International Semantic Web Conference (ISWC 2011)

1. Intro Indexation Extraction Repair Overlapping Evaluation
LogMap
Logic-based and Scalable Ontology Matching
Ernesto Jiménez-Ruiz Bernardo Cuenca Grau
Information Systems Group
Department of Computer Science, University of Oxford
International Semantic Web Conference
27th October 2011

2. Intro Indexation Extraction Repair Overlapping Evaluation
Outline
Introduction
Indexation
Mapping extraction
Mapping repair
Overlapping estimation
Evaluation

3. Intro Indexation Extraction Repair Overlapping Evaluation
Our approach in a nutshell
LogMap is a. . .
• Highly scalable ontology matching system,
can deal with very large ontologies containing tens (and even
hundreds) of thousands of classes (e.g. FMA, NCI and
SNOMED CT).
• Equipped with built-in reasoning and diagnosis capabilities.

4. Intro Indexation Extraction Repair Overlapping Evaluation
Motivation (I)
Why ontogy matching tools?
• To integrate and migrate data between applications.
• (Biomedical) ontologies are being developed by
different groups, and
• Use different classifications and naming schemas.

5. Intro Indexation Extraction Repair Overlapping Evaluation
Motivation (I)
Why ontogy matching tools?
• To integrate and migrate data between applications.
• (Biomedical) ontologies are being developed by
different groups, and
• Use different classifications and naming schemas.

6. Intro Indexation Extraction Repair Overlapping Evaluation
Motivation (II)
Challenges to be addressed
• Sufficient scalability to deal with large ontologies such as
FMA, NCI or SNOMED CT
• Detecting and repairing inconsistencies.
• Reasoning with O1 ∪ O2 ∪ M aggravates scalability problem
• Logic-based but scalable techniques

7. Intro Indexation Extraction Repair Overlapping Evaluation
Motivation (II)
Challenges to be addressed
• Sufficient scalability to deal with large ontologies such as
FMA, NCI or SNOMED CT
• Detecting and repairing inconsistencies.
• Reasoning with O1 ∪ O2 ∪ M aggravates scalability problem
• Logic-based but scalable techniques

8. Intro Indexation Extraction Repair Overlapping Evaluation
The anatomy of LogMap

9. Intro Indexation Extraction Repair Overlapping Evaluation
Outline
Introduction
Indexation
Mapping extraction
Mapping repair
Overlapping estimation
Evaluation

10. Intro Indexation Extraction Repair Overlapping Evaluation
Lexical indexation
Inverted Files
• Each entry is a “set” of words corresponding to entity labels
• Labels are extended with lexicons and stemming algorithms
Inverted index for NCI labels Index for NCI class URIs
Entry Cls ids Cls id URI
secretion 49901 49901 NCI:CellularSecretion
cellular,secretion 49901 37975 NCI:Trapezoid
cellular,secrete 49901 62999 NCI:TrapezoidBone
trapezoid 37975,62999 60791 NCI:Smegma
trapezoid,bone 62999
smegma 60791
Inverted index for FMA labels Index for FMA class URIs
Entry Cls ids Cls id URI
secretion 36792 36792 FMA:Secretion
bone,trapezoid 20948,47996 47996 FMA:Bone of Trapezoid
trapezoid 20948 20948 FMA:Trapezoid
smegma 60947 60947 FMA:Smegma

11. Intro Indexation Extraction Repair Overlapping Evaluation
Structural indexation
Interval labelling schema
• LogMap indexes the “classified” hierarchy.
• Each concept is associated with two preorders and intervals.
• The cost of typical taxonomical queries is reduced.

12. Intro Indexation Extraction Repair Overlapping Evaluation
Structural indexation
Interval labelling schema
• LogMap indexes the “classified” hierarchy.
• Each concept is associated with two preorders and intervals.
• The cost of typical taxonomical queries is reduced.

