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Updating ABoxes in DL-Lite

Updating ABoxes in DL-Lite. D. Calvanese 1 , E. Kharlamov 1,2 , W. Nutt 1 , D. Zheleznyakov 1 1 Free University of Bozen-Bolzano 2 INRIA Saclay, Ile de France AMW 2010, May 17th. Outline. Introduction to DL Update Model-Based Semantics Formula-Based Semantics: ∙ Naïve Semantics

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Updating ABoxes in DL-Lite

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  1. Updating ABoxes in DL-Lite D. Calvanese1, E. Kharlamov1,2,W. Nutt1, D. Zheleznyakov1 1 Free University of Bozen-Bolzano2 INRIA Saclay, Ile de France AMW 2010, May 17th

  2. Outline • Introduction to DL Update • Model-Based Semantics • Formula-Based Semantics: ∙Naïve Semantics ∙Careful semantics • Conclusion

  3. Description Logics (DLs) • A formalism to describe the area of interest by means of concepts and roles • 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 3/25

  4. 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 4/25

  5. DL Inference Tasks • Traditional inference tasks for static DL KBs: (i) checking concept satisfiability,(ii) building concept and role hierarchies,(iii) query answering • Ontology may evolve in time: the interest in ontology evolution has appeared 5/25

  6. 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, we need to support: ∙TBox evolution ∙ABox evolution ✓ 6/25

  7. PermStaff PermStaff Manager Manager AreaManager AreaManager TopManager TopManager Updating DL ABoxes Updated ABox ABox New data New KB: • has the same TBox (updates should not change TBoxes) • is consistent • entails the new data • is minimally different from the old KB Married(John) hasSpose(John, Mary) Nun(Rachel) Nun(Patty) Single(Mary)Nun(Jane) Married(John) Married(Frank) Single(MAry) Nun(Rachel) Nun(Patty) Nun(Jane)Single(Peter) hasSpouse(Tom, Pat)Nun(Haley) Update Operation New KB Old KB 7/25

  8. Technical Requirements • Closure under updates:Update result should be expressible in DL-Lite • Efficiency:Update result should be computable in PTIME 8/25

  9. Searching for Update Operator • Updates of logical theorieswere studied by the AI community • Two main types of approaches: • Model-based • Formula-based 9/25

  10. Outline • Introduction • Model-Based Semantics • Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics • Conclusion

  11. PermStaff Manager AreaManager TopManager Model-BasedSemantics (MBS) Mod(KB): KB: Married(John) Nun(Rachel) Nun(Patty) Minimaldistance New data Mod(New data): Single(Mary)Nun(Jane) ✓ ✓ ✗ ✓ 11/25

  12. PermStaff Manager Human AreaManager TopManager Single Spouse Unmarried Divorsed Model-BasedSemantics (MBS) Mod(KB): KB: Married(John) Nun(Rachel) Nun(Patty) KB’: ? ✓ ✓ ✗ ✓ Mod(KB’): 11/25

  13. Expressibility of Updates • Depends on distance btw models and the logics • Distance under Winslett’s Semantics (WS):symmetric difference and set inclusion • Winslett’s semantics:∙Well known∙There are works on DL-Lite ABox updates under WS∙Representative of MBS 12/25

  14. Distance of Winslett 1. Defining the distance I: A(John), A(Frank),B(Mary) distance(I, J) = diff(I, J) A(John)B(Mary) K: A(John)B(Jane) J: 13/25

  15. Distance of Winslett 1. Defining the distance I: A(John),A(Frank),B(Mary) distance(I, J) = diff(I, J) diff(I, J) = { A(Frank) } distance(I, J) A(John)B(Mary) K: A(John)B(Jane) J: 13/25

