Your SlideShare is downloading. ×
0
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation    Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Conc...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Initial Situation   Redesign Requirements    Design Decisions    Deployment    Benefits & Difficulties   Use Cases   Concl...
Upcoming SlideShare
Loading in...5
×

Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC)

1,750

Published on

Extended Semantic Web Conference 2012
Digital Libraries track
2012-05-30

Published in: Technology, Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
1,750
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
3
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC)"

  1. 1. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) Extended Semantic Web Conference 2012 Ch. Lange1,2,3 , P. Ion4,5,6 , A. Dimou5 , Ch. Bratsas5 , W. Sperber7 , M. Kohlhase2 , I. Antoniou5 1 School of Computer Science, Univ. of Birmingham, UK 2 Computer Science, Jacobs Univ. Bremen, DE 3 SFB/TR 8 “Spatial cognition”, Univ. of Bremen, DE 4 Mathematical Reviews/American Mathematical Society, US 5 Web Science, Aristotle Univ. Thessaloniki, GR 6 Univ. of Michigan, Math. Dept., US 7 Zentralblatt MATH/FIZ Karlsruhe, DE Project page: http://msc2010.org/mscwork/ 2012-05-30Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 1
  2. 2. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap The MSC in Paper Publications Three-level tree structure: 52 Convex and discrete geometry 53 Differential geometry 53A Classical differential geometry 53A04 Curves in Euclidean space 53A45 Vector and tensor analysis 53B Local differential geometryLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 2
  3. 3. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Browsing PlanetMath.org by SubjectLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 3
  4. 4. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Searching MathSciNet by SubjectLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 4
  5. 5. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Uploading to arXiv.orgLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 5
  6. 6. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap How to Know the Right MSC Code?Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 6
  7. 7. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap The MSC Master Source So Far MajorSub 53-++SubText Differential geometry SeeFor{For differential topology, see SbjNo 57Rxx. For foundational questions of differentiable manifolds, see SbjNo 58Axx} ... SecndLvl 53AxxSubText Classical differential geometry ... ThirdLvl 53A45SubText Vector and tensor analysis Processing MSC-related information (in applications and for maintenance) requires specially tailored scripts! Who knows how to write them?Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 7
  8. 8. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Redesign Requirements 1 facilitate use and reuse for Mathematical Reviews/Zentralblatt MATH services but also for 3rd-party publishers and authors 2 facilitate maintenance: preserve all existing information, leave room for semantic refinements use standard tools instead of custom scripts integrate maintenance-related information into the scheme 3 enable knowledge workers and service developers to adapt and extend the MSC: connections to related subjects e.g. in science add unofficial translations . . . without impairing the editorially controlled core scheme 4 allow end users to explore connections to related subjectsLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 8
  9. 9. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Our Choice: a SKOS Linked Dataset RDF linked dataset, using SKOS as vocabulary – same as these: ← Dewey Decimal Classification (DDC, http://dewey.info) Library of Congress Subject Headings (LCSH, http://id.loc.gov/ authorities/ subjects.html) →Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 9
  10. 10. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap The Basic Hierarchy (SKOS Core) 63 top-level nodes, 528 second-level nodes, 5606 leaves Straightforward application of SKOS vocabulary terms: hasTopConcept narrower Concept- Concept Concept Scheme topConceptOf broader inScheme inScheme msc2010:53A45 a skos:Concept ; skos:inScheme msc2010: ; skos:broader msc2010:53Axx ; skos:prefLabel "Vector and tensor analysis"@en ; skos:notation "53A45"^^mscsmpl:MSCNotation .Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 10
  11. 11. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Multilingual Labels (SKOS Core) TEX source had English labels Trusted parties contributed Chinese, Italian and Russian labels (stored externally) msc2010:53A45 skos:prefLabel "Vector and tensor analysis"@en, "向量与张量分析"@zh . Greek labels needed, but no official ones available? No problem, merge a separate graph! msc2010:53A45 skos:prefLabel "Διανυσµατική και τανυστική ανάλυση"@el .Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 11
