swim – a semantic wiki for mathematical knowledge management
DESCRIPTION
Mathematical User Interfaces 2007TRANSCRIPT
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
Abstract
SWiM is a semantic wiki for collaboratively . . .buildingeditingbrowsing
. . . mathematical knowledge represented in OMDoc.Target audience:
mathematicians developing new theoriesscholars learning mathematics
Outline:Current SWiM prototype: user interface and architecturePlans for further development: platform for semantic scientific services
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 2
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
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 andPlanetMath, which usepresentational LATEXIn principle possible (but notimplemented) in Connexions,thanks to Content MathML
All theorems about triangles forwhich a proof exists
Possible in semantic wikis
Neither system relates mathematicalsymbols to their (formal) definitionsor allows for formally structuredtheories.
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 4
Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion
Semantic Wikis
Conventional wikis do not understand the knowledge graph theycontainSemantic wikis address this problem:
usually: 1 page =̂ 1 real-world conceptpages 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
Motivation State of the Art OMDoc+Wiki Usability MathUI Knowledge Representation Services Conclusion
Structural Semantic Markup
Structural semantic markup: common way to represent scientificknowledgeFor OMDoc, e. g., there are services for
learning assistance (→ ActiveMath)semantic search (→ MathWebSearch)publishingtheory managementproof verification
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 6
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
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
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
Presenting OMDoc
Adapted OMDoc XSLTs (→ XHTML+MathML), with cachingSymbols in formulae point to their <symbol> declarations.Hyperlinked source code view
XSL transformation
xsl:include
generated fileitalic
transformto MathML
doc.xml
MathML outputdocument
omdoc2pmml.xsl
generic templatesfor OMDoc to MathMLtransformation
omdoc2pmml.xsl
generic templatesfor OMDoc to MathMLtransformation
omdoc2pmml.xsl
generic templatesfor OMDoc to MathMLtransformation
A.omdoc
and their presentationdefines symbols
compile XSLtemplates
from present−ation elements(expres.xsl)
A−tmpl.xsl
XSL templates forsymbols from A
doc.omdoc
uses symbols fromdocuments A, B, C
collect documentswhose symbols
are used(exincl.xsl)
doc2pmml.xsl
bind doc−incl.xsland omdoc2pmml.xsl
doc−incl.xsl
include −tmpl stylesheets of documentswhose symbols are used
(... and for other output formats)
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 10
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)
ExampleA wiki page:
<omdoc><proof id="pyth-proof"for="pythagoras">...
</proof></omdoc>
Extracted RDF triples (=̂ graph):
pyth-proof pythagoras
Proof Theorem
type typeproves
proves
<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
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 . . .
objects/statements/theoriescontainment, 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 inthe wiki or on knowledge extracted from it.
Ch. Lange (Jacobs University Bremen) SWiM – A Semantic Wiki for MKM June 27, 2007 14
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