13. Intro Indexation Extraction Repair Overlapping Evaluation
Outline
Introduction
Indexation
Mapping extraction
Mapping repair
Overlapping estimation
Evaluation

14. Intro Indexation Extraction Repair Overlapping Evaluation
Computing initial anchors
Intersection of inverted files
Inverted index for NCI labels Index for NCI class URIs
Entry Cls ids Cls id URI
secretion 49901 49901 NCI:CellularSecretion
cellular,secretion 49901 37975 NCI:Trapezoid
cellular,secrete 49901 62999 NCI:TrapezoidBone
trapezoid 37975,62999 60791 NCI:Smegma
trapezoid,bone 62999
smegma 60791
Inverted index for FMA labels Index for FMA class URIs
Entry Cls ids Cls id URI
secretion 36792 36792 FMA:Secretion
bone,trapezoid 20948,47996 47996 FMA:Bone of Trapezoid
trapezoid 20948 20948 FMA:Trapezoid
smegma 60947 60947 FMA:Smegma

15. Intro Indexation Extraction Repair Overlapping Evaluation
Computing initial anchors
Intersection of inverted files
Entry FMA ids NCI ids Mappings
secretion 36792 49901 FMA:Secretion ≡ NCI:CellularSecretion
smegma 60947 60791 FMA:Smegma ≡ NCI:Smegma
trapezoid 20948
37975, FMA:Trapezoid ≡ NCI:Trapezoid
62999 FMA:Trapezoid ≡ NCI:TrapezoidBone
trapezoid,bone
20948,
62999
FMA:Trapezoid ≡ NCI:TrapezoidBone
47996 FMA:Bone of Trapezoid ≡ NCI:TrapezoidBone

16. Intro Indexation Extraction Repair Overlapping Evaluation
Computation of confidence values
Based on. . .
• The string based algorithm ISUB
• A principle of locality
• Correct mappings (C1 ≡ C2) are likely to have similar scopes
• ISUB is used to “map” the corresponding scopes of C1 and C2
• Dice’s coeff. (adapted) provides the similarity between scopes

17. Intro Indexation Extraction Repair Overlapping Evaluation
Computation of confidence values
FMA:Trapezoid ≡ NCI:Trapezoid (no scope) vs
FMA:Trapezoid ≡ NCI:TrapezoidBone (with scope)

18. Intro Indexation Extraction Repair Overlapping Evaluation
Mapping discovery
Exploiting initial anchors
• Also based on the principle of locality
• If C1 ≡ C2 is a correct anchor. . .
• . . . their respective scopes are likely to have new mappings

19. Intro Indexation Extraction Repair Overlapping Evaluation
Mapping discovery
Exploiting initial anchors

20. Intro Indexation Extraction Repair Overlapping Evaluation
Outline
Introduction
Indexation
Mapping extraction
Mapping repair
Overlapping estimation
Evaluation

21. Intro Indexation Extraction Repair Overlapping Evaluation
Propositional Horn representation
• LogMap represents the “extended” hierarchies as
Propositional Horn clauses
• This is key to LogMap’s scalability
Propositional FMA (P1) Propositional NCI (P2)
(1) Smegma → Secretion (8) Smegma → ExocrineGlandFluid
(2) Secretion → PortionBodySusbstance (9) ExocrineGlandFluid → Anatomy
(3) PortionBodySusbstance → AnatomicalEntity (10) CellularSecretion → TransmembraneTransport
Computed mappings (PM ) (11) TransmembraneTransport → TransportProcess
(m4) FMA:Secretion → NCI:CellularSecretion (12) TransportProcess → BiologicalProcess
(m5) NCI:CellularSecretion → FMA:Secretion (13) Anatomy ∧ BiologicalProcess → false
(m6) FMA:Smegma → NCI:Smegma (14) ExocrineGlandFluid ∧ ExfolCells → Smegma
(m7) NCI:Smegma → FMA:Smegma

22. Intro Indexation Extraction Repair Overlapping Evaluation
Propositional Horn representation
• LogMap represents the “extended” hierarchies as
Propositional Horn clauses
• This is key to LogMap’s scalability
Propositional FMA (P1) Propositional NCI (P2)
(1) Smegma → Secretion (8) Smegma → ExocrineGlandFluid
(2) Secretion → PortionBodySusbstance (9) ExocrineGlandFluid → Anatomy
(3) PortionBodySusbstance → AnatomicalEntity (10) CellularSecretion → TransmembraneTransport
Computed mappings (PM ) (11) TransmembraneTransport → TransportProcess
(m4) FMA:Secretion → NCI:CellularSecretion (12) TransportProcess → BiologicalProcess
(m5) NCI:CellularSecretion → FMA:Secretion (13) Anatomy ∧ BiologicalProcess → false
(m6) FMA:Smegma → NCI:Smegma (14) ExocrineGlandFluid ∧ ExfolCells → Smegma
(m7) NCI:Smegma → FMA:Smegma

