1. D. Calvanese, E. Kharlamov, W. Nutt, and D. Zheleznyakov KRDB Research Centre Free University of Bozen-Bolzano FBK, January 2011 Understanding Evolution of Semantically Annotated Data

2. World Wide Web and Evolution  Web content is ubiquitously dynamic  (Textual) Web content has two flavors: 1/36 Plain (HTML) data ~ semantics understandable by people Semantically annotated data (knowledge) ~ semantics understandable by machines  We focus on the second kind of data which is believed to be the Web of tomorrow [TBL99] Our goal: To understand how to incorporate the new knowledge into the old one ~ to study evolution of knowledge datename lang.

3. Semantic Annotations  Ontologies are a prime mechanism to bring semantics to the Web, they provide annotations (e.g., date, name) meta annotations (e.g., class, property) classifications of annotations (e.g., subclass-of) properties of annotations (e.g., domain, range) …  Technologies behind ontologies Resource description Framework (RDF) Ontology Web Language (OWL) Rule Languages (e.g. OWL 2 RL)  We focus on OWL 2, its one profile: OWL 2 QL which is based on a Description Logics family: DL-Lite 2/36

4. Description Logics (DLs) ClericPriestHusband Concepts are classes of objects Roles are relations between objects ABox is for instances of concepts and roles TBox is for structure of the knowledge Carl John Adam Bob DL Ontology (Knowledge Base): TBox: ABox: 3/36

5. Example of a Knowledge Base SingleHusbandPriestWife hasHb Concepts: Roles: TBox: ABox: Wife, Husband, Single, Woman, Priest HasHb Wife ⊑ Woman Wife ≡ ∃ HasHb Husband ≡ ∃ HasHb – Husband ⊑ ¬ Single Priest ⊑ Single Husband ⊑ ¬ Priest Wife(Mary), hasHb(Mary,John) Priest(Adam), Priest(Bob) Woman Mary John Adam Bob (Mary, John) 1..n 4/36

6. DL-Lite Language  TBox assertions: Formulas of the form: inclusion: disjointness: functionality:  ABox assertions: instanciations: concept: role:  No disjunction and no negation on the left of inclusions  DL-Lite ~ a bit extended Horn Logic with existential variables in head 5/36 A ⊑ ∃ R, A ⊑ ∃ R −, A ⊑ B,... (func R),... A ⊑ ¬ ∃ R, A ⊑ ¬B,... B(a), ∃ R(a),... R(a,b),...

7. What if There Is New Information? SingleHusbandPriestWife hasHb New Inormation N: Single(John) How should the KB evolve? Woman Mary John Adam Bob (Mary, John) 1..n John 6/36

8. Is Evolution Solved for DLs?  Traditional inference tasks for DL KBs are static: concept satisfiability KB satisfiability concept and role hierarchies query answering  Research on ontology evolution is quite young ABoxes in expressive DLs: Liu, Lutz, Milicic, and Wolter ABoxes in DL-Lite: De Giacomo, Lenzerini, Poggi, Rosati TBoxes in DLs and DL-Lite: Qi, Du … 7/36 [Qi,Du’09] [Giacomo&al’06] [Liu&al‘06]

9. Outline I.The problem of evolution II.Formalizing evolution III.Attempt to apply classical approaches a) Model-Based approaches b) Formula-Based approaches IV.Our proposal a) Bold Semantics b) Careful Semantics V. Conclusion

10. Conceptual Requirements SingleHusband John RentSub Wife Mary hasHb 1..n Cleric Minister Carl Priest Adam Bob SingleHusband John Cleric Minister Carl RentSub Priest Adam Bob Wife Mary hasHb 1..n Old Knowledge:New Knowledge:Evolved Knowledge: DL-Lite KB Evolution Operator DL-Lite KB Evolved knowledge should  be consistent – no logical contradictions  be coherent – no empty concepts  entail New Knowledge  minimally different from the old KB – principle of minimal change Priest(Bob) ∧ ¬Priest(Bob)  Priest ⊑ Single Priest ⊑ ¬Single  9/36

11. Technical Requirements  Closure under evolution: Evolution result should be expressible in DL-Lite  Efficiency: Evolution result should be computable in PTime 10/36

12. Can Previous Work Help?  Knowledge evolution was studied by the AI community  Primarily for Propositional Logic (PL)  Two main types of approaches to evolution in PL: 1. Model-Based Approaches (MBAs) operate with set of models 2. Formula-Based Approaches (FBAs) operate with set of formulas 11/36 Are these approaches applicable to DL-Lite evolution?

