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Updating ABoxes in DL-Lite

Updating ABoxes in DL-Lite. D. Calvanese, E. Kharlamov, W. Nutt, D. Zheleznyakov Free University of Bozen-Bolzano AMW 2010, May 2010. Outline. Introduction Review of Model-Based Semantics Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics Conclusion. Example of DL-Lite KB.

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Updating ABoxes in DL-Lite

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  1. Updating ABoxes in DL-Lite D. Calvanese, E. Kharlamov,W. Nutt, D. Zheleznyakov Free University of Bozen-Bolzano AMW 2010, May 2010

  2. Outline • Introduction • Review of Model-Based Semantics • Formula-Based Semantics: ∙Naïve Semantics ∙Careful semantics • Conclusion

  3. Example of DL-Lite KB Concepts: Roles: TBox: ABox: Married Spouse Single Lonely Nun hasSpouse Married ⊑ ∃hasSpouse ∃hasSpouse ⊑ Married ∃hasSpouse– ⊑ Spouse Lonely ⊑ Single Spouse ⊑ ¬ Single Spouse ⊑ ¬Nun Married(John) hasSpose(John, Mary) Nun(Rachel), Nun(Patty) Single Nun Rachel,Patty vocabulary Spouse Mary Lonely schema hasSpouse▲ 1..n Married John instance 3/24

  4. Description Logics (DLs) • DL KB consists of two parts: TBox is for structure, similar to DB schema;ABox is instance level, like DB instance • DL-Lite is a tractable fragment of OWL 2 • Traditional inference tasks for static DL KBs: (i) concept satisfiability,(ii) concept and role hierarchies,(iii) query answering • Recent interest: ontology evolution 4/24

  5. DLs for Web Services • Services: software systems supportingmachine-to-machine interoperation • Services access data through ontologies • Services can be specified using ontologies • To reflect changes, there are needs in: ∙ABox evolution ∙TBox evolution 5/24

  6. Ontology Evolution • Two main types of ontology evolution:Revision and Update • Revision:∙ makes KB “closer” to the real world∙ the result depends on all models of a KB • Update:∙ reflects changes in the real world∙ the result is modelwise 6/24

  7. Updating DL-Lite Ontologies • We study updates for DL-Lite KBs • TBox updates:∙TBox revision studied in [Qi,Du:2009]∙ We studied TBox updates in [Zheleznyakov&al:2010] • ABox updates:– Initially studied in [De Giacomo&al:2006]– This talk: we revised and extended it. 7/24

  8. Requirements for ABox Update • Closure under updates:Update result should be expressible in DL-Lite • Efficiency:Update result should be computable in PTIME • Update should not contradict TBox • Minimal change principal:We discuss it later 8/24

  9. Outline • Introduction • Review of Model-Based Semantics • Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics • Conclusion

  10. Single Nun Rachel,Patty Spouse Mary Lonely hasSpouse▲ 1..n Married John Model-BasedSemantics (MBS) O: Mod(O): Minimaldistance U: Mod(U): ✓ ✓ ✗ ✓ 10/24

  11. Single Nun Rachel,Patty Spouse Mary Lonely Human hasSpouse▲ 1..n Single Spouse Married John Unmarried Divorsed Model-BasedSemantics (MBS) O: Mod(O): O’: ? ✓ ✓ ✗ ✓ Mod(O’): 10/24

  12. Winslett's Semantics (WS) • What does minimal distance mean?This depends on semantics. • Winslett’s semantics:∙Well known∙There are works on ABox update under Winslett’s semantics∙Representative of MBS • Distance under Winslett’s Semantics:based on symmetric difference and set inclusion 11/24

  13. Winslett's Semantics When distance(I, J) < distance(I, K) ? I: AI={ John, Rachel }BI={ Mary } distance(I, J) distance(I, K) AJ={ John }BJ={ Mary } K: AK={ John }BK=∅ J: 12/24

  14. Winslett's Semantics When distance(I, J) < distance(I, K) ? I: AI={ John, Rachel }BI={ Mary } diff(I, J) = ( {Rachel}, ∅ ) distance(I, J) distance(I, K) AJ={ John }BJ={ Mary } K: AK={ John }BK=∅ J: 12/24

  15. Winslett's Semantics When distance(I, J) < distance(I, K) ? I: AI={ John, Rachel }BI={ Mary } diff(I, J) = ( {Rachel}, ∅ ) diff(I, K) = ( {Rachel}, {Mary} ) diff(I, J) ⊂ diff(I, K)inclusion is componentwise So, distance(I, J) < distance(I, K)iff diff(I, J) ⊂ diff(I, K) distance(I, J) distance(I, K) AJ={ John }BJ={ Mary } K: AK={ John }BK=∅ J: 12/24

  16. WS: Inexpressibility in DL-Lite U: Single(Mary) Single Nun Rachel Patty Mary • What to do with John? • Intuition: two cases are most likely • John is not married • John is married to another girl • WS: gives the third case! • John is married to either Rachel, or Patty,but never both • Drawback 1: WS is counterintuitive • So, O’⊨ Nun(Rachel) ∨ Nun(Patty)O’⊭ Nun(Rachel)O’⊭ Nun(Patty) • Drawback 2: WS is inexpressible in DL-Lite Can Mary be Lonely? WS: No Intuition: Why not? The statement“Mary is Single, but not Lonely”is inexpressible in DL-Lite Drawback 3: No complete approximation of updating under WS exists Every MBS may have similar problems  Consider Formula-Based Semantics Spouse Lonely Mary Haley ? hasSpouse▲ 1..n Married John 13/24

