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

8. A little bit of Description Logics (DL) Knowledge Base Tbox (schema) Abox (data) Man  Human & Male Happy-Father  Man & some has- child Female and … John : Happy-Father h John, Mary i : has-child Inference System Interface

9. 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. ……

10. 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

11. Example I: Coherent and Inconsistent Ontology C1 C2 disjoint a

12. Example II: Incoherent and Inconsistent Ontology C1 C2 disjoint a C3

13. Example III: Incoherent and consistent Ontology C1 C2 disjoint b C3 a

14. Example IV: Inconsistent (and coherent?) Ontology C1 C2 disjoint {a}

15. Consistency Negation

16. Coherence Negation

17. Example

18. New Postulates for Ontology Revision

19. New Postulates for Ontology Changes

20. Levi and Harper Identities

21. 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