13. Outline I.The problem of evolution II.Formalizing evolution III.Attempt to apply classical approaches a) Model-Based approaches b) Formula-Based approaches IV.Our proposal a) Bold Semantics b) Careful Semantics V. Conclusion

14. Model-Based Approaches SingleHusband John RentSub Wife Mary hasHb 1..n Old Knowledge K: Cleric Minister Carl Priest Adam Bob New Knowledge N: Mod(K) Mod(N)  Take some models of Mod(N) (since new knowledge should be preserved)  Keep those that are “closest” to Mod(K)  Two flavours of Model-Based Approaches: Local Global  Take some models of Mod(N) (since new knowledge should be preserved)  Keep those that are “closest” to Mod(K)  Two flavours of Model-Based Approaches: Local Global 13/36

15. Local Model-Based Approaches SingleHusband John RentSub Wife Mary hasHb 1..n Old Knowledge K: Cleric Minister Carl Priest Adam Bob New Knowledge N: Mod(K) Mod(N)   The result of evolution: Minimal distance 14/36

16. Local Model-Based Approaches SingleHusband John RentSub Wife Mary hasHb 1..n Mod(K) Mod(K’)   The result of evolution: SingleHusba nd John Cleric Minist erCarl RentS ub Priest Adam Bob WifeM ary hasHb 1..n Is there a representation? Old Knowledge K: Evolved KB K’: 15/36

17. Global Model-Based Approaches Old Knowledge K: Cleric Minister Carl Priest Adam Bob New Knowledge N: Mod(K) Mod(N)   The result of evolution: SingleHusband John RentSub Wife Mary hasHb 1..n 16/36

18. Global Model-Based Approaches SingleHusband John RentSub Wife Mary hasHb 1..n Mod(K) Mod(K’)   The result of evolution: SingleHusba nd John Cleric Minist erCarl RentS ub Priest Adam Bob WifeM ary hasHb 1..n Is there a representation? Old Knowledge K: Evolved KB K’: 17/36

19. How to Measure Distance btw Models?  All MBAs are based on distances between interpretations  Distance in Propositional Logic: as a set as a number  Example: I = {p, q, r} J = {p, s} dist ⊖ (I,J) = I ⊖ J dist | ⊖ | (I,J) = |I ⊖ J| dist ⊖ (I,J) = {q, r, s} dist | ⊖ | (I,J) = 3 18/36

20. Dimensions of MBAs Approach What is distance Distance is built upon set: ⊖ number: | ⊖ | global: G local: L symbols: S atoms: A  Propositional Logic: two dimensions.  Description Logics: one more dimension! Distance is built upon symbols atoms 19/36

21. Dimensions of MBAs Approach What is distance Distance is built upon set: ⊖ number: | ⊖ | global: G local: L symbols: S atoms: A Example: I = {Priest(Bob), Wife(Mary)}, J = {Priest(Adam), Wife(Mary)} Atoms: dist ⊖ (I,J) = {Priest(Bob), Priest(Adam)} Symbols:dist ⊖ (I,J) = {Priest} 19/36

22. Dimensions of MBAs Approach What is distance Distance is built upon set: ⊖ number: | ⊖ | global: G local: L symbols: S atoms: A Two possibilities for each of three dimensions ⇒ eight possible semantics Theorem (Inexpressibility): For all of eight semantics the result of the evolution cannot be expressed in DL-Lite 19/36