23. Intro Indexation Extraction Repair Overlapping Evaluation
Unsatisfiability checking
Propositional Horn SAT with Dowling-Gallier (D-G)
• LogMap implements the SAT algorithm D-G
• D-G is call for every class C and the propositional theory PC :
• the rule (true → C);
• the propositional representations P1 and P2 of the input
ontologies; and
• the propositional representation PM of the mappings.

24. Intro Indexation Extraction Repair Overlapping Evaluation
Unsatisfiability checking

25. Intro Indexation Extraction Repair Overlapping Evaluation
Characteristics of our class satisfiability problem
Our class satisfiability algorithm is . . .
• sound
• If LogMap finds a class unsatisfiable, it is indeed unsatisfiable.
• worst-case linear in the size of the (classified) ontologies.
• incomplete, but incompleteness is mitigated:
• Most of the relevant non-propositional reasoning is already
performed when classifying input ontologies independently
• Mappings are Horn propositional axioms
• Most new entailments caused by the mappings likely to be
computable using Horn propositional reasoning only

26. Intro Indexation Extraction Repair Overlapping Evaluation
Computing repair plans
Recording conflictive mappings
• LogMap extends D-G to record conflictive mappings
• For example: {m4, m5, m6, m7}
• Equivalence mappings are split into two propositional rules.
• Repairs may only consider one of the rules.

27. Intro Indexation Extraction Repair Overlapping Evaluation
Computing repair plans
Recording conflictive mappings
• LogMap extends D-G to record conflictive mappings
• For example: {m4, m5, m6, m7}
• Equivalence mappings are split into two propositional rules.
• Repairs may only consider one of the rules.

28. Intro Indexation Extraction Repair Overlapping Evaluation
Computing repair plans
A “greedy” repair algorithm
• The repairs R are computed in order for each unsat. class
• The algorithm identifies subsets of the conflictive mappings of
increasing size, and stops when a repair is found.
• LogMap finds all repairs of “smallest” size.
• For example: R1 = {m4} and R2 = {m6}
• The repair with less confidence is selected .

29. Intro Indexation Extraction Repair Overlapping Evaluation
Computing repair plans
A “greedy” repair algorithm
• The repairs R are computed in order for each unsat. class
• The algorithm identifies subsets of the conflictive mappings of
increasing size, and stops when a repair is found.
• LogMap finds all repairs of “smallest” size.
• For example: R1 = {m4} and R2 = {m6}
• The repair with less confidence is selected .

30. Intro Indexation Extraction Repair Overlapping Evaluation
Repair of property anchors
• Also relies on the intersection of inverted files
• However their repair is not yect integrated with D-G
• Currently, a candidate mapping between p1 and p2 isvalid only
if both their respective domains D1, D2 and ranges R1, R2 are
“compatible”.
• That is, mappings D1 ≡ D2 and R1 ≡ R2 do not lead to
unsatisfiability.

31. Intro Indexation Extraction Repair Overlapping Evaluation
Repair of property anchors
• Also relies on the intersection of inverted files
• However their repair is not yect integrated with D-G
• Currently, a candidate mapping between p1 and p2 isvalid only
if both their respective domains D1, D2 and ranges R1, R2 are
“compatible”.
• That is, mappings D1 ≡ D2 and R1 ≡ R2 do not lead to
unsatisfiability.