  12. 12. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Mathematical Markup in Labels (SKOS Core) 215 out of 6198 labels (3,4 %) contain mathematical markup 26E10 C∞ -functions, quasi-analytic functions Unicode covers most of it, e.g. bold Greek letters, sub-/superscript digits, operators No two-dimensional markup (fractions, matrices) 23 remaining problematic labels: expressions in a sub-/superscript: Sn−1 non-standard sub-/superscript letters: 1k , Hp , vn sub-/superscript symbols: C ∞ overlined operators: ∂ Solution: MathML msc2010:26E10 skos:prefLabel "<mml:math alttext="$C^infty$"> <mml:msup><mml:mi>C</mml:mi><mml:mi>∞</mml:mi></mml:msup> </mml:math>-functions, quasi-analytic functions"^^rdf:XMLLiteral .Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 12
  13. 13. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Linking Partitively Related Concepts (Extension) Three types of non-symmetric links: 00A08 Recreational mathematics (see also 97A20) → straightforward SKOS extension property 20F60 Ordered groups (see mainly 06F15) → straightforward SKOS extension property 11Hxx Geometry of numbers (for applications in coding theory, see 94B75) → a bit trickier (next slide)Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 13
  14. 14. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Faithfully Representing “See For” Links scope for applications in coding theory fo or rT eF ar ge se t seeConditionally 11Hxx 94B75 ty pe pe ty Concept mscvocab seeFor ○ mscvocab forTarget ⊑ mscvocab seeConditionallyLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 14
  15. 15. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Linking Across Concept Schemes (SKOS Core) MSC2000 still widely in use explicit links to MSC2010 would assist migration Typical cases: no change → skos:exactMatch reclassification → skos:relatedMatch e.g. 05E40 “Combinatorial aspects of commutative algebra” partly replacing the MSC2000 classes 05E20 and 05E25 diversification → skos:broadMatch e.g. 97-XX “Mathematics education”: MSC2000: 49 concepts MSC2010: 160 conceptsLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 15
  16. 16. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Linking to non-SKOS Concepts (Extension) Some relevant classification schemes not fully available in SKOS DDC dataset only covers the top three levels (just 9 classes for mathematics ) We know more fine-grained mappings and represent them using local DDC placeholders msc:53A45 skos:relatedMatch [ a skos:Concept ; dcterms:isPartOf ddc:, msc: ; skos:notation "515.63"^^<http://dewey.info/schema-terms/Notation> ; skos:prefLabel "Vector, Tensor, Spinor Analysis"@en ] .Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 16
  17. 17. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Collections Besides the Hierarchy (SKOS Core) 01 History and biography (see also the classification number –03 in the other sections) – how to link there? 52 Convex and discrete geometry → 52-03 Historical 53 Differential geometry → 53-03 Historical msc:HistoricalTopics a skos:Collection ; skos:prefLabel "Historical topics"@en ; skos:member msc:03-03, ..., msc:97-03 . Further candidates: explicitly given: general reference works (–00), instructional expositions (–01), works on computational methods (–08) requiring conceptual analysis: stability of different mathematical structures (scattered all over the MSC)Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 17
  18. 18. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Co-Classification Policies (Extension?) 03-03 Historical (must also be assigned at least one classification number from Section 01) 01A55 19th century 01A70 Biographies, obituaries, personalia, bibliographies ... Not represented fully explicitly for now, . . . . . . but kept in one central place, separate from concept labels msc:HistoricalTopics skos:note "Any resource classified as -03 must also be assigned at least one classification number from Section 01." .Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 18
  19. 19. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap URI Format http://msc2010.org/resources/MSC/2010/53A45 expanded dataset has 92,000 triples (7 MB in RDF/XML) typical linked data clients need few MSC classes: publications typically classified with two MSC classes superclasses may also be of interest Therefore: “slash URIs” . . . . . . plus a SPARQL endpoint . . . plus all-in-one downloads for developersLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 19
  20. 20. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Development and Deployment of the Dataset one RDF/ core SKOS XML file (other serializations) split per resource cwm/ (Makefile) Python rdflib core SKOS expanded SKOS SPARQL TEX custom (RDF/XML) N3 (N-Triples) import endpoint Perl ruleset script (cwm) cwm/ (for “end users”) Python rdflib expanded SKOS (other serializations) all available from http://msc2010.org/mscwork/, licensed under CC-BY-NC-SALange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 20