23. What May Go Wrong? SingleHusbandPriestWife hasHb 1..n MBAs give more cases: 3.Mary is married to either Adam or Bob (but not to both) John AdamBob a guy New Knowledge: Single(John) What happened with Mary? Our intuition: 2 cases 1.Mary is single 2.Mary is married to another guy Drawback I: Mary married to one of the priest is counterintuitive K’ ⊭ Priest(Bob) K’ ⊭ Priest(Adam) K’ ⊨ Priest(Adam) ∨ Priest(Bob) Drawback II: Inexpressible in DL-Lite Woman Mary 1..n (Mary, John ) ? 20/36 Observation: In [Giacomo&al’06] evolution of ABoxes in DL-Lite fixed TBoxes under global semantics on atoms algorithm to compute semantics is provided ⇒ Their results are wrong Observation: In [Giacomo&al’06] evolution of ABoxes in DL-Lite fixed TBoxes under global semantics on atoms algorithm to compute semantics is provided ⇒ Their results are wrong

24. What Else May Go Wrong? SingleHusbandPriestWife hasHb 1..n MBAs give a strange models M: M = { Bishop(Carl), Priest(Carl), ¬Single(Carl), … } Thus, KB’ ⊭ Priest ⊑ Single John AdamBob New Knowledge: Bishop ⊑ Priest How does it affect the old KB? Our intuition: Just add the new assertion to the old KB Woman Mary 1..n (Mary, John ) 21/36 Bishop Carl Drawback 1: it is counterintuitive Drawback 2: inexpressible in DL-Lite Observation: In [Qi,Du’09] evolution of TBoxes in KBs with empty ABoxes under global semantics on atoms ⇒ Their operator does not work for general KBs in DL-Lite Observation: In [Qi,Du’09] evolution of TBoxes in KBs with empty ABoxes under global semantics on atoms ⇒ Their operator does not work for general KBs in DL-Lite

25. MBAs Do Not Work  … because they ignore structure of the KB the allow too many cases result of evolution cannot be expressed in DL-Lite  MBAs cannot be adopted for KB evolution in DL-Lite 22/36

26. Outline I.The problem of evolution II.Formalizing evolution III.Attempt to apply classical approaches a) Model-Based approaches b) Formula-Based approaches IV.Our proposal a) Bold Semantics b) Careful Semantics V. Conclusion

27. Formula-Based Approaches Idea: To take union K ∪ N What if K ∪ N is unsatisfiable? Cleric Minister Carl Priest Adam Bob Old Knowledge K: New Knowledge N: Cleric Minister Carl Priest Adam Bob SingleHusband John ClericRentSubWife Mary hasHb 1..n Unsatisfiable 24/36

28. Formula-Based Approaches Approach:  Choose a subset K max ⊆ K Consistent with N Coherent with N Maximal wrt set inclusion Result:  K max ∪ N Problem:  In general K max is not unique Cleric Minister Carl Priest Adam Bob Old Knowledge K: New Knowledge N: Cleric Minister Carl Priest Adam Bob SingleHusband John ClericRentSubWife Mary hasHb 1..n Single Cleric RentSub Husband John Wife Mary hasHb 1..n    Satisfiable Unsatisfiable  Cleric RentSub 25/36

29. What To Do?  What to do with several K max ? Classical approaches: When In Doubt Throw It Out: take intersection of K max Cross-Product: take disjunction of K max Loses too much data coNP-complete Not expressible in DL-Lite TempStaff Teaching PhD K ∪ NK ∪ N TempStaff Teaching PhD (K max2 ∩ K max1 ) ∪ N TempSta f Teaching PhD TempSta f Teaching PhD K max1 ∪ NK max2 ∪ N OR ∨ 26/36

30. Outline I.The problem of evolution II.Formalizing evolution III.Attempt to apply classical approaches a) Model-Based approaches b) Formula-Based approaches IV.Our proposal a) Bold Semantics b) Careful Semantics V. Conclusion

31. Our Proposal – Bold Semantics  Take an arbitrary K max Evolution(K, N) = K max ∪ N  The result is non-deterministic TempStaff Teaching PhD K ∪ NK ∪ N TempStaffTeachingPhD K max ∪ N  Can be computed in PTime 28/36

