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"The Justificatory Structure of the NCBO BioPortal Ontologies" @ ISWC 2011, Bonn, Germany

spbail
October 26, 2011

"The Justificatory Structure of the NCBO BioPortal Ontologies" @ ISWC 2011, Bonn, Germany

My talk on the justificatory structure of the NCBO BioPortal ontologies, held at the International Semantic Web Conference 2011 in Bonn, Germany.

spbail

October 26, 2011
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  1. Samantha Bail, Bijan Parsia, Uli Sattler
    The University of Manchester, UK
    The Justi catory Structure of the
    NCBO BioPortal Ontologies
    26/10/2011, ISWC 2011

    View full-size slide

  2. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Background: OWL Justi cations
    2
    entails
    ontology
    (set of axioms)
    entailment
    (axiom)
    A justi cation for an entailment η is a minimal subset of
    the ontology which is sufficient for the entailment to hold.
    De nition
    • Justi cations pinpoint the causes for an entailment
    ‣ We deal with a potentially smaller set of axioms
    ‣ Restrict attention to the relevant axioms

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  3. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Background: OWL Justi cations
    3
    entails
    justi cation
    (set of axioms)
    entailment
    (axiom)
    A justi cation for an entailment η is a minimal subset of
    the ontology which is sufficient for the entailment to hold.
    De nition
    • Justi cations pinpoint the causes for an entailment
    ‣ We deal with a potentially smaller set of axioms
    ‣ Restrict attention to the relevant axioms

    View full-size slide

  4. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Background: OWL Justi cations
    4
    entails
    justi cation
    (set of axioms)
    entailment
    (axiom)
    • Best understood explanation type
    ‣ for ontology debugging (understanding & xing errors)
    ‣ for ontology comprehension
    De nition
    A justi cation for an entailment η is a minimal subset of
    the ontology which is sufficient for the entailment to hold.

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  5. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Background: OWL Justi cations
    5
    entailment
    (axiom)
    • A single entailment can have more than 1 justi cation
    ‣ Potentially exponentially many justi cations
    ‣ Up to several thousand found in real-life ontologies
    De nition
    A justi cation for an entailment η is a minimal subset of
    the ontology which is sufficient for the entailment to hold.

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  6. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Multiple Justi cations Complicate Debugging
    • 1 justi cation for 1 entailment: OK (well, depends!)
    • Multiple justi cations for 1 entailment:
    ‣ We can consider them one by one...
    ‣ ...but this might lead to non-optimal repair!
    • Multiple justi cations for multiple entailments
    ‣ Where to start?
    • Dozens or hundreds: Give up!
    ‣ Cognitive overload for users
    6

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  7. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    • Thus far only little effort to tackle this problem
    • Approaches based on relations between justi cations:
    ‣ root & derived justi cations [1,2]
    ‣ axiom power (Swoop tool [3])
    • Can we get a more complete picture?
    7
    [1] A. Kalyanpur, B. Parsia, E. Sirin, and J. Hendler. Debugging unsatis able classes in OWL ontologies. J. Web Semantics, 2005.
    [2] T. Meyer, K. Moodley, and I. Varzinczak. First steps in the computation of root justi cations. In Proc. of ARCOE-10, 2010.
    [3] A. Kalyanpur, B. Parsia, E. Sirin, B. C. Grau, and J. A. Hendler. Swoop: A web ontology editing browser. J. Web Semantics, 2006.
    Multiple Justi cations Complicate Debugging

    View full-size slide

  8. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    • Thus far only little effort to tackle this problem
    • Approaches based on relations between justi cations:
    ‣ root & derived justi cations [1,2]
    ‣ axiom power (Swoop tool [3])
    • Can we get a more complete picture?
    7
    The set of structural relations between justi cations for
    single and multiple entailments in an ontology.
    Justi catory Structure
    [1] A. Kalyanpur, B. Parsia, E. Sirin, and J. Hendler. Debugging unsatis able classes in OWL ontologies. J. Web Semantics, 2005.
    [2] T. Meyer, K. Moodley, and I. Varzinczak. First steps in the computation of root justi cations. In Proc. of ARCOE-10, 2010.
    [3] A. Kalyanpur, B. Parsia, E. Sirin, B. C. Grau, and J. A. Hendler. Swoop: A web ontology editing browser. J. Web Semantics, 2006.
    Multiple Justi cations Complicate Debugging

    View full-size slide

  9. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Justi catory Structure: Motivation
    1. How prevalent are multiple justi cations?
    2. Can we make use of structural relationships for...
    a) improved debugging support?
    b) understanding the ontology?
    3. Can we derive useful metrics from the justi catory
    structure?
    8

