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Christoph Lange's Ph.D. defense (2011-03-11)

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- 1. Overview Service Integration Knowledge Representation Conclusion & Future Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration Christoph Lange Jacobs University, Bremen, Germany KWARC – Knowledge Adaptation and Reasoning for Content 2011-03-11 Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 1
- 2. Overview Service Integration Knowledge Representation Conclusion & FutureWhy Mathematics? Mathematics ubiquitous foundation of science, technology, and engineering these have in common: rigorous style of argumentation symbolic formula language similar process of understanding results Mathematical Knowledge complex structures . . . that have been well studied and understood Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 2
- 3. Overviewtime. Note factoring a quartic into two real quadratics is different than sign each Service Integration Knowledge Representation Conclusion & Future trying to ﬁnd four complex roots. Deﬁnition: A function f is analytic on an open subset R ⊂ C if f is complexSemiformal Mathematical Knowledge differentiable everywhere on R; f is entire if it is analytic on all of C.2 Proof of the Fundamental Theorem via Liouville Theorem 2.1 (Liouville). If f (z) is analytic and bounded in the complex plane, then f (z) is constant.Informal We now prove Theorem 2.2 (Fundamental Theorem of Algebra). Let p(z) be a polynomial Formalized = Computerized with complex coefﬁcients of degree n. Then p(z) has n roots. Proof. It is sufﬁcient to show any p(z) has one root, for by division we can then write p(z) = (z − z0 )g(z), with g of lower degree. Note that if p(z) = an z n + an−1 z n−1 + · · · + a0 , (2) then as |z| → ∞, |p(z)| → ∞. This follows as an−1 a0 p(z) = z n · an + + ··· + n . (3) z z 1 Assume p(z) is non-zero everywhere. Then p(z) is bounded when |z| ≥ R. 1 1 Also, p(z) = 0, so p(z) is bounded for |z| ≤ R by continuity. Thus, p(z) is a bounded, entire function, which must be constant. Thus, p(z) is constant, a contradiction which implies p(z) must have a zero (our assumption). [Lev] Semiformal – a pragmatic and practical compromise 2 anything informal that is intended to or could in principle be formalized combinations of informal and formal for both human and machine audience Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 3
- 4. Overview Service Integration Knowledge Representation Conclusion & FutureCollaboration in Mathematics History of collaboration in the small: Hardy/Littlewood in the large: hundreds of mathematicians classifying the finite simple groups “industrialization” of research Utilizing the Social Web research blogs: Baez, Gowers, Tao Polymath: collaborative proofs Collaboration = creation, formalization, organization, understanding, reuse, application Polymath wiki/blog: P ≠ NP proof Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 4
- 5. Overview Service Integration Knowledge Representation Conclusion & FutureAn Integrated View on a Collaboration WorkflowThe author(s): The reader(s): The reviewer(s): 0 original idea (in one’s “What does that 1 read paper (← ) mind) mean?”: missing 2 verify claims background, 1 formalize into used to different 3 point out problems structured document notation with the paper and 2 search existing its formal concepts “How does that knowledge to build work?” on “What is that good 3 validate formal for?” structure look up background 4 present in a information in cited comprehensible way publications 5 submit for review Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 5
- 6. Overview Service Integration Knowledge Representation Conclusion & FutureLooking up Background Knowledge “What does that mean?” Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 6
- 7. Overview Service Integration Knowledge Representation Conclusion & FutureAdapting the Presentation to FamiliarTerminology “What does that mean?” – here: unfamiliar unit system (imperial vs. metric) Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 7
