1. Service Computation 2013, Valencia, Spain1 Query Optimization in Cooperation with an Ontological Reasoning Service Hui Shi, Kurt Maly, and Steven Zeil Contact: maly@cs.odu.edu

2. 2 Outline Problem –What are we reasoning about? –What are the challenges? Background –Knowledge base using ontologies –Inference strategies –Query optimization methods –Benchmarks Dynamic Query Optimization with an Interposed Reasoner –Greedy Ordering –Deferral of joins Evaluation –Comparison against Jena Conclusions Service Computation 2013, Valencia, Spain

3. 3 Problem Efficiency of reasoning in the face of large scale and frequent change within a question/answer system over a semantic web Issues –Query (conjunction of individual clauses) optimization over databases – well understood –Having reasoner -> uncertainty regarding the size of solution space associated with resolving individual clauses –Query optimization in the presence of such uncertainty Service Computation 2013, Valencia, Spain

4. 4 Background Existing semantic application –Question/answer systems over domain of (researchers, publications, subjects) Knowledge base (KB) –Ontologies –Representation formalism: Description Logic (DL) Inference methods for First Order Logic –Materialization and forward chaining pre-computes inferred truths and starts with the known data suitable for frequent computation of answers with data that are relatively static Owlim and Oracle –Query-rewriting and backward chaining expands the queries and starts with goals suitable for efficient computation of answers with data that are dynamic and infrequent queries Virtuoso Service Computation 2013, Valencia, Spain

5. Background In conventional database management systems, query optimization –examines multiple query plans and –selects one that optimizes the time to answer a query In the Semantic Web, SPARQL optimization typically based on –selectivity estimations –graph optimization –cost models 5Service Computation 2013, Valencia, Spain

6. Background Benchmarks evaluate and compare the performances of different reasoning systems –The Lehigh University Benchmark (LUBM) –The University Ontology Benchmark (UOBM) 6Service Computation 2013, Valencia, Spain

7. Approach Dynamic Optimization with an Interposed Reasoner A greedy ordering of the proofs of the individual clauses according to estimated sizes anticipated for the proof results Deferring joins of results from individual clauses where such joins are likely to result in excessive combinatorial growth of the intermediate solution Service Computation 2013, Valencia, Spain 7

8. Greedy Ordering - Example Suppose there are 10,000 students, 500 courses, 50 faculty members and 10 departments in the knowledgebase and the query pattern is (?S takesCourse ?C) – What courses do students take? Estimate of response size –exploiting the fact that each pattern represents that application of a predicate with known domain and range types –accumulating statistics on typical response sizes for previously encountered patterns involving that predicate For the example an estimate might be100,000 if the average number of courses a student has taken is ten, although the number of possibilities is 500,000. 8Service Computation 2013, Valencia, Spain

9. Greedy Ordering - Example Let the query be: List all cases where any student took two courses from a specific faculty member We can represent this query as the sequence of the patterns in the following table 9Service Computation 2013, Valencia, Spain Clause # QueryPatternQuery Response Response Size 1 ?S1 takesCourse ?C1{(?S1=>s i,?C1=>c i )} i=1..100,000 100,000 2 ?S1 takesCourse ?C2{(?S1=>s j, ?C2=>c j )} j=1..100,000 100,000 3 ?C1 taughtBy fac1{(?C1=>c j )} j=1..3 3 4 ?C2 taughtBy fac1{(?C2=>c j )} j=1..3 3

10. Greedy Ordering - Example Storage requirement for joins: –Input size plus input size plus result size Processing complexity (using hashing to represent one set, then linear over other set): –Max(result size, input size) Service Computation 2013, Valencia, Spain 10

11. Greedy Ordering - Example Assume first that the patterns are processed in the order given Worst case (storage size) is join of clause 2, when the join of two sets of size 100,000 yields 1,000,000 tuples. 11Service Computation 2013, Valencia, Spain Clause Being Joined Clause Evaluation Resulting SolutionSpace SolutionSpace Size (initial) [ ]0 1 {(?S1=>s i,?C1=>c i )} i=1..100,000 [{(?S1=>s i, ?C1=>c i )} i=1..100,000 ]100,000 2 {(?S1=>s j, ?C2=>c j )} j=1..100,000 [{(?S1=>s i, ?C1=>c i, ?C2=>c i )} i=1..1,000,000 ] (based on an average of 10 courses / student) 1,000,000 3 {(?C1=>c j )} j=1..3 [{(?S1=>s i, ?C1=>c i, ?C2=>c i )} i=1..900 ] (Joining this clause discards courses taught by other faculty.) 900 4 {(?C2=>c j )} j=1..3 [{(?S1=>s i, ?C1=>c i, ?C2=>c i )} i=1..60 ]60