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  10. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Justi catory Structure: Representation
    • JGraph framework
    ‣ Justi cations and their relations represented as graph
    ‣ Nodes = {entailments, axioms in justi cations, justi cations}
    ‣ Edges = {axiom occurs in justi cation, justi cation for entailment}
    9
    ax9
    just2
    ax7
    just3
    ax6 just1
    ax8
    ax10
    ax2 just2

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  11. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Justi catory Structure: Structural Aspects
    • Justi cations per entailment
    • Size of justi cations (number of axioms)
    • Self-justi cations (J = η)
    • Trivial entailments (O \ η  ⊭η)
    • Graph components
    ‣ number
    ‣ size
    10
    ax9
    just2
    ax7
    just3
    ax6 just1
    ax8
    ax10
    ax2 just2

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  12. S. Bail, B. Parsia, U. Sattler
    • Axiom power (number of justi cations an axiom occurs in)
    • % of ontology axioms in justi cations
    • Overlapping justi cations
    ‣ 1 axiom (➞ axiom power)
    ‣ multiple axioms
    ‣ subsets (= root&derived)
    ‣ equality
    The Justi catory Structure of the NCBO BioPortal Ontologies
    Justi catory Structure: Structural Aspects
    11
    ax9
    just2
    ax7
    just3
    ax6 just1
    ax8
    ax10
    ax2 just2

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  13. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Work ow
    12
    Input:
    218 BioPortal
    OWL ontologies
    Compute entailments
    (atomic subsumptions)
    Prune ontologies
    with unsatis able classes,
    imports, only trivial entailments
    Compute justi cations
    for entailments
    Generate JGraphs for
    remaining 35 ont.
    Compute statistics

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  14. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Work ow
    12
    Input:
    218 BioPortal
    OWL ontologies
    Compute entailments
    (atomic subsumptions)
    Prune ontologies
    with unsatis able classes,
    imports, only trivial entailments
    Compute justi cations
    for entailments
    Generate JGraphs for
    remaining 35 ont.
    Compute statistics
    “Trivial”:
    O \ η  ⊭η  for all η

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  15. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Basic stats:
    ‣ 35 ontologies (ranging from 85 to ~170,000 axioms)
    ‣ 12,010 non-trivial entailments
    ‣ 7,176 distinct non-self-justi cations
    ‣ containing 14,616 axioms
    ‣ 2,340 self-justi cations
    • No correlations between
    ‣ ontology size and number of entailments (ρ=0.18)
    ‣ ontology size and number of justi cations (ρ=-0.21)
    13

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  16. Ontology DL Axioms Entailments Non-Self-Just Self-Just
    Vertebrate EL++ 307 6 6 0
    Evidence Codes EL++ 321 112 112 59

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  17. Ontology DL Axioms Entailments Non-Self-Just Self-Just
    Vertebrate EL++ 307 6 6 0
    Evidence Codes EL++ 321 112 112 59
    Vertebrate Anatomy

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  18. Ontology DL Axioms Entailments Non-Self-Just Self-Just
    Vertebrate EL++ 307 6 6 0
    Evidence Codes EL++ 321 112 112 59
    ax34
    just5
    ax35 ax29
    just2
    ax19
    just1
    just6
    ax23
    just4
    ax24
    ax32
    just3
    ax22
    ax28
    ax27 ax26 ax21
    ax25
    ax30 ax33 ax31
    ax36 ax20
    Vertebrate Anatomy

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  19. Ontology DL Axioms Entailments Non-Self-Just Self-Just
    Vertebrate EL++ 307 6 6 0
    Evidence Codes EL++ 321 112 112 59
    Evidence Codes (part)
    ax34
    just5
    ax35 ax29
    just2
    ax19
    just1
    just6
    ax23
    just4
    ax24
    ax32
    just3
    ax22
    ax28
    ax27 ax26 ax21
    ax25
    ax30 ax33 ax31
    ax36 ax20
    Vertebrate Anatomy

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  20. Ontology DL Axioms Entailments Non-Self-Just Self-Just
    Vertebrate EL++ 307 6 6 0
    Evidence Codes EL++ 321 112 112 59
    ax402
    just47
    117
    ax255
    just4
    just58 just107
    ax254
    just65 just120
    ax232
    just56
    ax238
    just33
    just84
    just98 just114
    ax262
    just2
    ax235
    just92
    ax264
    just14
    ax278
    just168
    ax236
    just133
    ax273
    just45
    ax295
    just15
    ax277
    just131
    ax263
    just23
    just76
    ax288
    just9
    49
    41
    ax275
    just110
    ax289
    just130
    ax260 ax243
    just85
    ax237
    ax244
    just70
    ax259
    just18
    a
    ax233
    just6
    ax256 ax365 ax239
    ax403 ax410 ax399 ax355
    ax261 ax421
    ax279
    Evidence Codes (part)
    ax34
    just5
    ax35 ax29
    just2
    ax19
    just1
    just6
    ax23
    just4
    ax24
    ax32
    just3
    ax22
    ax28
    ax27 ax26 ax21
    ax25
    ax30 ax33 ax31
    ax36 ax20
    Vertebrate Anatomy

