SPARQL and OWL How to Answer Conjunctive Queries

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

Querying Ontologies Client Application DL Reasoner Query Language OWL Ontology

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

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

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

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

SPARQL-DL example Retrieve all tuples (? x, ? y, ? z) such that ? x is an R 5_Phosphatase, ? x contains the phosphatase domains ? y and ? z, ? y is a Catalytic domain, and ? z is a Fibronectin domain. PREFIX rdf: hhttp: //www. w 3. org/1999/02/22 -rdf-syntax-nsi SELECT ? x, ? y, ? z FROM hontologyi WHERE { ? x rdf: type ontology: R 5_Phosphatase; ? x ontology: contains_p-domain ? y; ? x ontology: contains_p-domain ? z; ? y rdf: type ontology: Catalytic; ? z rdf: type ontology: Fibronectin }

Queries and Reasoning Tasks • Standard DL query languages (DIG, n. RQL) 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

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

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

Query Rewriting Example (? x) Ã has. Son(? x, ? y) Æ is. Parent. Of(? z, ? y) Æ has. Descendant(? x, ? z) Æ Lawyer(? z) is. Descendant. Of ? x has. Son ? y is. Parent. Of ? z: Lawyer

Query Rewriting Example Knowledge Base contains: has. Son v has. Child is. Parent. Of ´ has. Child v has. Descendant trans(has. Descendant) has. Son(Mary, Peter) 9 has. Child. Lawer(Peter) is. Descendant. Of ? x has. Son ? y is. Parent. Of ? z: Lawyer

Query Rewriting Example Knowledge Base contains: has. Son v has. Child is. Parent. Of ´ has. Child v has. Descendant trans(has. Descendant) has. Son(Mary, Peter) 9 has. Child. Lawer(Peter) is. Descendant. Of ? x has. Son ? y has. Child ? z: Lawyer

Query Rewriting Example Knowledge Base contains: has. Son v has. Child is. Parent. Of ´ has. Child v has. Descendant trans(has. Descendant) ? x has. Son ? y has. Son(Mary, Peter) 9 has. Child. Lawer(Peter) has. Child ? z: Lawyer

Query Rewriting Example Knowledge Base contains: has. Son v has. Child is. Parent. Of ´ has. Child v has. Descendant trans(has. Descendant) has. Son(Mary, Peter) 9 has. Child. Lawer(Peter) Retrieve instances of the concept 9 has. Son. (9 has. Child. Lawyer)