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Research Background and Application Context   Key Technology   The System    Use Cases and Applications   Conclusion




   SWiM – A Semantic Wiki for Mathematical Knowledge
                     Management
            5th European Semantic Web Conference 2008, Demo Track


                                              Christoph Lange

                                     Jacobs University, Bremen, Germany
                      KWARC – Knowledge Adaptation and Reasoning for Content


                                                June 3, 2008




    Ch. Lange (Jacobs University Bremen)      SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008
                                                                                                    June 3,       1
Research Background and Application Context   Key Technology   The System    Use Cases and Applications   Conclusion



Mathematical Knowledge Management

        Goal: support collaborative authoring of documents usable for
        knowledge management
        semantic markup common for documents in mathematics: MathML,
        OpenMath, OMDoc
        layers of knowledge: symbols, statements, theories, documents
        has many applications, but how to acquire the knowledge?
        ⇒ services to support the authoring workflow

Example (a simple formula?)
<apply>
  <csymbol definitionURL="http://openmath.org/cd/arith1#plus"/>
  <cn type="integer">1</cn>
  <ci>n</ci>
</apply>

    Ch. Lange (Jacobs University Bremen)      SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008
                                                                                                    June 3,       2
Research Background and Application Context   Key Technology   The System    Use Cases and Applications   Conclusion



Semantic Wiki and Ontologies
        Semantic wikis found usable to support collaborative formalisation
        Difference here is: deeply nested markup, lots of cross-references
        Right granularity of pages: one page = one theory, one statement,
        one formula?
        ⇒ extract knowledge relevant for search and navigation, build most
        services on top of that
        RDF graph in terms of an ontology that models the semantics of the
        markup; direct and inferred relationships: dependency, containment

Example
 A wiki page:                                    Extracted RDF triples (= graph):
                                                      Proof       proves        Theorem
 <omdoc>                                          type                                type
   <proof id="pyth-proof"
    for="pythagoras">                               pyth-proof proves          pythagoras
     ...</proof>                                 <pyth-proof, rdf:type, omdoc:Proof>
 </omdoc>                                        <pyth-proof, omdoc:proves, pythagoras>

    Ch. Lange (Jacobs University Bremen)      SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008
                                                                                                    June 3,       3
Research Background and Application Context   Key Technology   The System    Use Cases and Applications   Conclusion



SWiM: IkeWiki + Mathematical Markup

        editing, presentation, navigation, discourse, semantic services
        See http://swim.kwarc.info




    Ch. Lange (Jacobs University Bremen)      SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008
                                                                                                    June 3,       4
Research Background and Application Context   Key Technology   The System    Use Cases and Applications   Conclusion



Proof Formalisation and Dictionaries of Symbols



     Flyspeck: Formalising a Proof of the Kepler conjecture:
               hundreds of proof sketches, collaboratively transform them
               into something machine-verifiable
               formalising, annotating, discussing, project management
OpenMath 3: revision of the content dictionaries (collections of symbol
           definitions)
           user interface: editing formulae, metadata, symbol notations
           “Let’s write multiplication as a × b instead of a · b!”




    Ch. Lange (Jacobs University Bremen)      SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008
                                                                                                    June 3,       5
Research Background and Application Context   Key Technology   The System    Use Cases and Applications   Conclusion



The SWiM Approach: Good for Math and other Domains


        SWiM makes mathematical documents editable collaboratively and
        facilitates common workflows by exploiting the knowledge they
        contain.
        Domain-specific semantic markup and ontology allows for advantages
        over generic semantic wikis, and over non-semantic mathematical
        wikis (more and easier knowledge management)
        Approach considered transferable to other domains (e. g. chemistry):
        decide on page granularity, capture semantics in ontology, extract
        RDF, integrate suitable editors

                          Come and see the demo tonight!


    Ch. Lange (Jacobs University Bremen)      SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008
                                                                                                    June 3,       6

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SWiM – A Semantic Wiki for Mathematical Knowledge Management

  • 1. Research Background and Application Context Key Technology The System Use Cases and Applications Conclusion SWiM – A Semantic Wiki for Mathematical Knowledge Management 5th European Semantic Web Conference 2008, Demo Track Christoph Lange Jacobs University, Bremen, Germany KWARC – Knowledge Adaptation and Reasoning for Content June 3, 2008 Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008 June 3, 1
  • 2. Research Background and Application Context Key Technology The System Use Cases and Applications Conclusion Mathematical Knowledge Management Goal: support collaborative authoring of documents usable for knowledge management semantic markup common for documents in mathematics: MathML, OpenMath, OMDoc layers of knowledge: symbols, statements, theories, documents has many applications, but how to acquire the knowledge? ⇒ services to support the authoring workflow Example (a simple formula?) <apply> <csymbol definitionURL="http://openmath.org/cd/arith1#plus"/> <cn type="integer">1</cn> <ci>n</ci> </apply> Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008 June 3, 2
  • 3. Research Background and Application Context Key Technology The System Use Cases and Applications Conclusion Semantic Wiki and Ontologies Semantic wikis found usable to support collaborative formalisation Difference here is: deeply nested markup, lots of cross-references Right granularity of pages: one page = one theory, one statement, one formula? ⇒ extract knowledge relevant for search and navigation, build most services on top of that RDF graph in terms of an ontology that models the semantics of the markup; direct and inferred relationships: dependency, containment Example A wiki page: Extracted RDF triples (= graph): Proof proves Theorem <omdoc> type type <proof id="pyth-proof" for="pythagoras"> pyth-proof proves pythagoras ...</proof> <pyth-proof, rdf:type, omdoc:Proof> </omdoc> <pyth-proof, omdoc:proves, pythagoras> Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008 June 3, 3
  • 4. Research Background and Application Context Key Technology The System Use Cases and Applications Conclusion SWiM: IkeWiki + Mathematical Markup editing, presentation, navigation, discourse, semantic services See http://swim.kwarc.info Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008 June 3, 4
  • 5. Research Background and Application Context Key Technology The System Use Cases and Applications Conclusion Proof Formalisation and Dictionaries of Symbols Flyspeck: Formalising a Proof of the Kepler conjecture: hundreds of proof sketches, collaboratively transform them into something machine-verifiable formalising, annotating, discussing, project management OpenMath 3: revision of the content dictionaries (collections of symbol definitions) user interface: editing formulae, metadata, symbol notations “Let’s write multiplication as a × b instead of a · b!” Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008 June 3, 5
  • 6. Research Background and Application Context Key Technology The System Use Cases and Applications Conclusion The SWiM Approach: Good for Math and other Domains SWiM makes mathematical documents editable collaboratively and facilitates common workflows by exploiting the knowledge they contain. Domain-specific semantic markup and ontology allows for advantages over generic semantic wikis, and over non-semantic mathematical wikis (more and easier knowledge management) Approach considered transferable to other domains (e. g. chemistry): decide on page granularity, capture semantics in ontology, extract RDF, integrate suitable editors Come and see the demo tonight! Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for Mathematical Knowledge Management 2008 June 3, 6