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  21. Ontology DL Axioms Entailments Non-Self-Just Self-Just
    Vertebrate EL++ 307 6 6 0
    Evidence Codes EL++ 321 112 112 59
    ax299
    just132
    ax257
    just115
    ax402
    just47
    just117
    ax309
    just77
    ax294
    just51
    ax388
    just151
    ax384
    just88
    just90
    ax217
    just137 just157
    ax245
    just106
    ax274
    just100
    ax283
    just17
    just145
    ax280
    just3
    just108 just116
    ax318
    just155
    ax408
    just102
    just126
    ax255
    just4
    just58
    ax319
    just31 just35 just49
    just109
    just107 just146
    ax254
    just65 just120
    ax392
    just111
    ax311
    just158
    ax232
    just56
    ax285
    just87
    ax291
    just154
    ax282
    just29
    ax357
    just69
    ax383
    just32
    ax238
    just33
    just84
    just98 just114
    ax331
    just39
    ax262
    just2
    ax304
    just5
    just136 just167
    ax248
    just170
    ax328
    just150
    ax235
    just92
    ax264
    just14
    ax372
    just156
    ax251
    just22 just46
    just89
    ax338
    ax334
    just7
    ax353
    just147 just166
    ax362
    just105
    ax381
    just38
    just68
    ax278
    just168
    ax413
    just113
    ax241
    just129
    ax236
    just133
    ax415
    just8 just37
    ax406
    just138
    ax290
    just78
    ax218
    just160
    ax273
    just45
    ax360
    just11
    ax296
    just71
    ax295
    just15
    ax336
    just153
    ax341
    just72
    just135
    ax420
    just73
    ax416
    ax224
    just54
    ax242
    just16
    ax348
    just171
    ax220
    just30 just63
    ax356
    just57
    ax277
    just131
    ax400
    just144
    ax286
    just64
    ax391
    just112
    ax276
    just143
    ax407
    just149
    ax377
    just148
    ax322
    just28 just142
    ax398
    just83
    ax263
    just23
    just76
    ax225
    just79
    ax271
    just21 just62
    just162
    ax359
    just118
    ax229
    just24
    ax369
    ax234
    just13
    ax230
    just96
    ax288
    just9
    ax221 ax323
    ax301
    just140
    ax352
    just34
    ax343
    just60
    ax333
    just128
    ax249
    just41
    ax412
    just164
    ax247
    just53
    ax379
    just125
    ax216
    just80
    ax314
    just161
    ax292
    just42
    ax306
    just82
    just127
    ax270 ax258
    just43
    ax376
    just152
    ax246
    just123
    ax275
    just110
    ax380
    ax289
    just130
    ax347
    just139
    ax227
    just93
    ax350
    just97
    ax397
    just25
    ax317
    just20
    ax419
    just66
    ax298
    just36 just104
    ax260
    ax267
    just19 just124
    ax240
    just95
    ax313
    just74
    ax335
    just119
    ax389
    just52
    ax344
    just86
    ax354
    just67
    ax243
    just85
    ax340
    ax265
    just134
    ax363
    just159
    ax373
    just101
    ax326
    just75
    ax297
    just163
    ax250
    just169
    ax345
    just55
    ax315
    just44
    ax325
    ax237
    ax222
    just48
    ax244
    just70
    ax303 ax316
    just61
    ax252
    ax393 ax307
    ax266
    just59
    ax268 ax259
    just18
    ax367 ax212
    just121
    ax370
    just91
    ax366
    just122
    ax330
    just99
    ax390
    just94
    ax214
    just12
    ax395
    ax387
    just27
    ax226
    just10
    ax302
    just81
    ax404
    ax411
    just26
    ax321
    just50
    ax385
    ax233
    just6
    ax310
    just40
    ax281
    just141
    ax284
    just1
    ax213
    just165
    ax287
    just103
    ax337
    ax256
    ax417 ax361
    ax269
    ax371 ax365 ax231
    ax324
    ax327
    ax223 ax374
    ax239
    ax332 ax422
    ax403 ax320
    ax346
    ax410
    ax272 ax382 ax228
    ax342
    ax253
    ax386 ax418
    ax399 ax375
    ax355
    ax396
    ax364 ax261
    ax414 ax308 ax409
    ax215
    ax421 ax358
    ax305
    ax300 ax351
    ax293 ax219
    ax312 ax401
    ax394 ax405
    ax368
    ax378
    ax329 ax349 ax279
    ax339
    Evidence Codes (part)
    ax34
    just5
    ax35 ax29
    just2
    ax19
    just1
    just6
    ax23
    just4
    ax24
    ax32
    just3
    ax22
    ax28
    ax27 ax26 ax21
    ax25
    ax30 ax33 ax31
    ax36 ax20
    Vertebrate Anatomy

