1. Using the TBox to Optimise SPARQL Queries Birte Glimm Yevgeny Kazakov Ilianna Kollia and Giorgos Stamou CS 848 Paper Critique Vishnu Prathish

2. Preliminaries Description Logic SHIQ Notations: A concept atom is an expression A(x) and a role atom is an expression r(x, y) Concept axiom templates and role axiom templates

3. Conjunctive Instance and Complex Queries A conjunctive instance query q is a non-empty set of (concept or role) atoms. concept templates - set of SHIQ concepts, where a concept variable can be used in place of a concept name, and a role variable in place of a role name. Axiom templates – – role axiom template where – Concept axiom template has the form with c, d concept templates. A finite set of role axiom templates, concept axiom templates, and (concept or role) atoms is called a complex query Var(q) - set of variables in q. and |Var(q)| is called the arity of q.

4. Key Contributions An optimization that is applicable to conjunctive instance queries. We show that one can compute an equivalent query qˆ for a given query q by replacing the variables in q with fresh individual names. Then perform realization. Query optimization exploiting the polarity of variable occurrences in the query and the concept and role hierarchies.

5. Mapping functions and answers to query Mapping function: A mapping function is a certain answer for q if, denotes all the set of certain answers of q

6. Query Answering Via Approximate Instance retrieval Using approximate reasoning algorithms to answer query Either Sound and incomplete or Incomplete and Sound Rewrite the KB into a simpler logic and run query over it to obtain desired level of approximation

7. Approximate Instance Retrieval and Query answering algorithms

8. Example

9. intersecQans

10. intersecQans Algorithm

11. Restricting atoms A query atom restricts restricts a query if, Eg: B(x) in the example explained. To preserve certain answers, we should use restricting atoms that do not change the answers of q. Can be used to prune set of possible answers of query

12. Query Extension Find a way of computing restricting atoms Based on chase technique in relational database theory Basic Idea: – For a Abox,Query and a bijective function, – Compute(rewrite) an extended ABox and Query (using chase ) – Using approx. inst. retrieval algo., check if any atom of the new query restricts the initial query – Reduce the set of possible answers using query restriction

13. Polarity Based optimization Choose the next binding to test by traversing the concept hierarchy top down Based on the polarity of concept variable in the query the concept hierarchy can be safely pruned. Can not be used when a variable occurs both positively and negatively

14. Algorithm to get possible concept variable mapping

15. Evaluation On custom set of queries based on GALEN (Biomedical KB – SHIF expressivity) FBbt_XP ontology (SHI) Sys Config: Mac OS X Lion machine with a 2.53 GHz Intel Core i7 processor and Java 1.6 allowing 1GB of Java heap space.

16. Results GALEN Queries

17. Results FBbt XP Queries

18. Conclusion A TBOX based optimization of SPARQL queries Equivalent queries which can be exploited to produce reduce the set of mapping for conjunctive queries Polarity based pruning for queries that go beyond conjunctive queries Evaluation which shows that this optimization can reduce key evaluation times upto two orders of magnitude.

19. Thank you!