1. Applying Belief Change to Ontology Evolution PhD Student Computer Science Department University of Crete fgeo@csd.uoc.gr Giorgos Flouris Research Assistant Institute of Computer Science FORTH fgeo@ics.forth.gr PhD Thesis Summary ISWDS 05 07/11/05

2. Part  Overview (“Elevator Talk”)

3. Ontology Evolution and Belief Change We propose a different viewpoint on ontology evolution: –Addressing the problem of ontology evolution using techniques from belief change In particular: –AGM theory of contraction –In ontologies represented using some DL or OWL flavor

4. Summary of Results Logics (under Tarski’s model) AGM-compliant logics AGM Class Base-AGM-compliant logics DLs (OVA) DLs (CVA) OWL DLs

5. Part  Research Description

6. Ontology Evolution: Definition and Importance Ontology evolution is the process of modifying an ontology in response to a certain change in the domain or its conceptualization Main reasons for ontology evolution: –Dynamic domains –Change in users’ needs or perspective –New information (previously unknown, classified or unavailable) that improves the conceptualization –Errors during original conceptualization –Ontology dependency –…

7. Output Ontology Ontology Evolution Input Ontology Success Fail Change Representation  Semantics of Change  Implementation  Change Propagation  Validation  Change Capturing  “penguins can’t fly” Add_IsA(…) Penguin ⊑  Fly User: , , ,  System: ,  Current Approaches

8. Limitations Main limitations of current approaches: –Manual or semi-automatic approaches –Too many operators (complex and atomic) –No formal semantics Cause problems: –Automated agents and systems –Scalability –Formal properties unknown –Bottleneck for current research

9. Proposed Approach User:  System: , , , ,  Output Ontology Ontology Evolution Input Ontology Success Fail Change Representation  Semantics of Change  Implementation  Change Propagation  Validation  Change Capturing  “penguins can’t fly” Add_IsA(…) Penguin ⊑  Fly

10. Why Belief Change? (1/2) Knowledge should be up-to-date: –Keeping KBs up-to-date: belief change –Keeping ontologies up-to-date: ontology evolution Ontology evolution can be viewed as a special case of belief change: –View belief change techniques, ideas, intuitions, results, algorithms and methods under the prism of ontology evolution –We address ontology evolution using belief change

11. Why Belief Change? (2/2) Belief change properties: –Mature –Formal –Automatic Addresses important issues that have not been considered in ontology evolution: –Revision and Update –Revision and Contraction –Postulations vs Explicit Constructions –Foundational vs Coherence Theories –Principle of Minimal Change –Principle of Primacy of New Information

12. Difficulties and Methodology Belief change techniques are generally targeted at classical logic: –Their assumptions fail for DLs and other ontological languages –Cannot be directly used for such logics –But: the underlying intuitions are applicable Belief change techniques need to be migrated to the ontology evolution context PhD, Phase 1: –Set the foundations for future work on the subject –Very abstract, long-term and ambitious goal

13. A More Specific Approach: the AGM Theory For the purposes of this PhD, we restricted ourselves to deal with: –The most influential belief change theory (AGM theory) –The most fundamental operation (contraction) –The most promising languages for ontological representation (DLs and OWL) PhD, Phase 2: –Study the applicability of the AGM theory of contraction in DLs and OWL

14. AGM Theory AGM theory (Alchourron, Gärdenfors, Makinson): –The most influential approach in belief change Contraction: –The most fundamental operation for theoretical purposes –Deals with the removal of knowledge from a KB Main contribution: 6 AGM postulates that determine whether a contraction operator behaves “rationally” AGM theory is based on certain assumptions on the underlying logic, so, as usual: –Intuitions applicable in ontologies –Postulates and results not applicable in ontologies

15. AGM-Compliance Dropped the AGM assumptions and considered the class of logics studied by Tarski: –Very general class of logics (that contains DLs) We generalized the AGM theory (and postulates) to be applicable to Tarski’s class Noticed that only some of the logics in this class admit an operator satisfying the generalized postulates (i.e., a “rational” operator): –Termed AGM-compliant logics (3 characterizations)

16. Results (AGM-Compliance) Logics (under Tarski’s model) AGM-compliant logics AGM Class

17. Further Results Connection with lattice theory: –Every logic can be described by a lattice –AGM-compliance can be determined by the lattice’s structure Connection with the foundational model: –AGM theory based on the coherence model –There are logics in which a “foundational AGM theory” can be applied –Termed base-AGM-compliant logics (2 characterizations)

18. Results (Base-AGM-Compliance) Logics (under Tarski’s model) AGM-compliant logics AGM Class Base-AGM-compliant logics

19. AGM-Compliance and DLs Studied DLs (two types) –CVA (Closed Vocabulary Assumption): allows the description of the ontological signature using DL axioms –OVA (Open Vocabulary Assumption): ignores the signature because it cannot be described using DL axioms DLs (CVA): non-AGM-compliant DLs (OVA): some are AGM-compliant, some are not –Introduced results, heuristics, rules of thumb OWL (different flavors, CVA or OVA, annotation features, owl:imports): all non-AGM-compliant

20. Results (AGM-Compliance and DLs) Logics (under Tarski’s model) AGM-compliant logics AGM Class Base-AGM-compliant logics DLs (OVA) DLs (CVA) OWL

21. Partial List of DLs (OVA) AGM-compliant DLsNon-AGM-compliant DLs ALCO , ⊓ ALC , ⊓ with no Abox ALCO with no axioms involving role terms ALC with empty Abox and no axioms involving role terms All DLs with more operators (but no more connectives) than the above DLs ……… SH, SHI, SHIN, SHOIN, SHOIN(D), SHOIN +, SHOIN + (D), SHIQ, SHIF, SHIF(D), SHIF +, SHIF + (D) FL 0, FL  with role axioms All DLs between ALH and ALHCIOQ OWL DL, OWL Lite without annotations and all flavors of OWL with annotations ………

22. Conclusion Phase 1: –Proposed the study of ontology evolution from a different perspective, using belief change ideas and terminology Phase 2: –Focused on the AGM theory of contraction –Determined its applicability to DLs and OWL

23. Future Work Study other belief change approaches Connection of AGM-compliance with other AGM- related results: –The operation of revision –Levi identity –Representation theorems The development and/or implementation of a specific algorithm for integration into ontology evolution tools