1 / 29

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.

dorcas
Download Presentation

Updating ABoxes in DL-Lite

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related