Outline

1
Outline

• The Relevance of Reasoning
• and Alignment Incoherence in
• Ontology Matching

Christian Meilicke University of Mannheim,
Lehrstuhl Künstliche Intelligenz christian_at_informa
tik.uni-mannheim.de
2
Outline

• Introduction
• Problem Statement gt Goals and Contribution (in
  general)
• Theoretical Framework Reasoning and Incoherence
• Alignment Semantic
• Definition of Incoherence
• Contributions
• How to measure the degree of incoherence?
• How to improve the results of a matcher?
• How to support human alignment revision?
• Current Future Work
• Theoretical Foundations, Algorithms, Experiments

3
Introduction
Ontology O1
Ontology O2
People
Person
Author
Author
writes
lt Author, Author, , 0.97 gt lt Paper, Paper, ,
0.94 gt lt reviews, reviews, , 0.91 gt lt writes,
writes, , 0.7 gt lt Person, People, , 0.8 gt lt
Document, Doc, , 0.7 gt lt Reviewer, Review, ,
0.6 gt
CommitteeMember
Reviewer
PCMember
reviews
reviews
Doc
Document
Paper
Paper
Review
writes
4
Problem Statement

• Elements of an alignment between O1 and O2 are
  correspondences
• lt e1, e2, r, n gt

Entity of O1e.g. a concept
Entity of O2
Semantic relation e.g. subsumption
Confidence value e.g. n ? 0, 1
Even though i do not know exactly how to
interprete subsumption or equivalence don't
bug me, I can nevertheless do my job!
Well, I have an intuitive understanding of these
relations!
5
Major Contribution

• Show that he or shecan benefit from a
  well defined alignment semantic when doing their
  job!
• Better precision of matcher results
• Less revision effort for a human expert
• Too comprehensive/complex for a PHD-Thesis
• gt Focus on the role of incoherence!

6
Reductionistic alignment semantic

• A reductionistic alignment semantic S is a
  function that maps an alignment A between O1 and
  O2 on a set of DL axioms X.
• This is a little simplification, X has to be
  defined in a more precise way
• The merged ontology O1 A?S O2 is defined asO1 ?
  O2 ? X
• Example 1 Natural DL-Semantic
• X results from a 11 mapping from correspondences
  to axioms
• ? Person, Human, , 0.9 ? ? Person Human
• ? createdBy, writtenBy, gt, 0.75 ? ? createdBy ?
  writtenBy
• Example 2 Distributed Description Logics
  (DDL)See section "Relating DDL and ordinary DL"
  in Borgida Serafini Distributed Description
  Logics Assimilating Information from Peer
  Sources. Journal on Data Semantics, 2003

7
Advantages

• Easy to define notions like incoherence resp.
  entailment given reductionistic semantic S
• A is S-incoherent with respect to O1 and O2 iff
  iC is satisfiable in Oi with i 1,2 and
  unsatisfiable in O1 A?S O2
• Correspondence c followsS from A with respect to
  O1 and O2 iff O1 A?S O2 ? trans(c) where trans(c)
  is defined by S and c
• Works for each concrete specification of
  reductionistic semantic the same way
• State of the Art Reasoner available
• Natural Semantic is very close to intuitive
  understanding

8
Interlude
Well, as far as I understood, this is not really
relevant for the matching process!
Absolutely right, my yellow friend! This will not
help us with our practical problems
9
Measuring Incoherence (Contribution I)

• Classic measures for alignment evaluation are
  precision and recall (comparing A against
  reference alignment R)
• Precision(A, R) A n R / A
• 100 ? All correspondences in A are correct!
• Recall(A, R) A n R / R
• 100 ? Detected every correct correspondence!
• Let A ? A be a coherent subset such that there
  exists no coherent subset A' ? A with A' gt A
• Since R is coherent it can be concluded that A
  can be used to compute an upper bound for the
  precision of A
• In particular Precision(A, R) A / A
• Suprising result No prior knowledge about R
  available!

Meilicke Stuckenschmidt Incoherence as a Basis
for Measuring the Quality of Ontology Mappings.
OM-2008.
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Measuring Incoherence (Contribution I)

• First experimental results based on a variant of
  the natural semantic
• OAEI 2008 conference track, three matching
  systems participating
• Asmov (strong pattern based debugging component)
• ¼ of all alignments have precision less than 82
• Lily (pattern based debugging component)
• ¼ of all alignments have precision less than 78
• DSSim (no debugging component)
• ¼ of all alignments have precision less than 72
• For some alignments we measured that precision
  will be less than 0.5
• These statements can be given without any
  knowledge of the reference alignment!

