Keynote Talk at Int Conf on Case-based Reasoning

1. Ontologies and Similarity Steffen Staab Acknowledgements to Claudia d’Amato, Univ Bari, & WeST Team TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA

2. Agenda Kris: Brocoliisvegetableused in stirfry Motivation Whatareexamplesemanticapplications? FoundationWhatis an ontology? Reality Check Whataretypicalontologies? Survey Howissimilaritymeasured in ontologies? CritiqueWhatshouldbemeasured? Solution A preliminarysolution ConclusionWhatto do now?

3. Motivation SemanticApplications Check out: http://challenge.semanticweb.org/

4. Linked Data Cases withMetadatawithout Frontiers

5. Semantic Search & Browsing: Semantic Portals [WWW 2000] http://ontoprise.com

6. FacetedSemantic Media Browsing: Semaplorer Winner Billion Triples Challenge 2008 [JoWS 2009] http://kreuzverweis.com

7. Semantic Desktop Additional Semantic Meta Data, e.g. sender, subject Access to further PIM tools

8. Mobile Exploration ofLinked Data: Mobile Facets

13. SemanticSimilarity[Franz et al 09] [stuffhere], BUT

14. Whatis an Ontology? Foundation

15. Whatis an ontology? Whatfor? Agreements thatmakelinkeddatamoreuseful Reasoning Gruber 1993: An ontology is an “explicit specificationof a conceptualization” Oberle, Guarino, Staab. Whatis an ontology? Handbook on ontologies, Springer 2009.

16. Observations in the Real World

17. A Model ofthe Real World knows knows Manager(I034820) Researcher(I046758) knows cooperates Employee(I050000) Researcher(I044443)

18. Abstractingfromthe Individual Model knows knows Manager Researcher knows cooperates Employee Researcher

19. A Conceptual Model Intensional Relations Unary Manager Research Employee Binary cooperates knows Cognitive Bias Perception Knowledge Belief The conceptualmodelcaptureswhatis invariant accordingtoone‘sconceptualizationoftheworld

21. E.g. Lecturer1 = {Ashwin, Nirmalie, Steffen, Kris,…}

23. Conceptualization Perception Reality State of affairs State of affairs relevant invariants across presentation patterns:D,  Presentationpatterns Phenomena Bad Ontology Ontological commitmentK (selects D’D and ’) Models MD’(L) Ontology InterpretationsI Intended models for each IK(L) Ontology models Language L ~Good Slide by Nicola Guarino

24. Description Logics: First orderlanguage(s) forontology T-Box Describing Relations Intensionally Flight  Service. Flight  ∃to.Airport Flight  to.Airport Flight  ∃from.Airport Flight  from.Airport approachedBy ⊇ to-1 FlightFromDE = Flight ∩ ∃from.(Airport ∩part.{DE}) A-Box Describing Relations Extensionally Flight(LH123). Flight(BA121). Airport(FRA). from(LH123,FRA). to(LH123,LHR). … Key Feature: Classes (unaryrelations) aredefinedbyrelationstodefinitionsofotherclasses

26. Pragmaticallytractablefor 105concepts

31. Howissimilaritymeasured in ontologies? Survey

32. ExampleOntology Airport Service Europe part Hub part part Flight LHR IT UK FCO LCY DE FRA part part Including „invariant“ A-Box facts(like Airport(FRA)) to to to FRA-LCY FRA-LHR FRA-FCO

35. Graph comparison

36. Consideringthesemanticsofhierarchies

37. isa

38. part

43. Absolute similarityvaluesmostly irrelevant (like in CBR)

44. Most information in theontology will bediscardedFlight-DE-UK Flight-DE-IT FRA-LCY FRA-LHR FRA-FCO [Rada et al.'89] ff

45. IntensionalCountingof Path Length 𝑠𝑖𝑚𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑅𝐴−𝐿𝐶𝑌 ~ 1𝑃𝑎𝑡h1=1min2,3=12 Service 𝑠𝑖𝑚𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑅𝐴−𝐹𝐶𝑂 ~ 1𝑃𝑎𝑡h2=1min4,2=12 Flight Flight-DE-UK Flight-DE-IT FlightFromHub FlightToHub FlightFrom+ToHub FRA-LCY FRA-LHR FRA-FCO

46. `Improved´IntensionalCountingof Path Length 𝑐𝑜𝑡𝑜𝑝𝑦𝐶=𝐷 | 𝑖𝑠𝑎∗(𝐶,𝐷) Service 𝑠𝑖𝑚𝑐𝑜𝑡𝑜𝑝𝑦(𝐶,𝐷)~ |𝑐𝑜𝑡𝑜𝑝𝑦(𝐶) ∩𝑐𝑜𝑡𝑜𝑝𝑦(𝐷)||𝑐𝑜𝑡𝑜𝑝𝑦(𝐶)⋃𝑐𝑜𝑡𝑜𝑝𝑦(𝐷)| 𝑠𝑖𝑚𝑐𝑜𝑡𝑜𝑝𝑦𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑅𝐴−𝐹𝐶𝑂 ~ 59 Flight Further dampeningpossible Flight-DE-UK Flight-DE-IT FlightFromHub FlightToHub FlightFrom+ToHub FRA-LCY FRA-LHR FRA-FCO

