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

Outline I. Introduction II. Review of Model-Based Semantics III. Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics IV. Conclusion

Example of DL-Lite KB Single Lonely Spouse Mary Married John hasSpouse ▲ Nun Rachel, Patty 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) 1..n 3/24 vocabulary schema instance

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

DLs for Web Services Services: software systems supporting machine-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

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

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

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

Outline I. Introduction II. Review of Model-Based Semantics III. Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics IV. Conclusion

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

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

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

Winslett's Semantics I: J: K: distance( I, J )distance( I, K ) When distance( I, J ) < distance( I, K ) ? A I ={ John, Rachel } B I ={ Mary } A J ={ John } B J ={ Mary } A K ={ John } B K = ∅ 12/24

Winslett's Semantics I: J: K: distance( I, J )distance( I, K ) When distance( I, J ) < distance( I, K ) ? A I ={ John, Rachel } B I ={ Mary } A J ={ John } B J ={ Mary } A K ={ John } B K = ∅ diff( I, J ) = ( {Rachel}, ∅ ) 12/24

Winslett's Semantics I: J: K: distance( I, J )distance( I, K ) When distance( I, J ) < distance( I, K ) ? A I ={ John, Rachel } B I ={ Mary } A J ={ John } B J ={ Mary } A K ={ John } B K = ∅ 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) iffdiff( I, J ) ⊂ diff( I, K ) 12/24

WS: Inexpressibility in DL-Lite Single Lonely Spouse Married hasSpouse ▲ Nun 1..n John RachelPatty Mary Haley Single(Mary) U:U: What to do with John? Intuition: two cases are most likely 1.John is not married 2.John is married to another girl WS: gives the third case! 3.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 Mary ? 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 13/24

Outline I. Introduction II. Review of Model-Based Semantics III. Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics IV. Conclusion

Formula-Based Semantics (FBS) Married(John) Spouse(Marry) Nun(Rachel) Spouse(Marry) Nun(Patty) Married(John) Nun(Patty) Single(Haley) Married(John) Spouse(Marry) Nun(Rachel) Nun(Patty) Single(Haley) … Single Delighted Spouse Married hasSpouse ▲ Nun 1..n ABox: TBox: U:U: Satisfiable ✓ Unsatisfiable ✗ Satisfiable ✓ Single Delighted Spouse Married hasSpouse ▲ Nun 1..n FBS: closeness is measured between sets of formulas How?  In general, O max is not unique! There are: O 1 max, O 2 max, …  The result is: O max ∪ U  We take a satisfiable subset O max ⊆ O, which is maximal wrt: ∙cardinality, or ∙set inclusion, or ∙some preferences 15/24

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

Naïve Semantics. Algorithm 17/24 1. Add assertions from U 2. Find conflicting assertions 3. Delete conflicting assertions 4. Restore assertions that may be lost in Step 3 Single Lonely Spouse Married hasSpouse ▲ Nun 1..n John RachelPatty Mary Haley Mary Single(Mary), Happy(Haley) U:U: Possible sources of conflicts: ∙Spouse ⊑ ¬ Single ∙ Spouse ⊑ ¬ Nun ∙Lonely ⊑ ¬ Happy Happy Haley ABox:Lonely(Haley), Married(John), hasSpouse(John, Marry), Nun(Rachel), Nun(Patty) 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 TBox, Lonley(Haley) ⊨ Single(Haley) TBox, new ABox ⊭ Single(Haley) We lost Single(Haley)! So, we set Single(Haley) into the new ABox Haley Single(Haley), Happy(Haley), Single(Mary) new _wife Note that Married(John) ⊨ ∃ hasSpouse(John) John has divorsed, but he is still married! Drawback: Once married, John cannot divorse

Outline I. Introduction II. Review of Model-Based Semantics III. Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics IV. Conclusion

Careful subset Role-constraining formula (RCF) has form ∃x.Role(a, x)∧(x≠c 1 )∧…∧(x≠c n ) In our example: ∃_wife.hasSpouse(John, _wife)∧(_wife≠Mary) Subset A’ of ABox is careful wrt U iff for every RCF φ if A’ ∪ U ⊨ φ then A’ ⊨ φ or U ⊨ φ If it does not hold, we say that φ is unexpected 19/24

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

Careful Semantics. Algorithm 212/4 1. Run Naïve Semantics Algorithm 2. Find unexpected formulas φ’s 3. Delete assertions entailing φ’s Single Lonely Spouse Married hasSpouse ▲ Nun 1..n John RachelPatty Mary Haley Mary Happy Haley _wife ABox:Lonely(Haley), Married(John), hasSpouse(John, Marry), Nun(Rachel), Nun(Patty) Naïve Happy(Haley), Single(Mary) Single(Haley), Unexpected φ: ∃ _wife.hasSpouse(John, _wife) ∧ (_wife≠Mary) Old ABox ⊭ φ, Mary was John’s wife U ⊭ φ, it is easy to check Single(Mary), Happy(Haley) U:U: φ is entailed by: ∙Married(John) is from old ABox ∙Single(Mary) is from U new

Outline I. Introduction II. Review of Model-Based Semantics III. Formula-Based Semantics: ∙ Naïve Semantics ∙ Careful semantics IV. Conclusion

Conclusion MBS have drawbacks for DL-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

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

Thank you! ONTORULE Project ONTOlogies Meets Business RULes FP 7 grant, ICT Webdam Project Foundations of Web Data Management ERC FP7 grant, agreement n

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 23 rd International Workshop on Description Logics (DL 2010) [Qi,Du:2009]Model-based revision operators for terminologies in description logics. In: Proc. of the 21st Int. Joint Conf. on Artificial Intelligence (IJCAI 2009). 891–897