32. Intro Indexation Extraction Repair Overlapping Evaluation
Outline
Introduction
Indexation
Mapping extraction
Mapping repair
Overlapping estimation
Evaluation

33. Intro Indexation Extraction Repair Overlapping Evaluation
Overlapping estimation
• LogMap also returns two fragments representing the
overlapping between the input ontologies
• Correct mappings are unlikely to involve classes outside these
fragments.
• The overlapping is performed in two steps:
• Computation of ‘weak’ anchors
• Module extraction

34. Intro Indexation Extraction Repair Overlapping Evaluation
Overlapping estimation
Computation of ‘weak’ anchors
Extended inverted index for FMA Index for FMA class URIs
Lexical entry Cls ids Cls id Cls name
ductule,efferent,epithelium 45211 45211 EpitheliumOfEfferentDuctuleOfTestis
common,branch,artery 1170,7842 1170 BranchOfCommonCochlearArtery
7842 BranchOfCommonInterosseousArtery
Extended inverted index for NCI Index for NCI class URIs
Lexical entry Cls ids Cls id Cls name
ductule,efferent,epithelium 27924 27924 EfferentDuctuleEpithelium
common,branch,artery 1204,8087, 1204 CommonCarotidArteryBranch
27727 8087 CommonIliacArteryBranch
27727 CommonFemoralArteryBranch
• Not valid (in general) as candidate mappings.
• Useful to detect concepts with similar lexicon

35. Intro Indexation Extraction Repair Overlapping Evaluation
Overlapping estimation
Computation of ‘weak’ anchors
Extended inverted index for FMA Index for FMA class URIs
Lexical entry Cls ids Cls id Cls name
ductule,efferent,epithelium 45211 45211 EpitheliumOfEfferentDuctuleOfTestis
common,branch,artery 1170,7842 1170 BranchOfCommonCochlearArtery
7842 BranchOfCommonInterosseousArtery
Extended inverted index for NCI Index for NCI class URIs
Lexical entry Cls ids Cls id Cls name
ductule,efferent,epithelium 27924 27924 EfferentDuctuleEpithelium
common,branch,artery 1204,8087, 1204 CommonCarotidArteryBranch
27727 8087 CommonIliacArteryBranch
27727 CommonFemoralArteryBranch
• Not valid (in general) as candidate mappings.
• Useful to detect concepts with similar lexicon

36. Intro Indexation Extraction Repair Overlapping Evaluation
Overlapping estimation
Module extraction
• Classes involved in (weak) mappings are used as the module
signature.
• Concretely, locality-based modules have been used.

37. Intro Indexation Extraction Repair Overlapping Evaluation
Outline
Introduction
Indexation
Mapping extraction
Mapping repair
Overlapping estimation
Evaluation

38. Intro Indexation Extraction Repair Overlapping Evaluation
Evaluation
Used ontologies
• SNOMED CT Jan. 2009 version (306, 591 classes)
• NCI version 08.05d (66, 724 classes)
• FMA version 2.0 (78, 989 classes)
• OAEI ontologies: NCI Anatomy (3, 304 classes), Mouse
Anatomy (2, 744 classes), conference and benchmarck
ontologies (< 200 classes).

39. Intro Indexation Extraction Repair Overlapping Evaluation
Evaluation
Tasks
• Repair of gold standards
• Matching large ontologies
• Overlapping estimation
• Participation in the OAEI 2011

40. Intro Indexation Extraction Repair Overlapping Evaluation
Repair of gold standards
• UMLS as a reference to align FMA-NCI, FMA-SNOMED and
SNOMED-NCI
• The OAEI 2010 anatomy track gold standard
GS Mappings Repaired Mappings
Ontologies Total Unsat. Total v Time (s)
FMA-NCI 3,024 655 (96%) 2,898 78 10.6
FMA-SNOMED 9,072 6,179 (89%) 8,111 1,619 81.4
SNOMED-NCI 19,622 20,944 (93%) 18,322 837 812.4
Mouse-NCIAnat 1,520 0 1,520 - -

41. Intro Indexation Extraction Repair Overlapping Evaluation
Repair of gold standards
Non reported/repaired unsatisfiable class

42. Intro Indexation Extraction Repair Overlapping Evaluation
Matching large ontologies
Mappings computed by LogMap
Found Mapp. Output Mapp. Time (s)
Ontologies Total Unsat. Total v Anchors Total
FMA-NCI 3,185 597 (94%) 3,000 43 28.3 69.8
FMA-SNOMED 2,068 570 (99%) 2,059 32 35.6 92.2
SNOMED-NCI 14,250 10,452 (95%) 13,562 1,540 528.6 1370.0

