Static Analysis of Semantic Web Queries

Query containment is defined as the problem of determining if the result of a query is included in the result of another query for any given dataset. It has major applications in query optimization and knowledge base verification. The main objective of this thesis is to provide sound and complete procedures to determine containment of SPARQL queries under expressive description logic axioms. Further, we implement these procedures to support theoretical results by experimentation. To date, testing query containment has been performed using different techniques: containment mapping, canonical databases, automata theory techniques and through a reduction to the validity problem in logic. In this thesis, we use the later technique to test containment of SPARQL queries using an expressive logic called μ-calculus. In doing so, RDF graphs are encoded as transition systems which preserves its characteristics, and queries and schema axioms are encoded as μ-calculus formulae. Thereby, query containment can be reduced to the validity test in the logic. This thesis identifies various fragments of SPARQL (and PSPARQL) and description logic schema languages for which containment is decidable. Additionally, it provides theoretically and experimentally proven procedures to check containment of those decidable fragments. Finally, this thesis proposes a benchmark for containment solvers. This benchmark is used to test and compare the current state-of-the-art containment solvers.