Poster Edit Discussionhistory Mathematical Knowledge Management Semantic Wiki and Ontologies Swim = Ikewiki + Omdoc + Σ Σi,Σi

Poster Edit Discussion History SWiM – A Semantic Wiki for References • hasDemo Mathematical Knowledge Management http://swim.kwarc.info • homepageURL http://kwarc.info/projects/ SWiM is a semantic wiki for collaboratively building, editing, brows- swim/ User ing, and discussing collections of mathematical knowledge represented in • presentedAt Christoph Lange structural semantic markup. It motivates users to contribute by instantly Semantic Wiki Workshop sharing the benefits of knowledge-powered services with them. Mathematics) MathUI Workshop • rdfs:seeAlso Mathematical Knowledge Management PlanetMath Semantic MediaWiki Goal: web collaboration on structured mathematical knowledge Connexions • semantic markup common for documents in ActiveMath • rdf:type mathematics: MathML, OpenMath, OMDoc, sTEX Semantic Wiki School of Engineering and Science Browser • applications: e-learning, publishing, proof verification 1 n Digital Enterprise Research Institute • but how to acquire the knowledge? Conclusion NUI Galway, Ireland • ⇒ services to motivate the user and support the authoring workflow A “simple” semantic formula • SWiM makes mathematical documents editable collaboratively and fa- cilitates common workflows by ex- Semantic Wiki and Ontologies ploiting the knowledge they contain. • Domain-specific markup and on- • Semantic wikis found usable to support collaborative formalisation tology allows for advantages over Search • Difference here is: deeply nested markup, lots of cross-references generic semantic wikis and non- semantic mathematical wikis w. r. t. Z ? s2(t)dt • Right granularity of pages: one page = one theory, one statement, one formula? knowledge management ? • ⇒ extract knowledge relevant for search and navigation, build most services on top of that • Approach transferable to other do- Go! mains (e. g. chemistry): decide on • RDF graph in terms of an ontology that models the semantics of the markup; direct and page granularity, capture semantics in inferred relationships: dependency, containment ontology, extract RDF, integrate suit- Proof Theorem able editors Import proves type type • OpenMath CD Roadmap • OMDoc pyth-proof proves pythagoras • ontology for narrative structures • formalisation workflow . . . extraction •LATEX • dependency graph navigation • refactoring support Export • adaptive presentation • OpenMath CD ∞ SWiM = IkeWiki + OMDoc + Σ σi, σi ∈ service • OMDoc i=1 Acknowledgments • XHTML+MathML Technical foundations: • RDF • IkeWiki [Schaffert] • PDF • OMDoc [Kohlhase] Features: • editing Studienstiftung des deutschen Volkes • presentation • navigation • discourse • import/export • refactoring • semantic services OpenMath 3 Case Study Flyspeck Case Study • revision of the content dictionaries (collec- • Formalising a Proof of the Kepler conjec- tions of symbol definitions) ture [Hales 1998] • user interface: editing formulae, metadata, • hundreds of proof sketches (400 pages symbol notations LATEX), collaboratively transform them into Examples for notational preferences: something machine-verifiable n k n • formalising, annotating, discussing, project • language: k , Cn, Ck √ √ management • domain: −1 = i, −1 = j 00 (2) d2y d2 • taste: f (x), f (x), dx2, dx2f(x) • exactness: f ∈ O(n), f = O(n)