Inconsistencies, Negations and Changes in Ontologies

1
Inconsistencies, Negations and Changes in
Ontologies

• Zhisheng Huang
• Vrije University Amsterdam
• The Netherlands
• Collaborative work with
• Giorgos Flouris and Dimitris Plexousakis (FORTH,
  Greece)
• Jeff Z. Pan (University of Aberdeen, UK)
• Holger Wache (VU)
• (AAAI 2006 Paper)

2
Outline of This Talk

• Ontology Evolution
• Inconsistency and Incoherence
• Negations
• Postulates of Ontology Changes
• Conclusions

3
Ontology Evolution
4
AGM Postulates for Belief Revision
5
Postulates for Contraction
6
Levi and Harper Identities
7
Problems for Ontology Revisions

• Many description logics (including OWL DL) are
  not AGM-compliant
• Problem (implicit) negation and base recovery
  postulate

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A little bit of Description Logics (DL)
Knowledge Base
Tbox (schema)
Man ? Human Male Happy-Father ? Man some
has-child Female and
Interface
Inference System
Abox (data)
John Happy-Father hJohn, Maryi has-child
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Variants of Inconsistencies in SW

• Schlobach at el.(IJCAI03) Incoherence
  unsatisfiable concept in Tbox
• Huang at el. (IJCAI05) Classical sense of
  logical inconsistency
• Haase at el. (ISWC05) Example in a footnote.

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Incoherence and Inconsistency

• Unsatisfiable concept in a Tbox its
  interpretation is empty in any interpretation of
  Tbox
• Incoherent Tbox there exists unsatisfiable
  concept
• Incoherent Ontology its Tbox is incoherent
• Inconsistent Ontology there exists no models

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Example I Coherent and Inconsistent Ontology
disjoint
C1
C2
a
12
Example II Incoherent and Inconsistent Ontology
disjoint
C1
C2
C3
a
13
Example III Incoherent and consistent Ontology
disjoint
C1
C2
C3
b
a
14
Example IV Inconsistent (and coherent?)
Ontology
disjoint
C1
C2
a
15
Consistency Negation
16
Coherence Negation
17
Example
18
New Postulates for Ontology Revision
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New Postulates for Ontology Changes
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Levi and Harper Identities
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Conclusions

• Framework accounts for negation, inconsistency
  and change for DL-based ontologies for management
  of dynamic ontologies.
• Proposed negations achieve the Harper identity
  and Levi identity for ontology changes
• Distinction between incoherence and inconsistency
  provides us two different approaches covering
  different needs in different application scenarios