  16. Distance of Winslett 1. Defining the distance I: A(John),A(Frank),B(Mary) distance(I, J) = diff(I, J) diff(I, J) = { A(Frank) } diff(I, K) = { A(Frank), B(Mary), B(Jane) } distance(I, K) 2. Comparing distances distance(I, J) < distance(I, K) iff distance(I, J) ⊂ distance(I, K) A(John)B(Mary) K: A(John)B(Jane) J: { A(Frank) } ⊂ { A(Frank), B(Mary), B(Jane) } Hence distance(I, J) < distance(I, K) 13/25

  17. WS: Inexpressibility in DL-Lite ND: 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, KB’ ⊨ Nun(Rachel) ∨ Nun(Patty)KB’ ⊭ Nun(Rachel)KB’ ⊭ Nun(Patty) • Drawback 2: WS is inexpressible in DL-Lite Every MBS may have similar problems  Consider Formula-Based Semantics Spouse Lonely Mary Haley hasSpouse▲ 1..n Married John 14/25

  18. Outline • Introduction • Model-Based Semantics • Formula-Based Semantics: ∙Naïve Semantics ∙ Careful semantics • Conclusion

  19. Single Single Nun Nun Spouse Spouse Delighted Delighted hasSpouse▲ hasSpouse▲ 1..n 1..n Married Married Formula-Based Semantics (FBS) ABox: Married(John) Nun(Patty) Single(Haley) Spouse(Marry) Nun(Patty) Married(John) Spouse(Marry) Nun(Rachel) Nun(Patty) Single(Haley) … Married(John) Spouse(Marry) Nun(Rachel) ✓ ✓ Satisfiable We choose satisfiable subsets We choose Amax⊆ A, which is maximal wrt: ∙ cardinality, or ∙ set inclusion, or ∙ some preferences TBox: ✗ Unsatisfiable ✗ • Result is: Amax∪ New data ✓ New data Satisfiable • Problem:in general, Amaxis not unique Single(Mary)Nun(Jane) Single(Mary)Nun(Jane) … 16/25

  20. Naïve Semantics • Preference:We want an Amax to be max wrt set inclusion • Theorem:For every DL-Lite KB and ND there is a uniqueAmax wrt set inclusion 17/25

  21. Naïve Semantics. Algorithm • Add assertions from ND • 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 ND Since, the result must satisfy ND,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 divorced, but he is still married! Drawback: Once married, John cannot divorce Single(Mary), Happy(Haley) ND: hasSpouse▲ 1..n Happy Married 2 Haley John 18/25

  22. Outline • Introduction • Model-Based Semantics • Formula-Based Semantics: ∙ Naïve Semantics ∙Careful semantics • Conclusion

  23. Careful Subset of ABox • Formula φ is unexpected if Amax∪ ND ⊨ φ and Amax ⊭ φ nor ND ⊭ φ • In our example:∃_wife.hasSpouse(John,_wife)∧(_wife≠Mary) • Role-constraining formula (RCF) has form∃x.Role(a, x)∧(x≠c1)∧…∧(x≠cn) 20/25

  24. Careful Semantics • Preference:We want an Amax to be max wrt set inclusionand for every RCF φif Amax∪ ND ⊨ φ then Amax ⊨ φ or ND⊨ φ(1) • Theorem:For every DL-Lite KB and ND there is a uniqueAmax wrt set inclusion that satisfies (1) 21/25

  25. Careful Semantics. Algorithm • Run Naïve Semantics Algorithm • Find unexpected formulas φ • Delete assertions entailing φ Single Nun Mary Haley Rachel Patty ND: 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) from old ABox, and ∙ Single(Mary) from ND Unexpected φ:∃_wife.hasSpouse(John,_wife) ∧(_wife≠Mary) hasSpouse▲ 1..n Happy Married Haley John 22/25

  26. Outline • Introduction • Model-Based Semantics • Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics • Conclusion

  27. Conclusion • We revised Model Based Semantics • We found MBS inapplicable for DL-Lite ABox updates • We proposed two novel Formula Based Semantics • We developed polynomial time algorithms to compute updates 24/25

  28. Future work • Combining ABox and TBox updates • Implementing update algorithms • Extension to more expressive DLs 25/25

  29. 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/

  30. 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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