12. Greedy Ordering Assume that the same patterns are processed in ascending order of estimated size, shown in the following table Worst case (storage size) is final addition of clause 2, when a set of size 100,000 is joined with a set of 270 12Service Computation 2013, Valencia, Spain Clause Being Joined Clause EvaluationResulting SolutionSpace SolutionSpace Size (initial) [ ]0 3 {(?C1=>c j )} j=1..3 [[{(?C1=>c i )} i=1..3 ]3 4 {(?C2=>c j )} j=1..3 [{(?C1=>c i, ?C2=>c i )} i=1..3, j=1..3 ]3 1 {(?S1=>s i,?C1=>c i )} i=1..100,000 [{(?S1=>s i, ?C1=>c i, ?C2=>c’ i )} i=1..270 ]270 2 {(?S1=>s j, ?C2=>c j )} j=1..100,000 [{(?S1=>s i, ?C1=>c i, ?C2=>c i )} i=1..60 ]60

13. Deferring joins - Example Suppose that we were processing the query: What mathematics courses are taken by computer science majors? Assume The Math department teaches 150 different courses, there are 1,000 students in the CS Dept, and there are 500 faculty overall with 50 in Math The Query is represented as the sequence of the following QueryPatterns 13 Service Computation 2013, Valencia, Spain ClauseQueryPatternQuery ResponseResponse Size 1 (?S1 takesCourse ?C1){(?S1=>s j,?C1=>c j )} j=1..100,000 100,000 2 (?S1 memberOf CSDept){(?S1=>s j )} j=1..1,000 1,000 3 (?C1 taughtby ?F1){(?C1=>c j, ?F1=>f j )} j=1..1,500 1,500 4 (?F1 worksFor MathDept){(?F1=>f i )} i=1..50 50

14. Deferring joins - Example Assume the greedy ordering that we have already advocated all joins are done immediately The worst step in this trace is the final join, between sets of size 100,000 and 150,000. 14Service Computation 2013, Valencia, Spain Clause Being Joined Clause Evaluation Resulting SolutionSpace SolutionSpace Size (initial) []0 4 {(?F1=>f i )} i=1..50 [{(?F1=>f i )} i=1..50 ]50 2 {(?S1=>s j )} j=1..1,000 [{(?F1=>f i, ?S1=>s i )} i=1..50,000 ]50,000 3 {(?C1=>c j, ?F1=>f j )} j=1..1,500 [{(?F1=>f i, ?S1=>s i, ?C1=>c i )} i=1..150,000 ]150,000 1 {(?S1=>s j,?C1=>c j )} j=1..100,000 [{(?F1=>f i, ?S1=>s i, ?C1=>c i )} i=1..1,000 ]1,000

15. Deferring joins - Example Joins be carried out immediately only if the input QueryResponses share at least one variable, otherwise defer the join Replace the input QueryResponse set in the solution space with the result of the join The worst join performed would have been between sets of size 100,000 and 150, a considerable improvement over the non- deferred case. 15Service Computation 2013, Valencia, Spain Clause Being Joined Query ResponseResulting SolutionSpace SolutionSpace Size (initial) []0 4 {(?F1=>f i )} i=1..50 [{(?F1=>f i )} i=1..50 ]50 2 {(?S1=>s j )} j=1..1,000 [{(?F1=>f i )} i=1..50,{(?S1=>s j )} j=1..1,000 ](50+1000) 3 {(?C1=>c j, ?F1=>f j )} j=1..1,500 [{(?F1=>f i, ?C1=>c i )} i=1..150, {(?S1=>s j )} j=1..1,000 ](150+1000) 1 {(?S1=>s j,?C1=>c j )} j=1..100,000 [{(?F1=>f i, ?S1=>s i, ?C1=>c i )} i=1..1,000 ]1000

16. Evaluation Compare our algorithm against Jena (in-memory, backward- chaining reasoner, limited capabilities to handle some OWL semantic rules, hence only used RDFS semantics) Using LUBM benchmarks representing a knowledge base: – describing a single university – ~100,000 triples – describing10 universities – ~1,000,000 triples Using a set of 14 queries taken from LUBM, requiring reasoning over rules associated with either –both RDFS and OWL semantics, –purely on the basis of the RDFS rules. Comparison metrics is response time Response size is used for Sanity check on correctness of results Indicator of complexity of reasoning 16Service Computation 2013, Valencia, Spain

