SWiM – A Semantic Wiki for Mathematical Knowledge Management

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Mathematical User Interfaces 2007

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SWiM – A Semantic Wiki for Mathematical Knowledge Management

  1. 1. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion SWiM – A Semantic Wiki for Mathematical Knowledge Management Workshop on Mathematical User Interfaces at MKM 2007 Christoph Lange Jacobs University, Bremen, Germany (formerly International University Bremen) KWARC – Knowledge Adaptation and Reasoning for Content June 27, 2007 Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 1
  2. 2. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Abstract SWiM is a semantic wiki for collaboratively . . . building editing browsing . . . mathematical knowledge represented in OMDoc. Target audience: mathematicians developing new theories scholars learning mathematics Outline: Current SWiM prototype: user interface and architecture Plans for further development: platform for semantic scientific services Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 2
  3. 3. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Collaborative Mathematics on the Web Current collaborative projects for maths: Wikipedia – wiki encyclopedia covering (almost) anything PlanetMath – wiki-like system dedicated to mathematics Connexions – courseware repository and content management system ... Easy to create and link knowledge items ⇒ wikis also suitable for non-public research projects Scientific services currently not available Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 3
  4. 4. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Deficiencies of Wikipedia etc. in Knowledge Management Imagine a scholar searching for: sqrt{a^2 + b^2} = c, or: x^2 + y^2 = z^2 Impossible in Wikipedia and PlanetMath, which use A presentational LTEX In principle possible (but not implemented) in Connexions, thanks to Content MathML All theorems about triangles for which a proof exists Possible in semantic wikis Neither system relates mathematical symbols to their (formal) definitions or allows for formally structured theories. Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 4
  5. 5. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Semantic Wikis Conventional wikis do not understand the knowledge graph they contain Semantic wikis address this problem: usually: 1 page = 1 real-world concept pages and links typed with terms from ontologies Examples: Semantic MediaWiki, IkeWiki, . . . Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 5
  6. 6. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Structural Semantic Markup Structural semantic markup: common way to represent scientific knowledge For OMDoc, e. g., there are services for learning assistance (→ ActiveMath) semantic search (→ MathWebSearch) publishing theory management proof verification Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 6
  7. 7. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion OMDoc in a Semantic Wiki – Meeting Users’ Needs Semantic wikis are appropriate base system for community-authored knowledge models: support stepwise formalisation workflow offer enhanced navigation and search Who is willing to author OMDoc and OpenMath? Share the benefits of structural semantics with the author Offer added-value services for the situation the author is in Instant gratification: show up-to-date links to related pages Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 7
  8. 8. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion The SWiM Prototype SWiM prototype: IkeWiki+OMDoc (http://kwarc.info/projects/swim/) editing, presentation, navigation Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 8
  9. 9. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Editing OMDoc So far, only raw OMDoc XML editing supported Minimum feedback when XML is invalid Adapting OMDoc to a wiki: Small, reusable pages: allow theory-constitutive statements to appear in their own document Simple link syntax: theory expands to theory.omdoc#theory. Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 9
  10. 10. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Presenting OMDoc Adapted OMDoc XSLTs (→ XHTML+MathML), with caching Symbols in formulae point to their <symbol> declarations. Hyperlinked source code view doc.omdoc A−tmpl.xsl A.omdoc uses symbols from compile XSL documents A, B, C XSL templates for templates defines symbols symbols from A from present− and their presentation ation elements collect documents (expres.xsl) whose symbols are used (exincl.xsl) doc−incl.xsl omdoc2pmml.xsl omdoc2pmml.xsl omdoc2pmml.xsl include −tmpl style generic templates generic templates sheets of documents forgeneric templates OMDoc to MathML for OMDoc to MathML whose symbols are used transformation to MathML for OMDoc transformation transformation (... and for other output formats) doc2pmml.xsl transform to MathML bind doc−incl.xsl and omdoc2pmml.xsl XSL transformation xsl:include doc.xml italic generated file MathML output document Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 10
  11. 11. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Exploiting Knowledge Semantic wiki: One page = one concept SWiM: One page = one statement or theory (small, reusable pages, but not too small) Note: presentation process allows for includes! Relations between theories and statements made explicit as RDF subject–predicate–object triples Incoming and outgoing links displayed in a box, grouped by type (→ instant gratification) Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 11
  12. 12. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion An Ontology of OMDoc OMDoc allows for modeling three layers of mathematical knowledge: objects, statements, and theories. Make these layers explicit – formalise OMDoc’s structures in an ontology (OWL-DL; description logic) Partly done for OMDoc; further steps: extending, generalising imports Theory lives in contains-1 Concept depends on Statement Symbol defined by Definition Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 12
  13. 13. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Extracting Knowledge from OMDoc Pages are in OMDoc – knowledge buried in the markup Semantic Web tools need more explicit representation of the knowledge (RDF) Extract RDF from markup (so far only on page level) Example A wiki page: Extracted RDF triples (= graph): proves <omdoc> Proof Theorem <proof id="pyth-proof" type type for="pythagoras"> proves ... pyth-proof pythagoras </proof> </omdoc> <pyth-proof, rdf:type, omdoc:Proof> <pyth-proof, omdoc:proves, pythagoras> (omdoc:* → OMDoc document ontology) Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 13
  14. 14. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Extension Towards Sciences We are concerned with a technology transfer of MKM applications to general scientific knowledge management. OMDoc has already been successfully extended towards physics; other sciences will follow Need an “upper” ontology of scientific markup languages with . . . objects/statements/theories containment, dependency . . . as an abstraction layer for services exploiting the knowledge. Need to support tools scientists use Editing wiki pages with a local text editor . . . . . . or a specialised application like Mathematica. I. e. allow for internal and external services operating on the data in the wiki or on knowledge extracted from it. Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 14
  15. 15. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Planned Services Goal: support the way scientists work and collaborate! Dependency maintenance (lightweight in SWiM, or enhance backend by change manager like locutor ) Learning assistance by suggesting annotated or inferred prerequisites (in SWiM, or using ActiveMath’s web services) Editing aids like ontology-based auto-completion Search using MathWebSearch in the backend and offering interface in the UI Community-aware reading and browsing: lectora case study Feed lectora with log of users’ interactions Adapt e. g. presentation to preferences of a user or his community Case study in education from September 2007 Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 15
  16. 16. Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion Conclusion SWiM supports the basic wiki features for OMDoc content. On top of that base system, several services for science and education will be prototyped and evaluated in case studies. Easy Editing Search Proof for … 1 1 z −2 ? 2 pythagoras ∫−∞ e d ? partial-diff-eqn ¿ proton 1.------- --------- 2.------- --------- SWiM+ Publishing Learning Assistance Change Management <xml> ... </xml> Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 16

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