- 8. Overview Service Integration Knowledge Representation Conclusion & FutureLooking up Related Information “What can I reuse — what is that good for — where/how is it applied?” Sussex St. Reading Andrews NDL Audio- Lists Resource subjects t4gm MySpace scrobbler Lists Moseley (DBTune) (DBTune) RAMEAU Folk NTU SH lobid GTAA Plymouth Resource Lists Organi- Reading Lists sations Music The Open ECS Magna- Brainz Music DB tune Library LCSH South- (Data Brainz LIBRIS ampton Tropes lobid Ulm Incubator) (zitgist) Man- EPrints Resources chester Surge Reading biz. Music RISKS Radio Lists The Open ECS data. John Brainz Discogs Library PSH Gem. UB South- gov.uk Peel (DBTune) FanHubz (Data In- (Talis) Norm- Mann- ampton (DB cubator) Jamendo datei heim RESEX Tune) Popula- Poké- DEPLOY Last.fm tion (En- pédia Artists Last.FM Linked RDF AKTing) research EUTC (DBTune) (rdfize) LCCN VIAF Book Wiki data.gov Produc- Pisa Eurécom P20 Mashup semantic NHS .uk tions classical web.org (EnAKTing) Pokedex (DB Mortality Tune) PBAC ECS (En- AKTing) BBC MARC (RKB Budapest Program Codes Explorer) Energy education OpenEI BBC List Semantic Lotico Revyu OAI (En- CO2 data.gov mes Music Crunch SW AKTing) (En- .uk Chronic- Linked Dog NSZL Base AKTing) ling Event- MDB RDF Food IRIT America Media Catalog ohloh BBC DBLP ACM IBM Good- BibBase Ord- Wildlife (RKB Openly Recht- win nance Finder Explorer) Local spraak. Family DBLP legislation Survey Tele- New VIVO UF .gov.uk nl graphis York flickr (L3S) New- VIVO castle Times URI wrappr OpenCal Indiana RAE2001 UK Post- Burner ais DBLP codes statistics (FU VIVO CiteSeer Roma data.gov LOIUS Taxon iServe Berlin) IEEE .uk Cornell Concept Geo World data ESD Fact- OS dcs Names book dotAC stan- reference Project Linked Data NASA (FUB) Freebase dards data.gov Guten- .uk for Intervals (Data GESIS Course- transport DBpedia berg STW ePrints CORDIS Incu- ware data.gov bator) (FUB) Fishes ERA UN/ .uk of Texas Geo LOCODE Uberblic Euro- Species The stat dbpedia TCM SIDER Pub KISTI (FUB) lite Gene STITCH Chem JISC London Geo KEGG DIT LAAS Gazette TWC LOGD Linked Daily OBO Drug Eurostat Data UMBEL lingvoj Med (es) Disea- YAGO Medi some Care ChEBI KEGG NSF Linked KEGG KEGG Linked Drug Cpd GovTrack rdfabout Glycan Sensor Data CT Bank Pathway US SEC Open Reactome (Kno.e.sis) riese Uni Cyc Lexvo Path- totl.net way Pfam PDB Semantic HGNC XBRL WordNet KEGG KEGG (VUA) Linked Taxo- CAS Reaction rdfabout Twarql UniProt Enzyme EUNIS Open nomy US Census Numbers PRO- ProDom SITE Chem2 UniRef Bio2RDF Climbing WordNet SGD Homolo Linked (W3C) Affy- Gene Cornetto GeoData metrix PubMed Gene UniParc Ontology GeneID Airports Product DB UniSTS MGI Gen Bank OMIM InterPro As of September 2010 e-science data – with opaque mathematical models statistical datasets – without mathematical derivation rules publication databases – without mathematical content Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 8
- 9. Overview Service Integration Knowledge Representation Conclusion & FuturePointing out and Discussing Problems Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 9
- 10. Overview Service Integration Knowledge Representation Conclusion & FutureCollaboration Still has to be Enabled! Many collaboration tasks not currently well supported by machines For other tasks there is (limited) support creating and formalizing documents – semiformal!? search existing knowledge to build on – semiformal!? computation (recall unit conversion) – but not inside documents publishing in textbook style – could it be more comprehensible? adapting notation (e.g. ⋅ ×, n k Cn ) – not quite on demand k Existing machine services only focus on primitive tasks Can’t simply be put together, as they . . . . . . speak different languages . . . take different perspectives on knowledge Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 10
- 11. Overview Service Integration Knowledge Representation Conclusion & FutureDocument Perspective: XML Markup XHTML+MathML(+OpenMath) ... is <math> <mn>9144</mn> <mo>⁢</mo> <mo>m</mo> </math> from city ... Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 11
- 12. Overview Service Integration Knowledge Representation Conclusion & FutureNetwork Perspective: RDF GraphsLook up Related Information: Point out and Discuss Problems: Sussex St. hasDiscussion ` forum1 definition Reading Andrews NDL Audio- Lists Resource subjects (IkeWiki ontology) t4gm MySpace scrobbler Lists Moseley (DBTune) (DBTune) RAMEAU Folk NTU SH lobid GTAA Plymouth Resource Lists Organi- Reading sations exemplifies Lists Music The Open ECS Magna- Brainz Music DB Library LCSH South- post1: Issue tune (Data Brainz LIBRIS lobid ampton Ulm Tropes Incubator) (zitgist) Man- Resources EPrints chester Surge Reading (UnclearWh.Useful) biz. Music RISKS Radio Lists The Open ECS data. Brainz example John Discogs Library PSH Gem. UB South- gov.uk Peel (DBTune) FanHubz (Data In- (Talis) Norm- Mann- ampton (DB has_reply cubator) Jamendo datei heim RESEX elaborates_on Tune) Popula- Poké- DEPLOY Last.fm tion (En- pédia Artists Last.FM Linked RDF AKTing) research EUTC (DBTune) (rdfize) LCCN VIAF Book Wiki data.gov Produc- Pisa Eurécom P20 Mashup semantic NHS