17. Evaluation Comparison against Jena with Backward Chaining 17Service Computation 2013, Valencia, Spain LUBM:1 University, 100,839 triples10 Universities, 1,272,871 triples answerAQueryJena BackwdanswerAQueryJena Backwd response time result size response time result size response time result size response time result size Query1 0.20 4 0.32 4 0.43 40.864 Query2 0.50 0 130 0 2.1 28n/a Query3 0.026 6 0.038 6 0.031 61.56 Query4 0.52 34 0.021 34 1.1 340.4134 Query5 0.098 719 0.19 678 0.042 7191.0678 Query6 0.43 7,790 0.49 6,463 1.9 99,5663.282,507 Query7 0.29 67 45 61 2.2 678,10061 Query8 0.77 7,790 0.91 6,463 3.7 7,790526,463 Query9 0.36 208 n/a 2.5 2,540n/a Query10 0.18 4 0.54 0 1.8 41.40 Query11 0.24 224 0.011 0 0.18 2240.0320 Query12 0.23 15 0.0020 0 0.33 150.0160 Query13 0.025 1 0.37 0 0.21 330.890 Query14 0.024 5,916 0.58 5,916 0.18 75,5472.675,547

18. Evaluation Our algorithm generally is faster than Jena, sometimes by multiple orders of magnitude. Exceptions queries with very small result set sizes or queries 10-13, which rely upon OWL semantics and so could not be answered correctly by Jena. In two queries (2 and 9), Jena timed out. 18Service Computation 2013, Valencia, Spain

19. Evaluation Comparison against Jena with Hybrid reasoner 19Service Computation 2013, Valencia, Spain LUBM1 University, 100,839 triples10 Universities, 1,272,871 triples answerAQueryJena HybridanswerAQueryJena Hybrid response time result size response time result size response time result size response time result size Query1 0.20 4 0.37 4 0.43 40.934 Query2 0.50 0 1,400 0 2.1 28n/a Query3 0.026 6 0.050 6 0.031 61.56 Query4 0.52 34 0.025 34 1.1 340.5534 Query5 0.098 719 0.029 719 0.042 7192.7719 Query6 0.43 7,790 0.43 6,463 1.9 99,5663.782,507 Query7 0.29 67 38 61 2.2 67n/a Query8 0.77 7,790 2.3 6,463 3.7 7,790n/a Query9 0.36 208 n/a 2.5 2,540n/a Query10 0.18 4 0.62 0 1.8 41.60 Query11 0.24 224 0.0010 0 0.18 2240.080 Query12 0.23 15 0.0010 0 0.33 150.0160 Query13 0.025 1 0.62 0 0.21 331.20 Query14 0.024 5,916 0.72 5,916 0.18 75,5472.575,547

20. Evaluation Jena Hybrid means that Jena materializes some rules starts with longer list of tuples. avoiding combinatorial explosions through deferral even more important The times here tend to be somewhat closer, but the Jena system has even more difficulties returning any answer at all when working with the larger benchmark. 20Service Computation 2013, Valencia, Spain

21. 21 Conclusions We reported on our efforts to use backward-chaining reasoners to accommodate the changing knowledge base. We developed a query-optimization algorithm that will work with a reasoner interposed between the knowledge base and the query interpreter. We compared our implementation with traditional backward- chaining reasoners and found, that our implementation –could handle much larger knowledge bases –with more complete rule sets (OWL Horst) –is faster Service Computation 2013, Valencia, Spain

22. Future Work We will address the issue of being able to scale the knowledgebase to the level forward-chaining reasoners can handle We will be working on creating a hybrid reasoner that will combine the best of forward-chaining and backward- chaining 22Service Computation 2013, Valencia, Spain

23. Answering a query 23Service Computation 2013, Valencia, Spain QueryResponseanswerAQuery(query: Query) { // Set up initial SolutionSpace SolutionSpacesolutionSpace = empty;  // Repeatedly reduce SolutionSpace by applying // the most restrictive pattern while (unexplored patterns remain in the query) { computeEstimatesOfReponseSize (unexplored patterns);  QueryPattern p = unexplored pattern withsmallest estimate;  // Restrict SolutionSpace via // exploration of p QueryResponseanswerToP = BackwardChain(p);  solutionSpace.restrictTo (answerToP);  } return solutionSpace.finalJoin();  }