1. SPARQL and OWL: How to Answer Conjunctive Queries with an Expressive Ontology Language Birte Glimm

2. Querying Ontologies DL Reasoner OWL Ontology Query Language Client Application

3. The Reasoner’s Task We do not just want to retrieve explicitly stated knowledge Reasoner should also infer implicitly stated knowledge We do not have complete information (Open World Assumption) We have to check entailment and an ontology can have several (possibly infinite) models

4. Standard Reasoning Tasks All reasoners support queries for the standard reasoning tasks such as –Satisfiability of classes/ontologies –Subsumption between classes –Retrieval of class instances The DL Implementation Group (DIG) developed DIG 1.1 as an interface standard

5. The Query Language DL based query languages (DIG, nRQL) –not very powerful –clear semantics –SPARQL-DL is promising Several RDF-based query languages available (RDQL, SeRQL, SPARQL) –Hard to define semantics –Too powerful

6. Conjunctive Queries The focus of our research is to develop algorithms for database-style conjunctive queries OWL is much more expressive than standard database schema languages SPARQL-DL is a subset of SPARQL that corresponds to conjunctive queries in DLs

7. SPARQL-DL example Retrieve all tuples (?x,?y,?z) such that ?x is an R5_Phosphatase, ?x contains the phosphatase domains ?y and ?z, ?y is a Catalytic domain, and ?z is a Fibronectin domain. PREFIX rdf:hhttp://www.w3.org/1999/02/22-rdf-syntax-nsi SELECT ?x, ?y, ?z FROM hontologyi WHERE { ?x rdf:type ontology:R5_Phosphatase; ?x ontology:contains_p-domain ?y; ?x ontology:contains_p-domain ?z; ?y rdf:type ontology:Catalytic; ?z rdf:type ontology:Fibronectin }

8. Queries and Reasoning Tasks Standard DL query languages (DIG, nRQL) can be reduced to standard reasoning tasks such as knowledge base satisfiability More expressive query languages (SPARQL-DL, conjunctive queries) do not directly correspond to standard reasoning taks

9. Answering Conjunctive Queries For OWL-Lite, we developed a decision procedure for conjunctive queries Answering a conjunctive query is reduced to (possibly several) ontology consistency checks Standard DL Reasoners can be used Practical implementations not yet available Future work on optimisations and extension to OWL DL

10. Query Rewriting Tree-shaped queries can directly be rewritten as class expressions The main problem are cyclic queries Classes can only describe tree-shaped structures We use this Tree Model Property and show that all cyclic queries can be rewritten into a set of tree-shaped queries

11. Query Rewriting Example (?x) Ã hasSon(?x, ?y) Æ isParentOf(?z, ?y) Æ hasDescendant(?x, ?z) Æ Lawyer(?z) hasSon isParentOf isDescendantOf ?z: Lawyer ?y ?x

12. Query Rewriting Example Knowledge Base contains: hasSon(Mary, Peter) 9hasChild.Lawer(Peter) hasSon v hasChild isParentOf ´ hasChild - hasChild v hasDescendant trans(hasDescendant) hasSon isParentOf isDescendantOf ?z: Lawyer ?y ?x

13. Query Rewriting Example Knowledge Base contains: hasSon(Mary, Peter) 9hasChild.Lawer(Peter) hasSon v hasChild isParentOf ´ hasChild - hasChild v hasDescendant trans(hasDescendant) hasSon hasChild isDescendantOf ?z: Lawyer ?y ?x

14. Query Rewriting Example Knowledge Base contains: hasSon(Mary, Peter) 9hasChild.Lawer(Peter) hasSon v hasChild isParentOf ´ hasChild - hasChild v hasDescendant trans(hasDescendant) hasSon hasChild ?z: Lawyer ?y ?x

15. Query Rewriting Example Knowledge Base contains: hasSon(Mary, Peter) 9hasChild.Lawer(Peter) hasSon v hasChild isParentOf ´ hasChild - hasChild v hasDescendant trans(hasDescendant) Retrieve instances of the concept 9hasSon.(9hasChild.Lawyer)