Upload
christoph-lange
View
945
Download
0
Embed Size (px)
DESCRIPTION
Meeting on Mathematical Notations, Open University, 2007
Citation preview
Motivation State of the Art MathUI Knowledge Representation Services Conclusion
Editing and Using Mathematics in a Semantic WikiMeeting on Mathematical Notations 2007
Christoph Lange
Jacobs University, Bremen, Germany(formerly International University Bremen)
KWARC – Knowledge Adaptation and Reasoning for ContentThis 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
Motivation State of the Art MathUI Knowledge Representation Services Conclusion
Abstract
SWiM is a semantic wiki for collaboratively . . .buildingeditingbrowsing
. . . mathematical knowledge represented in OMDoc [Kohlhase06].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) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 2
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 itemsScientific services currently not availableE. g. a search for:
\sqrt{a^2 + b^2} = c, or: x^2 + y^2 = z^2All theorems about triangles for which a proofexists
Neither system relates mathematical symbols totheir (formal) definitions or allows for formallystructured theories.
Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 3
Motivation State of the Art MathUI Knowledge Representation Services Conclusion
Semantic Wikis and Semantic Markup
Semantic wikis understand the knowledge graph they containusually: 1 page =̂ 1 real-world conceptpages and links typed with terms from ontologies
Structural semantic markup: In math, there are OMDoc-basedservices for
learning assistance (→ ActiveMath [Melis+06])semantic search (→ MathWebSearch [KohlhaseŞucan07])publishingtheory managementproof verification
The challenge of joining both: Motivating the authors to structuretheir knowledge!
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) Editing and Using Mathematics in a Semantic Wiki October 23, 2007 4
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
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
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
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
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
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 documentSimple link syntax: theory expands to theory.omdoc#theory.Symbols and their notation defined in the wiki itself – requires flexiblepresentation mechanism
Working on integration of mmlproc (MathML 3) [Müller07]http://kwarc.info/projects/mmlkit/mmlproc/
Exploit structural knowledge: navigate through RDF knowledge graphextracted from markup
Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 200710
Motivation State of the Art MathUI Knowledge Representation Services Conclusion
Extracting Knowledge from OMDoc using an Ontology
Semantic web tools need explicit knowledge representationExtract RDF from OMDoc markup, using document ontology asvocabularyThree layers of knowledge: objects, statements, theoriesFormally modeled in OWL-DL (description logic)
ExampleA wiki page:<omdoc>
<proof id="pyth-proof"for="pythagoras">...
</proof></omdoc>
Extracted RDF triples (=̂ graph):
pyth-proof pythagoras
Proof Theoremtype type
proves
proves
<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, 200711
Motivation State of the Art MathUI Knowledge Representation Services Conclusion
Services for Science
Case studies in science and education plannedHypothesis: other sciences structure knowledge similarly tomathematicsNeed to support tools scientists use, e. g. MathematicaIntegrate available tools, e. g. the MathWebSearch engineConnecting to the semantic web: allow external services to operate onthe knowledge from the wiki
Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 200712
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 educationwill be prototyped and evaluated in case studies.
SWiM+
1
¿∫
−∞
ze−12?2
d ?
1.----------------2.----------------
<xml> ...</xml>
ChangeManagement
Publishing
Search
LearningAssistance
pythagoraspartial-diff-eqnproton
Proof for …
Easy Editing
Ch. Lange (Jacobs University Bremen) Editing and Using Mathematics in a Semantic Wiki October 23, 200713