43. Intro Indexation Extraction Repair Overlapping Evaluation
Matching large ontologies
Precision and recall w.r.t. Gold Standard
Found Mappings Output Mappings
Ontologies Precision Recall F-score Precision Recall F-score
FMA-NCI 0.767 0.843 0.803 0.811 0.840 0.825
FMA-SNOMED 0.767 0.195 0.312 0.771 0.195 0.312
SNOMED-NCI 0.753 0.585 0.659 0.786 0.582 0,668

44. Intro Indexation Extraction Repair Overlapping Evaluation
Matching large ontologies
Lexical similarity of GS mappings
GS ISUB ≥ 0.95 GS ISUB ≥ 0.80 GS ISUB ≥ 0.50
Ontologies % Mapp. Recall % Mapp. Recall % Mapp. Recall
FMA-NCI 88% 0.96 93% 0.90 97% 0.87
FMA-SNOMED 21% 0.95 64% 0.30 92% 0.21
SNOMED-NCI 62% 0.94 75% 0.77 89% 0.65

45. Intro Indexation Extraction Repair Overlapping Evaluation
Overlapping estimation
Overlapping computed by LogMap
Ontologies Overlapping for O1 Overlapping for O2
O1-O2 O0
1 % O1 Recall O0
2 % O2 Recall
FMA-NCI 6,512 8% 0.95 12,867 19% 0.97
FMA-SNOMED 20,278 26% 0.92 50,656 17% 0.94
SNOMED-NCI 70,705 23% 0.86 33,829 51% 0.96

46. Intro Indexation Extraction Repair Overlapping Evaluation
Participation in the OAEI Campaign 2011
Anatomy track (2nd out of 6)
System Precision Recall F-score Time (s) Incoherence
AgrMaker 0.943 0.892 0.917 634 -
LogMap 0.948 0.846 0.894 24 0%
CODI 0.965 0.825 0.889 1,890 -
Lily 0.814 0.734 0.772 563 -
AROMA 0.742 0.625 0.679 39 -
CSA 0.465 0.757 0.576 4,685 -

47. Intro Indexation Extraction Repair Overlapping Evaluation
Participation in the OAEI Campaign 2011
Conference track (3rd out of 14)
System Precision Recall F-score Incoherence
YAM++ 0.78 0.56 0.65 -
CODI 0.74 0.57 0.64 -
LogMap 0.84 0.5 0.63 0%
AgrMaker 0.65 0.59 0.62 -
MassMatch 0.83 0.42 0.56 -
CSA 0.5 0.6 0.55 -
CIDER 0.64 0.45 0.53 -
. . . . . . . . . . . . . . .

48. Intro Indexation Extraction Repair Overlapping Evaluation
Participation in the OAEI Campaign 2011
Benchmark track (8 out of 14)
• LogMap relies on the lexical similarities
• LogMap (Precision: 0.99, Recall: 0.50, F-measure: 0.67)
• MapSSS (Precision: 0.97, Recall: 0.64, F-measure: 0.77)

49. Conclusions and future work
• LogMap is a highly scalable ontology matching tool with
builtin reasoning and diagnosis capabilities.
• LogMap is the only matching system that has shown to be
able to deal with ontologies containing tens and hundreds
of thousands of classes.
• There is still plenty of room for improvement.
• LogMap 2.0
• Major improvements w.r.t. the current version
• Will be soon available for download.

50. Conclusions and future work
• LogMap is a highly scalable ontology matching tool with
builtin reasoning and diagnosis capabilities.
• LogMap is the only matching system that has shown to be
able to deal with ontologies containing tens and hundreds
of thousands of classes.
• There is still plenty of room for improvement.
• LogMap 2.0
• Major improvements w.r.t. the current version
• Will be soon available for download.

51. Questions?
Contact
• LogMap Project:
http://www.cs.ox.ac.uk/isg/projects/LogMap/
• ernesto.jimenez.ruiz@gmail.com
Thank you for your attention
Acknowledgements
• Funding support of the Royal Society and EPRSC.
• Organizers of the OAEI campaign.
• R. Berlanga and V. Nebot.