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Model Theory and Calculus for DL-Lite

Model Theory and Calculus for DL-Lite. Evgeny Kharlamov Diego Calvanese, Werner Nutt Free University of Bozen-Bolzano Dresden University of Technology October 2006. Motivation. Query: q. User Interface. Information Sources. Motivation. Problem: Data Integration. Ontology.

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Model Theory and Calculus for DL-Lite

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  1. Model Theory and Calculus for DL-Lite Evgeny Kharlamov Diego Calvanese, Werner Nutt Free University of Bozen-Bolzano Dresden University of Technology October 2006

  2. Motivation

  3. Query: q User Interface Information Sources Motivation Problem: Data Integration

  4. Ontology Data Integration System q Information Sources Motivation Solution:

  5. Ontology Data Warehouse q Information Sources Motivation Solution:

  6. Motivation Pre-process (data from the sources): Incompleteness of the sources wrt the ontology • VW is a Car VW Car

  7. Ontology Data Warehouse q Information Sources Motivation Solution: DL-Lite Size??

  8. Ontology Data Integration System q Information Sources Motivation Solution: q1, . . . , qn

  9. L1 L2 L3 q q1, . . . , qn Motivation Evaluation of Mediators: • Response time • Correctness of answers

  10. UCQs CQs DL-Lite q q1, . . . , qn Motivation Evaluation of Mediators: • Response time ~ LogSpace • Correctness of answers ~ correct

  11. Ontology Data Integration System q Information Sources QuOnto QuOnto: DL-Lite UCQ CQ q1, . . . , qn

  12. Aim of this Thesis Better understanding of properties of DL-Lite • Relationship: ontology - size of the Warehouse • Relationship: ontology - query answering • Response time • Correctness of answers

  13. DL-Lite

  14. DL-Lite Vocabulary (of the ontology): • Classes: • Car • Elements that participate in a relation: A = {x | there is y s.t. Has_engine(x,y)} B = {y | there is x s.t. Has_engine(x,y)} • Relations: Has_engine

  15. DL-Lite Ontology: • Inclusion dependency: VW IsA Car VW IsAHas_engine • Disjointness: VW IsA ¬ Mercedes Has_engine IsA¬Animal

  16. DL-Lite Ontology: • Functional dependency func (Has_id) func (Has_engine)

  17. DL-Lite Data (sources): Car(vw_golf) Has_engine(vw_golf, td)

  18. Universal Models

  19. Universal Models VW  Car Mercedes  Car VW ¬Mercedes Car ¬Animal func (Has_id) func (Has_engine) . . .

  20. Universal Models Properties: • If there is a completion  UM • If there is a UM  there is a class of Ums • Chase of a DB with an Ontology is a UM

  21. Universal Models … Infinite universal models: • Bob is a Person • Every person has a father • Every father is a person • No one can be an ancestor of him/herself Father Sam Person Father Bill Person Bob Person

  22. VW  Car Mercedes  Car VW ¬Mercedes Car ¬Animal func (Has_id) func (Has_engine) . . . pol(n+m) m weakly-acyclic ontology n Chase of Polynomial Size

  23. User Interface weakly-acyclic Ontology q = Information Sources Chase of polynomial size: Chase as Data Warehouse

  24. Results • Introduced the notion of UM • Shown that any chase is a UM • Proposed weakly-acyclic ontologies for which chase is finite and of polynomial size

  25. Deduction as Query Answering

  26. T(Ontology) T(Information Sources) T(Query) Deduction as Query Answering Ontology Information Sources Query Extended Horn Logic (EHL) All Answers Derivation Calculus

  27. Extended Horn Logic HL: X Y Z bro(X,Z):- bro(X,Y), bro(Y,Z) EHL: X Y Z bro(bob,Z):- bro(X,Y), bro(Y,bob)

  28. Calculus Extends Resolution-based calculus with • Extended resolution • Query homorphisms

  29. Results • Introduced EHL • Defined reduction from DL-Liteto EHL • Introduced a calculus for EHL • Shown soundness and completeness of the calculus wrt query answering  query answering in DL-Liteis reducible to reasoning in EHL

  30. Conclusion We investigated properties of DL-Litelogic: • Model theory: • Universal models • other properties • Proof Theory • Calculus as a tool for query answering

  31. Further work • Extend query language (in QuOnto) • Find good algorithms and optimisations

  32. Thank you

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