Christian Meilicke

1
Repairing Ontology Mappings

• Christian Meilicke
• Heiner Stuckenschmidt

Andrei Tamilin
July 25, 2007
2
Motivation

• Semantic Heterogeneity
• Naturally multi-ontological semantic web
• Mapping
• A solution for overcoming heterogeneity
• Matching
• Completely automatic
• Error free

3
Outline

• Matching ? Mapping ? Errors
• Debugging/Repairing Task
• Mapping Formalization and Evaluation with DDL
• Debugging/Repairing Method
• Experimental Evaluation
• Conclusion

4
Matching
O
Resources (e.g., grammar, thesauri, )
Matching system (e.g., Coma, Falcon, HMatch,
SMatch, CtxMatch, etc.)
M
O
Parameters (e.g., thresholds, )
5
Mapping

• Mapping elements are tuples (e,e,r,c)
• e and e are entities of mapped ontologies
• r is a relation between entities, e.g., , ,
  
• c is a confidence measure

6
Example
(Tutorial, Tutorial, , 0.99) (Social_Event,
Social_event, , 0.99) (Paper, Paper, ,
0.96) (Poster_Paper, Poster, , 0.82) (PC_Member,
Member_PC, , 0.81) (Regular_Paper, Regular, ,
0.81) (PC_Chair, Chair_PC, , 0.79) (Paper_Author,
Author, , 0.76) (Review, Reviewing_event, ,
0.74) (Camera_Ready_Pape, Camera_Ready_event, ,
0.70) (Conference_Participant, Participant, ,
0.71) etc.
7
Mapping cont.

• Mapping elements are tuples (e,e,r,c)
• e and e are entities of mapped ontologies
• r is a relation between entities, e.g., , ,
  
• c is a confidence measure
• Mapping is not always completely correct
• Leads to incorrect utilization of mapping, e.g.,
  in query answering
• Detect and fix defective elements in mapping is
  an important issue

8
Debugging/Repairing Task

• Given a mapping C, and a reference mapping G, let
  us define subsets of C
• C C ? G
• C C G
• Debugging
• Determine for each c?C, wheather c? C or c? C
• Repairing
• Delete all elements of C from C
• Standard approach uses ?onfidence threshold
• Where to put the threshold?
• Confidence value is not always accurate

9
Challenges
Challenges / Our Approach

• How to figure out automatically that a mapping is
  erroneous
• encode in DDL and use logical reasoning to
  analyze the impact of mapping on ontologies it
  connects
• the claim a mapping, if correct, does not cause
  any inconsistency (unsatisfiability) in mapped
  ontologies
• How to figure out automatically which are
  defective mapping elements
• define a debugging procedure by adapting Reiter
  diagnosis

10
Distributed Description Logics - I

• Captures the case of multiple ontologies Oi
  pairwise linked by directed semantic mappings Mij
• Ontologies DLs
• Mappings bridge rules

11
Distributed Description Logics - II

• Principle property of bridge rules is their
  ability to propagate knowledge across ontologies

O1
O2
Participant
Person
isA
isA
isA
Organizer
Volunteer

• DL tableaux propagation rule DDL tableaux
  reasoning

12
Formalization of Mapping in DDL
O1
O2
(Paricipant, Person, , 0.9)
Participant
Person
Effect on O2
Participant
Person
Effect on O1
Participant
Person
13
Effect of Mappings

• Knowledge propagation in DDL can cause undesired
  changes in mapped ontologies

O2

• A mapping is consistent if all locally
  satisfiable concepts in mapped ontologies stay
  satisfiable in a distributed setting, otherwise
  mapping is inconsistent

14
Reiter Diagnosis

• A Reiter Diagnosis of system (COMP, SD, OBS)
• COMP is a set of components
• SD is a system description
• OBS is a set of observations (or symptoms)
• is a minimal set ? of components explaining
  symptoms
• Diagnose algorithm
• Minimal conflict sets per symptom
• Hit conflict sets

15
Debugging as Diagnosis

• Debugging as Reiter Diagnosis
• Mappings - components
• DDL system description
• Observed DDL unsatisfiabilities symptoms
• Debugging/Repairing algorithm
• find unsatisfiabilities
• compute minimal conflicting sets of bridge rules
  jointly causing unsatisfiabilities
• eliminate unsatisfiability by removing bridge a
  single rule from conflicting sets

16
Example
O1
O2
?
(c 0.47)
Author
Authorization ? ?Person
(c 1.0)
isA
(c 0.47)
Person
Person
?
(c 1.0)

• Matching

2. Reasoning
17
Example
O1
O2
?
(c 0.47)
Author
Authorization ? ?Person
(c 1.0)
isA
(c 0.47)
Person
Person
?
(c 1.0)

• Matching

3. Compute Conflict Sets
4. Select problematic bridge rules and repair
mapping
2. Reasoning
18
Mapping Removal

• Selection strategies
• Naive random selection
• Faithful based on confidence
• Doubtful based on WordNet similarity
• Remark
• Deleting a bridge rule means deleting the
  correponding mapping

19
Experimental Evaluation

• Ontologies
• OntoFarm (modeling the domain of conference
  organization)
• Matching Systems
• falcon, OWL-CTXmatch, coma, and hmatch,
• Matching results for OAEI-2006
• Different removal strategies
• Random, confidence, Wordnet similarity

20
Examples of Errors Detected

• Obvious Errors
• Document Topic
• Decision Location
• Reception Rejection
• Non-Obvious Errors
• Regular_Paper Regular
• Reviewing_event review
• Main_office Location

These Errors should not occur !!
Here is the real benefit of our debugging method
21
Lessons Learned

• Observations
• Method works well for highly precise matchers
  (e.g., falcon)
• Results of the confidence-based removal depends
  on the matcher
• WordNet similarity outperforms the other
  approaches (strange enough!)
• Analysis of experiments
• Run-time performance depends on number of
  unsatisfiabilities and conflicts found
• Precision depends on selection strategy
• Recall depends on the relation between the amount
  of wrong mappings and amount of observed
  unsatisfiabilities caused by these mappings

22
Possible Improvement

• Define siblings as being disjoint to enable the
  reasoner to detect inconsistencies ( Schlobach,
  ESWC-2005)
• Learning disjointness Voelker, ESWC-2007

Thing
Person
Document
Reviewer
Chair
Author
Paper
Person disjointWith Document
23
Conclusion

• We proposed a completely automatic method for
  reparing errors in automatically generated
  mappings based on the logical reasoning
• Tests on the data generated by the real matching
  systems show that we actually improve the quality
  of mappings
• Direct integration into matching methods can
  improve their performance