  21. 21. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Expanding a Dataset with N3 Rules As little manual maintenance as possible, . . . . . . with maximum convenience for stupid linked data clients. # infer skos:broader back-links from skos:narrower # (actually hard-coding the semantics of owl:inverseOf) { ?concept skos:narrower ?narrowerConcept } => { ?narrowerConcept skos:broader ?concept }. similarly for un-reifying the “see for” links dumbing down MSC-specific links to rdfs:seeAlso Makefile applies this using cwm --rdf msc2010-core.skos --n3 expand-skos-rules.n3 --think (expansion from 79,000 triples to 92,000 triples = + 16 %)Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 21
  22. 22. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Benefits Benefits experienced immediately: all information preserved, in most cases more explicitly (hierarchy, cross-references) links to other concept schemes and translations included with the core scheme rigorous conceptual modeling helped to uncover conceptualization issues in the MSC easy maintainability (in our deployment workflow) Benefits envisaged potentially: easy maintainability (in the editorial workflow) promoting widespread adoption thanks to existing search, query, editing, consistency checking, and annotation tools supporting reuse in linked data settings, and in legacy settings (by easier conversion to non-RDF formats)Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 22
  23. 23. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Multilingual Labels vs. Mathematical Markup (I) Two warm-up questions: 1 Who thinks that XML literals in RDF are obsolete?Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 23
  24. 24. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Multilingual Labels vs. Mathematical Markup (I) Two warm-up questions: 1 Who thinks that XML literals in RDF are obsolete? We do not think so! 2 Who knows why RDF literals may either have a language or a datatype?Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 23
  25. 25. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Multilingual Labels vs. Mathematical Markup (I) Two warm-up questions: 1 Who thinks that XML literals in RDF are obsolete? We do not think so! 2 Who knows why RDF literals may either have a language or a datatype? I would like to get your advice!Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 23
  26. 26. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Multilingual Labels vs. Mathematical Markup (II) Multilingual labels? No problem! (Plain literals) Mathematical formulas in labels? No problem! (XML literals) (just violates a “convention” from the SKOS recommendation) Both plain and datatyped literals? ☇ Potential workaround: Encode language into the XML <math xml:lang="en">...</math> removes language information from the RDF data model slows down SPARQL filtering by language multiple prefLabels with “no language”? Note: Cutting mathematical formulas out of the label texts is not an option! Not sure how other SKOS tools like this. . .Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 24
  27. 27. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap In Use (I): http://www.math.auth.gr RDF StorageLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 25
  28. 28. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap In Use (II): Exploring Connections within AUTH connections between three AUTH researchers (using MSC research topics and other linked data), powered by RelFinder (http://www.visualdataweb.org/relfinder.php)Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 26
  29. 29. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap In Use (III): http://alpha.planetmath.orgLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 27
  30. 30. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Conclusion & Roadmap Conclusion LODified the central classification scheme in mathematics (actually one of the first mathematical LOD sets) SKOS and LOD largely satisfied our requirements, . . . . . . but still semantic web standards are not quite ready for mathematics. Roadmap for the MSC dataset itself: soon official announcement by Math. Reviews/Zentralblatt adding precise definitions of the MSC classes adding index terms to classes introducing a faceted structure (beyond collections) Roadmap for the Mathematical Web of Data (next slide)Lange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 28
  31. 31. Initial Situation Redesign Requirements Design Decisions Deployment Benefits & Difficulties Use Cases Conclusion & Roadmap Roadmap: The Mathematical Web of Data Connection points (besides the obvious DBpedia): OpenMath Content Dictionaries (defining the semantics of MathML; we have previously LODified them ) ACM Computing Classification System (soon officially in SKOS ) PlanetMath (soon exposing its metadata as LOD) Physics and Astronomy Classif. Scheme (on our own agenda) European Digital Mathematics Library (interested in LOD) MSC and other datasets enable fine-grained classification of mathematical resources smaller than articles (e.g. blog posts) democratization of scientific publishing, ⇒ towards networked scienceLange et al. Bringing Mathematics To the Web of Data: the Case of the Mathematics Subject Classification (MSC) 2012-05-30 29
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×