47. `Improved´ IntensionalCountingof Path Length - Jaccard 𝑐𝑜𝑡𝑜𝑝𝑦𝐶=𝐷 | 𝑖𝑠𝑎∗(𝐶,𝐷) Service 𝑠𝑖𝑚𝑐𝑜𝑡𝑜𝑝𝑦(𝐶,𝐷)~ |𝑐𝑜𝑡𝑜𝑝𝑦(𝐶) ∩𝑐𝑜𝑡𝑜𝑝𝑦(𝐷)||𝑐𝑜𝑡𝑜𝑝𝑦(𝐶)⋃𝑐𝑜𝑡𝑜𝑝𝑦(𝐷)| 𝑠𝑖𝑚𝑐𝑜𝑡𝑜𝑝𝑦𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑅𝐴−𝐹𝐶𝑂 ~ 59 Flight 𝑠𝑖𝑚𝑐𝑜𝑡𝑜𝑝𝑦𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑅𝐴−𝐿𝐶𝑌 ~ 48 Flight-DE-UK Flight-DE-IT FlightFromHub FlightToHub FlightFrom+ToHub FRA-LCY FRA-LHR FRA-FCO

48. Intension basedSimilarity Measurement Strengths Works somehow Weaknesses Bothpathcounting/Cotopyheavilysufferfrommodellingartefacts in theontology

49. CountingExtensions – Jaccard-likeMetrics 𝑠𝑖𝑚𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑙𝑖𝑔h𝑡𝑇𝑜𝐻𝑢𝑏 ~ |𝐹𝑅𝐴−𝐿𝐻𝑅 ∩𝐹𝑙𝑖𝑔h𝑡𝑇𝑜𝐻𝑢𝑏||𝐹𝑅𝐴−𝐿𝐻𝑅 𝐹𝑙𝑖𝑔h𝑡𝑇𝑜𝐻𝑢𝑏|=36 Service 𝑠𝑖𝑚𝐹𝑅𝐴−𝐿𝐻𝑅,𝐹𝑅𝐴−𝐿𝐶𝑌 ~ |𝐹𝑅𝐴−𝐿𝐻𝑅 ∩𝐹𝑅𝐴−𝐿𝐶𝑌||𝐹𝑅𝐴−𝐿𝐻𝑅 𝐹𝑅𝐴−𝐿𝐶𝑌|=04 Flight Flight-DE-UK Flight-DE-IT FlightFromHub FlightToHub FlightFrom+ToHub FRA-LCY FRA-LHR FRA-FCO Disjointnessincompatibility LH127 LH123 BA124 BA121 LH345 LH567 AI234 [Resnik ‘95-‘99]

51. Housecat – LionExtensionsareuncountable Ontologiessupposedtoabstractfromspecificextensions! Extensionsmaybe infinite

52. Class Syntax basedSimilarity Quitefrequent in theliterature Listedhere just forsakeofcompleteness, because… Class syntaxbasedsimilarityis equivalenceunsound

53. WhatshouldSimilarityDeliver? Critique [d‘Amato et al 2008]

54. Core criteriaforsimilaritymeasures– almostunchanged Positiveness: C,D sim(C,D)  0 Strong reflexivity:Csim(C,C) = 1 Upperbound: C,D sim(C,D)  1 Symmetry: C,D sim(C,D) = sim(D,C) Problem with strong reflexivity: FlightFromDEHub = Flight ∩∃from.(Hub ∩part.{DE}) FromHubAndFromDE = ∃from.Hub∩∃from.part.{DE} Reasoningisneededtodiscoverthat sim(FlightFromDEHub,FromHubAndFromDE) = 1 But problem: FlightFromDEHub = Flight ∩∃from.(Hub ∩part.{DE}) FromHubAndFromDE = ∃from.Hub∩∃from.part.{DE} Reasoningisneededtodiscoverthat sim(FlightFromDEHub,FromHubAndFromDE) = 1

55. Additional Ones in Ontologies! 5. PreventDisjointnessIncompatibility (seenbefore) 6. Equivalence Soundness: C,D,E DE  sim(C,D)=sim(C,E) Example: sim(Flight,FlightFromDEHub) = sim(Flight,FromHubAndFromDE) Proposition:Reflexivityandtriangleinequalityimplyequivalencesoundness

56. Additional Ones in Ontologies! 7. Monotonicity CL, DL, CU, DU, EU, E⊆L ∃H such thatCH, EH, DH  sim(C,D)  sim(C,E) U L C D E Myfeelingis: weneedmore! (continuity,…)

57. A Preliminary Solution Solution [d‘Amato et al 2010]

58. Core idea: Combine Cotopy & Extension-basedApproaches Cotopy-based: IntersectionattheLeastCommonSubsumer Extension-based: Count instances (orsubclasses) Venndiagramsindicates: sim(C,D) > sim(C,E) E gcs(C,D) C C D gcs(C,E)

59. Indirect (tentative) Indicationof Correctness Growingindexingtreebyclusteringwithnewsimilaritymeasure Comparingquerying time for different ontologiesusingthe original hierarchyandtheindexingtreederivedfromsimilaritymeasure Problem: similaritycomputationtoo expensive [d‘Amato et al 2010]

60. Whatto do now? Conclusion

62. Ontologiesprovidethemodelingbackboneandareevenfound in unexpectedplaces

63. Similaritymeasuresforontologiesexistandgive back someresults

64. Criteriaforsemanticsimilaritymeasuresare still in themaking

65. Thereis a lack oftheoryforontology-basedsimilarity

66. Thereis a lack ofefficientrealizationofontology-basedsimilarityTargeted Side Effect: ClarificationofSomeOftenMistakenUseofTerminologyaroundOntologies

67. Institut WeST – Web Science & Technologies ThankYou! Semantic Web Web Retrieval Interactive Web Multimedia Web Software Web eGovernment eMedia eScience eOrganizations eCitizen