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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

Log scale

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

6 0 Evidence Codes EL++ 321 112 112 59 Vertebrate Anatomy

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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]

"The Justificatory Structure of the NCBO BioPor...

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

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