Data quality assessment and data cleaning are context dependent activities. Starting from this observation, in previous work a context model for the assessment of the quality of a database was proposed. A context takes the form of a possibly virtual database or a data integration system into which the database under assessment is mapped, for additional analysis, processing, and quality data extraction. In this work, we extend contexts with dimensions, and by doing so, multidimensional data quality assessment becomes possible. At the core of multidimensional contexts we find ontologies written as Datalog
programs with provably good properties in terms of query answering. We use this language to represent dimension hierarchies, dimensional constraints, dimensional rules, and specifying quality data. Query answering relies on and triggers dimensional navigation, and becomes an important tool for the extraction of quality data.