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  22. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Multiple justi cations
    ‣ occur in 71.4% of ontologies
    ‣ 1.3 justi cations per entailment
    (without self-justi cations)
    ‣ max: 236 (Gene Ontology Ext.)
    19

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  23. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Multiple justi cations
    ‣ occur in 71.4% of ontologies
    ‣ 1.3 justi cations per entailment
    (without self-justi cations)
    ‣ max: 236 (Gene Ontology Ext.)
    19
    >2 justi cations
    14.3%
    (1, 2] justi cations
    57.1%
    1 justi cation
    28.6%
    Average justi cations per
    entailment across ontologies

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  24. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Axiom power
    ‣ avg axiom power 3.0 (axiom occurs
    in 3 justi cations)
    ‣ max 510 justi cations for 1 axiom
    20

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  25. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Axiom power
    ‣ avg axiom power 3.0 (axiom occurs
    in 3 justi cations)
    ‣ max 510 justi cations for 1 axiom
    20
    3%
    34%
    51%
    11%
    Average axiom power
    (proportion of ontologies)
    exactly 1
    >1, <=2
    >2, <=10
    > 10

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  26. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Justi cation equality
    ‣ 51% of justi cations have more than 1 entailment
    ‣ average: 2.17 entailments for a justi cation
    21

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  27. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Justi cation equality
    ‣ 51% of justi cations have more than 1 entailment
    ‣ average: 2.17 entailments for a justi cation
    21
    Basic Formal Ontology (BFO)

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  28. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    BioPortal Survey: Results
    • Justi cation equality
    ‣ 51% of justi cations have more than 1 entailment
    ‣ average: 2.17 entailments for a justi cation
    21
    Basic Formal Ontology (BFO)

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  29. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Conclusions
    1. How prevalent are multiple justi cations?
    ‣ 71.4% of surveyed ontologies have multiple
    justi cations
    ‣ Small number of multiple justi cations on average
    ‣ Size & DL expressivity of ontology are no indicators for
    justi catory structure
    22

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  30. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Conclusions
    2. a) Can we make use of structural relationships for
    improved debugging support?
    ‣ Large degree of interaction between justi cations
    ‣ Considering entailments and justi cations in isolation
    ignores these relationships
    ‣ Optimal repair strategies: Look at multiple justi cations
    ‣ Future work: Explore possible repair strategies
    23

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  31. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Conclusions
    2. b) Can we make use of structural relationships for
    understanding the ontology?
    ‣ Self-justi cations, equal justi cations, axiom power,
    activity... make implicit structure explicit
    ‣ Representation helps exploring multiple justi cations
    ‣ This may support understanding
    24

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  32. S. Bail, B. Parsia, U. Sattler The Justi catory Structure of the NCBO BioPortal Ontologies
    Conclusions
    3. Can we derive useful metrics from the justi catory
    structure?
    ‣ See Vertebrate Anatomy vs Evidence Codes
    ‣ More information than counting axioms
    ‣ DL expressivity does not imply complexity
    ‣ Structural aspects may be indicators for richness of an
    ontology
    25

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  33. ax107
    just12
    ax118
    just15
    just18
    ax85 just24
    ax123
    just3
    ax114
    ax94
    ax105 just27
    ax84
    just10
    ax95 just26
    ax132
    just8
    ax103
    ax74
    ax87
    just9
    ax129
    ax97
    just21
    ax100
    just23
    ax121
    just4
    ax86
    ax88 just16
    ax99 just13
    ax77
    just11
    ax108
    ax128
    ax104
    just2
    ax124
    ax110
    ax82
    just20
    ax79
    ax140
    ax127
    ax101
    ax120 just19
    ax122
    ax92
    ax102
    ax90
    ax75
    ax133
    ax113 just25
    ax98
    ax119
    ax76 just5
    ax106 just1
    ax91
    ax78
    ax126
    ax73
    ax96
    ax93
    ax72
    ax130
    ax136
    ax80
    ax125
    ax131
    Thank you!
    [email protected]

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