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Understanding Evolution of Semantically Annotated Data

Understanding Evolution of Semantically Annotated Data. D. Calvanese , E. Kharlamov , W. Nutt, and D. Zheleznyakov KRDB Research Centre Free University of Bozen -Bolzano FBK, January 2011. World Wide Web and Evolution. date. name. Web content is ubiquitously dynamic

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Understanding Evolution of Semantically Annotated Data

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

  2. World Wide Web and Evolution date name • Web content isubiquitouslydynamic • (Textual) Web content has two flavors: lang. • Plain (HTML) data • ~ semantics understandable by people • Semanticallyannotated 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 1/36

  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 QLwhich is based on a Description Logics family: DL-Lite 2/36

  4. Description Logics (DLs) DL Ontology (Knowledge Base): • Concepts are classes of objectsRoles are relations between objects • ABoxisfor instances of concepts and roles • TBoxis for structure of the knowledge TBox: Cleric Priest Husband ABox: Carl Bob John Adam 3/36

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

  6. DL-Lite Language • TBoxassertions: Formulas of the form: • inclusion: • disjointness: • functionality: • ABoxassertions: 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 A ⊑ ∃R, A ⊑ ∃R− , A ⊑ B, ... A ⊑ ¬∃R, A ⊑ ¬B, ... (func R), ... B(a), ∃R(a), ... R(a,b), ... 5/36

  7. What if There Is New Information? New InormationN: Single(John) How should the KB evolve? John John Single Husband Priest Wife Woman 1..n hasHb (Mary, John) Adam Bob 1..n Mary 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, andWolter • ABoxes in DL-Lite: De Giacomo, Lenzerini, Poggi, Rosati • TBoxesin DLs and DL-Lite: Qi, Du • … [Liu&al‘06] [Giacomo&al’06] [Qi,Du’09] 7/36

  9. Outline • The problem of evolution • Formalizing evolution • Attempt to apply classical approaches • Model-Based approaches • Formula-Based approaches • Our proposal • Bold Semantics • Careful Semantics • Conclusion

  10. Conceptual Requirements Old Knowledge: New Knowledge: Evolved Knowledge: Single Husband John Cleric Minister Carl Priest Adam Bob Single Husband John Cleric Minister Carl Priest Adam Bob Wife Mary Wife Mary RentSub RentSub hasHb hasHb 1..n 1..n 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 ⊑ SinglePriest ⊑ ¬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: • Model-Based Approaches (MBAs)operate with set of models • Formula-Based Approaches (FBAs)operate with set of formulas Are these approaches applicable to DL-Lite evolution? 11/36

  13. Outline • The problem of evolution • Formalizing evolution • Attempt to apply classical approaches • Model-Based approaches • Formula-Based approaches • Our proposal • Bold Semantics • Careful Semantics • Conclusion

  14. Model-Based Approaches Old Knowledge K: Mod(K) Single Husband John Cleric Minister Carl Priest Adam Bob Wife Mary RentSub • 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 hasHb 1..n New Knowledge N: Mod(N) 13/36

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

  16. Local Model-Based Approaches Old Knowledge K: Mod(K) Single Husband John MinisterCarl Cleric Husband John Single Priest Adam Bob WifeMary Wife Mary RentSub RentSub hasHb hasHb 1..n 1..n Is there a representation? Evolved KB K’: The result of evolution: Mod(K’)    15/36

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

  18. Global Model-Based Approaches Old Knowledge K: Mod(K) Priest Adam Bob MinisterCarl Cleric Husband John Single Single Husband John Wife Mary WifeMary RentSub RentSub hasHb hasHb 1..n 1..n Is there a representation? Evolved KB K’: The result of evolution: Mod(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 global: G local: L set: ⊖ number: |⊖| What is distance symbols: S atoms: A Distance is built upon • Propositional Logic: two dimensions. • Description Logics: one more dimension! • Distance is built upon • symbols • atoms 19/36