32. How To Avoid Non-Determinism?  Preferences “reduce” non-determinism: Order over assertions Minimality wrt cardinality etc.  Evolution in specific cases may be deterministic: ABox evolution 29/36

33. ABox Evolution Is Deterministic 1.Add assertions from N 2.Find conflicting assertions 3.Resolve conflicts Drawback: Mary cannot get divorced SingleHusbandPriestWife John Mary AdamBob a guy John  Assumptions: N is a set of ABox assertions Evolution does not change TBox  Theorem: For a DL-Lite KB the result of ABox evolution is unique and computable in PTime.  New knowledge N: Single(John) Woman 30/36 hasHb 1..n (Mary, John ) ? Recall: Our intuition: 2 cases 1.Mary is single 2.Mary is married to another guy Recall: Our intuition: 2 cases 1.Mary is single 2.Mary is married to another guy  

34. Outline I.The problem of evolution II.Formalizing evolution III.Attempt to apply classical approaches a) Model-Based approaches b) Formula-Based approaches IV.Our proposal a) Bold Semantics b) Careful Semantics V. Conclusion

35. Careful Semantics for ABox Evolution  Formula φ is unexpected for K max and N if K max ∪ N ⊨ φ and K max ⊭ φ nor N ⊭ φ  In our example an unexpected formula is: φ = ∃ a guy.hasHb(Mary, a guy) ∧ (a guy≠John)  Role-constraining formula (RCF): φ = ∃ x.R(a,x) ∧ (x≠c 1 ) ∧... ∧ (x≠c n )  Preference: We want K max to be careful: no unexpected RCF are allowed K max ∪ N ⊨ φ then K max ⊨ φ or N ⊨ φ  Theorem: For every DL-Lite KB K and new data N, careful K max exists, is unique, and is computable in PTime 32/36

36. Careful Semantics for ABox Evolution New knowledge N: Single(John) 1.Run bold semantics algorithm for ABox evolution 2.Find unexpected formulas φ 3.Delete assertions entailing φ SingleHusbandWife John Mary a guy John Unexpected formulas: φ = ∃ a guy.hasHb(Mary, a guy) ∧ (a guy≠John) Priest AdamBob Woman Mary 33/36 hasHb 1..n (Mary, John ) ? Recall: Our intuition: 2 cases 1.Mary is single 2.Mary is married to another guy Recall: Our intuition: 2 cases 1.Mary is single 2.Mary is married to another guy  

37. Outline I.The problem of evolution II.Formalizing evolution III.Attempt to apply classical approaches a) Model-Based approaches b) Formula-Based approaches IV.Our proposal a) Bold Semantics b) Careful Semantics V. Conclusion

38. Conclusion  We reviewed Model-Based Approaches to evolution Found MBAs are inapplicable for DL-Lite evolution  We reviewed classical Formula-Based Approaches Showed hardness or inapplicability of them  We proposed two novel Formula-Based Approaches - Bold Semantics - Careful Semantics  We developed polynomial time algorithms for new semantics 35/36

39. Thank you ONTORULE Project ONTOlogies Meets Business RULes FP 7 grant, ICT-231875 http://ontorule-project.eu/ Webdam Project Foundations of Web Data Management ERC FP7 grant, agreement n. 226513 http://webdam.inria.fr/ ACSI Project Artifact-Centric Service Interoperation FP 7 grant, agreement n. 257593 http://www.acsi-project.eu/

40. References  [TBL’99] - M. Fischetti, T. Berners-Lee. Weaving the Web. HarperSanFrancisco, 1999.  [Liu&al’06] - H. Liu, C. Lutz, M. Milicic, and F. Wolter. Updating Description Logic ABoxes. KR06.  [Giacomo&al’06] - G. De Giacomo, M. Lenzerini, A. Poggi, R. Rosati: On the Update of Description Logic Ontologies at the Instance Level. AAAI 2006  [Qi,Du’09] - G. Qi, J. Du: Model-based Revision Operators for Terminologies in Description Logics. IJCAI 2009