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Editing and Using Mathematics in a Semantic Wiki
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Editing and Using Mathematics in a Semantic Wiki

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Meeting on Mathematical Notations, Open University, 2007

Meeting on Mathematical Notations, Open University, 2007

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  • 1. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Editing and Using Mathematics in a Semantic Wiki Meeting on Mathematical Notations 2007 Christoph Lange Jacobs University, Bremen, Germany (formerly International University Bremen) KWARC – Knowledge Adaptation and Reasoning for Content This work was supported by JEM-Thematic-Network ECP-038208. October 23, 2007 Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 1
  • 2. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Abstract SWiM is a semantic wiki for collaboratively . . . building editing browsing . . . mathematical knowledge represented in OMDoc [Kohlhase06]. 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) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 2
  • 3. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Collaborative Mathematics on the Web Current projects: Wikipedia, PlanetMath, . . . Easy to create and link knowledge items Scientific services currently not available E. g. a search for: sqrt{a^2 + b^2} = c, or: x^2 + y^2 = z^2 All theorems about triangles for which a proof exists Neither system relates mathematical symbols to their (formal) definitions or allows for formally structured theories. Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 3
  • 4. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Semantic Wikis and Semantic Markup Semantic wikis understand the knowledge graph they contain usually: 1 page = 1 real-world concept pages and links typed with terms from ontologies Structural semantic markup: In math, there are OMDoc-based services for learning assistance (→ ActiveMath [Melis+ 06]) semantic search (→ MathWebSearch [KohlhaseŞucan07]) publishing theory management proof verification The challenge of joining both: Motivating the authors to structure their knowledge! 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) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 4
  • 5. Motivation State of the Art MathUI Knowledge Representation Services Conclusion The SWiM Prototype SWiM prototype: IkeWiki [Schaffert06] with OMDoc (http://kwarc.info/projects/swim/) editing, presentation, navigation Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 5
  • 6. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Demo (A mathematical document) Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 6
  • 7. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Demo (Editing formulae) Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 7
  • 8. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Demo (Editing notation definitions) Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 8
  • 9. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Demo (An OpenMath content dictionary; old SWiM) Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 9
  • 10. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Editing and Presenting OMDoc Adapting OMDoc’s structures 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. Symbols and their notation defined in the wiki itself – requires flexible presentation mechanism Working on integration of mmlproc (MathML 3) [Müller07] http://kwarc.info/projects/mmlkit/mmlproc/ Exploit structural knowledge: navigate through RDF knowledge graph extracted from markup Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 10
  • 11. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Extracting Knowledge from OMDoc using an Ontology Semantic web tools need explicit knowledge representation Extract RDF from OMDoc markup, using document ontology as vocabulary Three layers of knowledge: objects, statements, theories Formally modeled in OWL-DL (description logic) 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) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 11
  • 12. Motivation State of the Art MathUI Knowledge Representation Services Conclusion Services for Science Case studies in science and education planned Hypothesis: other sciences structure knowledge similarly to mathematics Need to support tools scientists use, e. g. Mathematica Integrate available tools, e. g. the MathWebSearch engine Connecting to the semantic web: allow external services to operate on the knowledge from the wiki Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 12
  • 13. Motivation State of the Art 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) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 13