post2: Elaboration .uk tions classical Pokedex web.org (EnAKTing) (DB Mortality Tune) PBAC ECS (En- AKTing) BBC MARC (RKB Budapest Codes has_container Program Explorer) OpenEI BBC agrees_with Energy education Semantic Lotico Revyu OAI List (En- CO2 data.gov mes Music Crunch SW AKTing) (En- .uk Chronic- Linked Dog NSZL Base AKTing) ling Event- MDB RDF Food IRIT Catalog resolvesInto America Media ohloh BBC DBLP ACM post3: Position Good- BibBase IBM Ord- Wildlife (RKB Openly Recht- win nance Finder Explorer) Local spraak. Family DBLP legislation Survey Tele- New proposes_ VIVO UF .gov.uk nl graphis York flickr (L3S) New- VIVO castle Times URI wrappr OpenCal Indiana RAE2001 UK Post- Burner ais DBLP codes statistics data.gov .uk LOIUS Taxon Concept Geo World iServe VIVO Cornell (FU Berlin) data IEEE CiteSeer Roma solution_for knowledge post4: Idea items ESD Fact- OS dcs Names book dotAC stan- reference Project Linked Data NASA (FUB) Freebase dards data.gov Guten- .uk for Intervals (Data GESIS Course- (ProvideExample) STW CORDIS (OMDoc ontology) transport Incu- DBpedia berg ePrints (FUB) ware data.gov bator) Fishes ERA UN/ .uk of Texas Geo LOCODE Uberblic on wiki pages Euro- Species supports The stat dbpedia TCM SIDER Pub KISTI (FUB) lite Gene STITCH Chem JISC decides London Geo KEGG DIT LAAS Gazette TWC LOGD Linked Daily OBO Drug Eurostat Data UMBEL lingvoj Med Disea- post5: Evaluation (es) YAGO Medi some Care ChEBI KEGG NSF Linked KEGG KEGG Linked Drug Cpd GovTrack rdfabout Glycan Sensor Data CT Bank Pathway Open agrees_with US SEC riese Reactome (Kno.e.sis) Cyc Uni Lexvo Path- totl.net way Pfam PDB Semantic HGNC XBRL KEGG post6: Position WordNet KEGG (VUA) Linked Taxo- CAS Reaction rdfabout Twarql UniProt Enzyme EUNIS Open nomy US Census Numbers PRO- ProDom SITE Chem2 UniRef Bio2RDF Climbing WordNet SGD Homolo Linked (W3C) Affy- Gene Cornetto GeoData metrix PubMed Gene post7: Decision UniParc Ontology GeneID Airports Product DB UniSTS Gen MGI supported_by Bank OMIM InterPro argumentative As of September 2010 physical structure structure (SIOC Core) discussion page (SIOC Arg.) Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 12
- 13. Overview Service Integration Knowledge Representation Conclusion & FutureHow to Enable Collaboration? Integrate a wide range of different services As they currently speak different languages, . . . first create a unified interoperability layer for knowledge representations (document vs. network perspective) then translate between different representations Tool: semantic web technology Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 13
- 14. Overview Service Integration Knowledge Representation Conclusion & FutureContribution Building a collaboration environment is not trivial Collection of foundational, enabling technologies OMDoc+RDF(a), a unified interoperability layer for representing semiformal mathematical knowledge (document and network perspective) Design patterns for integrating services interactive assistance in published documents translations inside knowledge bases Evaluation of how effectively an integrated environment built that way (a semantic wiki for mathematics) supports practical workflows Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 14
- 15. Overview Service Integration Knowledge Representation Conclusion & FutureSWiM, an Integrated Collaboration Environment Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 15
- 16. Overview Service Integration Knowledge Representation Conclusion & FutureSWiM, an Integrated Collaboration Environment Semantic wiki, combining knowledge production and consumptionEditor for documents, Graph-based Localized discussionformulæ, metadata navigation forums Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 16
- 17. Overview Service Integration Knowledge Representation Conclusion & FutureUsability Evaluation of the SWiM Prototype Integration is feasible, but is the result usable? learnable? effective? useful? satisfying to use? Can we effectively support maintenance workflows (on the OpenMath CDs)? Quick local fixing of minor errors (in text, formalization, or presentation) Peer review, and preparing major revisions by discussion In general: What particular challenges to usability does the integration of heterogenenous services entail? Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 17
- 18. Overview Service Integration Knowledge Representation Conclusion & FutureFeedback Statements from Test Users positive statement successful 93 action 95 understood concept 36 18 not understood concept 18 unexpected bug negative 61 statement 43 dissatisfaction 52 44 51 confusion/uncertainty not understood expectation what to do not met Understanding only seems marginal, but had a high impact on successfully accomplishing tasks! Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 18