But how strong is the upper bound in practice?
But how strong is the upper bound in practice?
Caracciolo et al. Results of the OAEI 2008.
OM-2008.
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Interlude
I know that im not perfect! But this
information is not useful as long as i do not
know how to exploit it!
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Alignment Debugging (Contribution II)

• Try this approach

while A is incoherent find minimal conflict
set C ? A let correspondence c have lowest
confidence in C remove c from A end while.

• Results of previous experiments (based on DDL)
• Removed 22 to 56 of all incorrect
  correspondences (Recall of Debugging)
• 85 have been correctly removed (Precision of
  Debugging)
• Room for improvement
• Not included correspondences between properties
• Algorithm does not remove a minimum number of
  correspondences
• Disjointness incompletely modeled in dataset

Meilicke et al Repairing Ontology Mappings.
AAAI-2007.
13
Interlude
I should think about this reasoning, seems to be
quite useful for a matching system!
I should think about this reasoning, seems to be
quite useful for a matching system!
But what about me ?
14
Alignment Revision (Contribution III)

• Automated Debugging is problematic
• Removal decision is based on a a heuristic
  decision, e.g. the confidence value
• Manual Revision is also problematic
• Very complex interdependencies
• Lots of effort for experts necessary
• Idea Support manual revision of matcher
  generated alignments by logical reasoning
• Resulting alignment will be coherent
• Saves effort for the user compared to a complete
  manual revision
• Results
• Saves in average 30 effort!

not evaluated by user
conflicts
entails
Meilicke et al. Supporting Manual Mapping
Revision using Logical Reasoning. AAAI-2008.
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Interlude
and what will be next?
16
Current Work

• Theoretical Framework
• Define several reductionistic alignment semantics
• Define different types of diagnosis
• Global optimal diagnosis
• Local optimal diagnosis
• Algorithms / Implementation
• Implement translations for different semantics
• Develop algorithms specialized reasoning
  techniques
• Experiments
• Run experiments for automized debugging with new
  features/options
• Correspondences between properties
• Different semantics
• Different types of diagnosis

A coherent subset of an incoherent alignment of
a specific type
17
Future Work

• Theoretical Framework
• Relate diagnosis theory to theory of belief
  revision (AGM)
• Compare with the work of Guilin Qi et al.
• Philosophical foundations, in particular
  coherence theory of truth
• Algorithms / Implementation
• Faster algorithms gt Applicable on larger
  datasets
• Extend prototype for manual mapping revision
• Provide stable and easy to use debugging API
• Experiments
• Find more/better datasets for experiments
• Use debugging as final step in matching system

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Thanks for your attention, Any questions ?
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Backup - Slides
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Instance migration and Incoherence
O2
O1
(1) O1RedWoodAnt ? O2WoodPlant
WoodPlant
Plant
Animal
Insect
RedWoodAnt
disjoint
Animal
(2) O1Animal O2Animal
This alignment is incoherent!
O2 is inconsistent after instance migration!
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Sketch of Algorithm

• Preprocessing Compute and store conflict sets of
  size 2 based on checking certain patterns
• Incomplete very efficient, but experiments show
  that most conflicts sets can be detected this way
• Searchalgorithm Branch for each conflict and
  reduce alignment step by step

• Found an alignment x coherent due to stored
  conflicts ...
• Check coherency of merged ontology, if coherent,
  node is solution!
• If incoherent
• find MUPS-alignment,
• branch by removing MUPS elements
• store MUPS as conflict

x
x
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Incoherent reference alignments?

• Computed degree of incoherence for benchmark
  testcases 301 to 304 of OAEI benchmark
  subtrack
• First added manually disjointness axioms
  otherwise no incoherence can be detected
• Results are based on modified natural
  translation)
• 301 gt 0.032
• 302 gt 0.0
• 303 gt 0.0
• 304 gt 0.026

Only minor deviationfrom coherency
Coherence criteria to strict ?!
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Subset of a reference alignment
O101
xsdgYear
year
Date
Reference -Book -Report -...
date
month
xsdgMonth
(1) 101Reference 301Entry(2) 101month
301hasMonth
(1) 101Reference 301Entry(2) 101date
101month 301hasMonth
O301
xsdNonNegativeInteger
hasYear
Entry -Book -TechReport -...
xsdString
hasMonth