  17. Outline • Introduction • Review of Model-Based Semantics • Formula-Based Semantics: ∙Naïve Semantics ∙ Careful semantics • Conclusion

  18. Single Single Nun Nun Spouse Spouse Delighted Delighted hasSpouse▲ hasSpouse▲ 1..n 1..n Married Married Formula-Based Semantics (FBS) ABox: Spouse(Marry) Nun(Patty) Married(John) Nun(Patty) Single(Haley) Married(John) Spouse(Marry) Nun(Rachel) Nun(Patty) Single(Haley) … Married(John) Spouse(Marry) Nun(Rachel) FBS: closeness is measuredbetween sets of formulas How? ✓ Satisfiable • We take a satisfiable subsetOmax⊆ O, which is maximal wrt: ∙ cardinality, or ∙ set inclusion, or ∙ some preferences TBox: ✗ Unsatisfiable • The result is: Omax∪U • In general, Omaxis not unique! • There are: O1max, O2max, … U: ✓ Satisfiable 15/24

  19. Naïve Semantics • Preference:We want an Omax such thatOmax and U are satisfiable wrt TBox • Theorem:In DL-Lite KB O there is a unique maximal subset Omax wrt set inclusion such thatOmax and U are satisfiable wrt TBox 16/24

  20. Naïve Semantics. Algorithm • Add assertions from U • Find conflicting assertions • Delete conflicting assertions • Restore assertions that may be lost in Step 3 Single Nun 1 Mary Haley Rachel Patty ABox: Lonely(Haley), new Married(John), Single(Haley), Spouse hasSpouse(John, Marry), Happy(Haley), Single(Mary) 1 Mary _wife Lonely 2 Haley Nun(Rachel), Nun(Patty) TBox, Lonley(Haley) ⊨Single(Haley) TBox, new ABox⊭ Single(Haley) We lost Single(Haley)! So, we set Single(Haley) into thenew ABox Conflicts are only btw two assertions: one is implied by the old KB,another one is implied by U Since, the result must satisfy U,we delete the assertions from the old KB Possible sources of conflicts: ∙ Spouse ⊑ ¬ Single ∙ Spouse ⊑ ¬ Nun ∙ Lonely ⊑ ¬ Happy Note thatMarried(John) ⊨ ∃hasSpouse(John) John has divorsed, but he is still married! Drawback: Once married, John cannot divorse U: Single(Mary), Happy(Haley) hasSpouse▲ 1..n Happy Married 2 Haley John 17/24

  21. Outline • Introduction • Review of Model-Based Semantics • Formula-Based Semantics: ∙ Naïve Semantics ∙Careful semantics • Conclusion

  22. Careful subset • Role-constraining formula (RCF) has form∃x.Role(a, x)∧(x≠c1)∧…∧(x≠cn) • In our example:∃_wife.hasSpouse(John,_wife)∧(_wife≠Mary) • Subset A’ of ABox is careful wrt Uifffor every RCF φif A’ ∪ U ⊨ φ then A’ ⊨ φ or U ⊨ φ • If it does not hold,we say that φ is unexpected 19/24

  23. Careful Semantics • Preference:We want an Omax such thatOmax and U are satisfiable wrt TBox andOmax is careful wrt U • Theorem:In DL-Lite KB O there is a unique maximal subset Omax wrt set inclusion such thatOmax and U are satisfiable wrt TBox andOmax is careful wrt U 20/24

  24. Careful Semantics. Algorithm • Run Naïve Semantics Algorithm • Find unexpected formulas φ’s • Delete assertions entailing φ’s Single Nun Mary Haley Rachel Patty U: Single(Mary), Happy(Haley) ABox: Lonely(Haley), Naïve new Married(John), Single(Haley), Spouse hasSpouse(John, Marry), Happy(Haley), Single(Mary) _wife Mary Lonely Haley Nun(Rachel), Nun(Patty) φ is entailed by: ∙ Married(John) is from old ABox ∙ Single(Mary) is from U Unexpected φ: ∃_wife.hasSpouse(John,_wife) ∧(_wife≠Mary) Old ABox ⊭φ, Mary was John’s wife U⊭ φ, it is easy to check hasSpouse▲ 1..n Happy Married Haley John 212/4

  25. Outline • Introduction • Review of Model-Based Semantics • Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics • Conclusion

  26. Conclusion • MBS have drawbacks forDL-Lite TBox updates • We proposed Naïve semantics • We proposed Careful semantics • We developed a polynomial time algorithms to compute update under both of the semantics 23/24

  27. Future work • Combining ABox and TBox updates • Implementing update algorithms • Extend it to more expressive DLs 24/24

  28. Thank you! ONTORULE ProjectONTOlogies Meets Business RULesFP 7 grant, ICT-231875http://ontorule-project.eu/ Webdam Project Foundations of Web Data Management ERC FP7 grant, agreement n. 226513http://webdam.inria.fr/

  29. References • [De Giacomo&al:2006] On the update of description logic ontologies at the instance level. In: Proc. of the 21st Nat. Conf. on Artificial Intelligence (AAAI 2006). 1271–1276 • [Zheleznyakov&al:2010] Updating TBoxes in DL-Lite. In: Proc. of the 23rd International Workshop on Description Logics (DL 2010) • [Qi,Du:2009] Model-based revision operators forterminologies in description logics.In:Proc. of the 21st Int. Joint Conf.on ArtificialIntelligence (IJCAI 2009).891–897

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