- 19. Overview Service Integration Knowledge Representation Conclusion & FutureInterpretation and Consequences Usability hypotheses largely hold, but: Users with previous knowledge of related knowledge models or UIs had advantages Less experienced users frequently taken in by misconceptions; requested better explanations Users expected a more coherent integration User interfaces need Semantic Transparency (for learnability): self-explaining user interfaces familiar and consistent terminology (despite XML/RDF heterogeneity under the hood!) The SWiM user interface is not yet self-explaining Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 19
- 20. Overview Service Integration Knowledge Representation Conclusion & FutureSelf-explaining Publicationsand Assistive Services Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 20
- 21. Overview Service Integration Knowledge Representation Conclusion & FutureStructures of Mathematical Knowledge (MK) Goal: design unified interoperability layer for all relevant aspects of MK Different degrees of formality: informal, formalized, semiformal Classification of structural dimensions: logical/functional: symbols, objects, statements, theories rhetorical/document: from chapters down to phrases presentation: e.g. notation of symbols metadata: general administrative ones; applications/projects/people discussions about MK (e.g. about problems) Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 21
- 22. Overview Service Integration Knowledge Representation Conclusion & FutureRequirements for Representing MK Structure Coverage Formal. Linking Comprh. satisfies Requirementa S.L.* S.R S.N S.M S.D F.R F.C L.A L.→ L.← C.S C.H O S T MathML 3 ++ – – – – – – ++ + + + + – + OpenMath 2 Objects ++ – – – – – – + – + – OpenMath 2 CDs ++b – – – – – – – OMDoc 1.2/S EX T ++b ++ + ++ + – ++ + – + – – MathLang ++ ++ – – – – – ++ + – – – DocBook 5 ++b – – – – +d – – – – + + – – TEI P5 ++c – – – – – ++ + + – + – – DITA 1.1 ++c – – – – +d – – – + + + – – EPUB 2.0.1/DTBook 3 ++c – – – – + – – – – – + – – CNXML 0.7/CollXML/mdml ++b + – – – – – – – – + – – Formalized languages ++ ++ – + – – – – – + – RDF(a) 1.1 (depends on vocabulary) + ++ ++ ++ + OMDoc 1.3/1.6 ++b ++ ++ ++ ++ ++e – ++ + ++e ++e ++e e +e Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 22
- 23. Overview Service Integration Knowledge Representation Conclusion & FutureOMDoc+RDF(a) as an Interoperability Layer forExchanging and Reusing MK 1 Translate OMDoc to RDF formalize conceptual model as an ontology reused existing ontologies for rhetorics, metadata, etc. specified an XML→RDF translation for identifiers and structures 2 Embed RDFa into OMDoc extend OMDoc beyond mathematics embed arbitrary metadata into mathematical documents Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 23
- 24. Overview Service Integration Knowledge Representation Conclusion & FutureCreating an RDF Resource from an XML Node<theory name="group"> <http://ma.th/group> <symbol name="op"> rdf:type omdoc:Theory ; Theory symbol <type> omdoc:homeTheoryOf M×M→M <http://ma.th/group#symbol> . rdf:type </type> <http://ma.th/group#symbol> rdf:type homeTheoryOf </symbol> rdf:type omdoc:Symbol ; . . . /group . . . /group#op</theory> omdoc:declaredType ... . Algorithm: Require: b, p, u, T , P ∈ U, n is an XML node, T is the URI of an ontology class or empty, P is the URI of an ontology property or empty Ensure: R ∈ U × U × (U ∪ L) is an RDF graph R← if u = ε then {if no explicit URI is defined by the rule, . . . } u ← mint(b, n) {. . . try to mint one, using built-in or custom minting functions (configurable per extraction module)} end if if u ≠ ε then {if we got a URI, . . . } if T ≠ ε then R ← R ∪ { u, rdf type, T } {make this resource an instance of the given class} end if if P ≠ ε then R ← R ∪ add_uri_property( , p, P, u) {create a link (e.g. of a type like hasPart) from the parent subject to this resource} end if for all c ∈ π NS ($n ∗ $n @∗) do {from each element and attribute child node (determined using an XPath evaluation function returning a nodeset) . . . } R ← R ∪ extract(b, c, u) {. . . recursively extract RDF, using the newly created resource as a parent subject} end for{i.e. the recursion terminates for nodes without children} end if return R Christoph Lange Enabling Collaboration on Semiformal Mathematical Knowledge by Semantic Web Integration 2011-03-11 24

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