  21. Dimensions of MBAs Approach global: G local: L set: ⊖ number: |⊖| What is distance symbols: S atoms: A Distance is built upon • 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 global: G local: L set: ⊖ number: |⊖| What is distance symbols: S atoms: A Distance is built upon • Two possibilities for each of three dimensions • ⇒ eight possible semantics • Theorem (Inexpressibility): • For all of eight semantics the result of the evolutioncannot be expressed in DL-Lite 19/36

  23. What May Go Wrong? New Knowledge: Single(John) What happened with Mary? Our intuition: 2 cases • Mary is single • Mary is married to another guy John a guy 1..n Husband Priest Single Wife Woman hasHb (Mary, John ) ? • 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 Adam Bob 1..n Mary • MBAs give more cases: • Mary is married to either Adam or Bob (but not to both) Drawback I: Mary married to one of the priest is counterintuitive Drawback II: Inexpressible in DL-Lite K’⊭ Priest(Bob) K’⊭ Priest(Adam) K’ ⊨ Priest(Adam) ∨Priest(Bob) 20/36

  24. What Else May Go Wrong? New Knowledge: Bishop ⊑ Priest How does it affect the old KB? Our intuition: Just add the new assertion to the old KB John 1..n Single Husband Priest Bishop Wife Woman hasHb (Mary, John ) Adam Bob • 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 1..n Mary Carl • MBAs give a strange models M: • M = { Bishop(Carl), Priest(Carl), ¬Single(Carl), … } • Thus, KB’ ⊭ Priest ⊑ Single • Drawback 1: it is counterintuitive • Drawback 2: inexpressible in DL-Lite 21/36

  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 • The problem of evolution • Formalizing evolution • Attempt to apply classical approaches • Model-Based approaches • Formula-Based approaches • Our proposal • Bold Semantics • Careful Semantics • Conclusion

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

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

  29. What To Do? • What to do with several Kmax? Classical approaches: • When In Doubt Throw It Out: take intersection of Kmax • Cross-Product: take disjunction of Kmax TempStaf Teaching TempStaf Teaching Teaching TempStaff Teaching TempStaff PhD PhD PhD PhD • Loses too much data • coNP-complete Not expressible in DL-Lite Kmax1∪ N Kmax2∪ N (Kmax2 ∩ Kmax1)∪ N OR K ∪ N ∨ 26/36

  30. Outline • The problem of evolution • Formalizing evolution • Attempt to apply classical approaches • Model-Based approaches • Formula-Based approaches • Our proposal • Bold Semantics • Careful Semantics • Conclusion

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

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

  33. ABox Evolution Is Deterministic • 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. • Add assertions from N • Find conflicting assertions • Resolve conflicts Drawback: Mary cannot get divorced a guy John John 1..n Priest Single Husband Woman Wife Recall: Our intuition: 2 cases Mary is single Mary is married to another guy hasHb (Mary, John ) ? Adam Bob 1..n   Mary • New knowledge N: Single(John) 30/36

  34. Outline • The problem of evolution • Formalizing evolution • Attempt to apply classical approaches • Model-Based approaches • Formula-Based approaches • Our proposal • Bold Semantics • Careful Semantics • Conclusion

  35. Careful Semantics for ABox Evolution • Formula φ is unexpected for Kmaxand Nif Kmax∪ N ⊨ φ and Kmax⊭ φ nor N⊭ φ • In our example an unexpected formula is:φ = ∃a guy.hasHb(Mary, a guy)∧(aguy≠John) • Role-constraining formula (RCF): φ = ∃x.R(a,x)∧(x≠c1)∧...∧(x≠cn) • Preference: We want Kmax to be careful:no unexpected RCF are allowedKmax ∪ N ⊨ φ then Kmax⊨ φ or N ⊨ φ • Theorem: For every DL-Lite KB K and new data N, careful Kmaxexists, is unique, and is computable in PTime 32/36

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

  37. Outline • The problem of evolution • Formalizing evolution • Attempt to apply classical approaches • Model-Based approaches • Formula-Based approaches • Our proposal • Bold Semantics • Careful Semantics • 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 ACSI ProjectArtifact-Centric Service InteroperationFP 7 grant, agreement n. 257593http://www.acsi-project.eu/ 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/

  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

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