227-018-2705-y
Auer SKovtun VPrinz MKasprzik AStocker MVidal M(2018)Towards a Knowledge Graph for ScienceProceedings of the 8th International Conference on Web Intelligence, Mining and Semantics10.1145/3227609.3227689(1-6)Online publication date: 25-Jun-2018
https://dl.acm.org/doi/10.1145/3227609.3227689
Li XMartinez JEckert MRubio G(2017)Uncertainty Quantification in Mathematics-Embedded Ontologies Using Stochastic Reduced Order ModelIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2017.265181929:4(912-920)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1109/TKDE.2017.2651819
Constantin APeroni SPettifer SShotton DVitali F(2016)The Document Components Ontology (DoCO)Semantic Web10.3233/SW-1501777:2(167-181)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.3233/SW-150177
Zhang LTao B(2016)A framework for ontology integration based on genetic algorithmJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/IFS-15187230:3(1643-1656)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.3233/IFS-151872
Morente-Molinera JPérez IUreña MHerrera-Viedma E(2016)Creating knowledge databases for storing and sharing people knowledge automatically using group decision making and fuzzy ontologiesInformation Sciences: an International Journal10.1016/j.ins.2015.08.051328:C(418-434)Online publication date: 20-Jan-2016
https://dl.acm.org/doi/10.1016/j.ins.2015.08.051
Morente-Molinera JPérez IUreña MHerrera-Viedma E(2015)Building and managing fuzzy ontologies with heterogeneous linguistic informationKnowledge-Based Systems10.1016/j.knosys.2015.07.03588:C(154-164)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1016/j.knosys.2015.07.035
Do CPauwels E(2013)Harnessing Mathematics for Improved Ontology AlignmentProceedings of the 4th International Joint Conference on Ambient Intelligence - Volume 830910.5555/2721999.2722022(249-254)Online publication date: 3-Dec-2013
https://dl.acm.org/doi/10.5555/2721999.2722022
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents