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
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SWiM – A Semantic Wiki for Mathematical Knowledge Management
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Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion
SWiM – A Semantic Wiki for Mathematical KnowledgeManagement
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
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)anythingPlanetMath – wiki-like system dedicated tomathematicsConnexions – courseware repository and contentmanagement system. . .
Easy to create and link knowledge items⇒ wikis also suitable for non-public researchprojects
Scientific services currently not available
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 3
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-authoredknowledge models:
support stepwise formalisation workflowoffer enhanced navigation and search
Who is willing to author OMDoc and OpenMath?Share the benefits of structural semantics with the authorOffer added-value services for the situation the author is inInstant gratification: show up-to-date links to related pages
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 7
Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion
Editing OMDoc
So far, only raw OMDoc XML editing supportedMinimum feedback when XML is invalidAdapting OMDoc to a wiki:Small, reusable pages: allow theory-constitutive statements to appear
in their own documentSimple link syntax: theory expands to theory.omdoc#theory.
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 9
Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion
Exploiting Knowledge
Semantic wiki: One page = one conceptSWiM: 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 RDFsubject–predicate–object triplesIncoming 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
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 anontology (OWL-DL; description logic)Partly done for OMDoc; further steps: extending, generalising
Theory
Concept
Statement
Symbol
Definition
vimports
contains-1 depends on
defined by
lives in
v
v
v
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 12
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 markupSemantic Web tools need more explicit representation of theknowledge (RDF)Extract RDF from markup (so far only on page level)
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 togeneral scientific knowledge management.OMDoc has already been successfully extended towards physics; othersciences will followNeed an “upper” ontology of scientific markup languages with . . .
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 backendby 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-completionSearch using MathWebSearch in the backend and offering interface inthe UICommunity-aware reading and browsing: lectora case study
Feed lectora with log of users’ interactionsAdapt e. g. presentation to preferences of a user or his communityCase study in education from September 2007
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 15
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 educationwill be prototyped and evaluated in case studies.
SWiM+
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<xml> ...</xml>
ChangeManagement
Publishing
Search
LearningAssistance
pythagoraspartial-diff-eqnproton
Proof for …
Easy Editing
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 16