We motivate, formalize and investigate the notions of data quality assessment and data quality query answering as context dependent activities. Contexts for the assessment and usage of a data source at hand are modeled as collections of external databases, that can be materialized or virtual, and mappings within the collections and with the data source at hand. In this way, the context becomes "the complement" of the data source wrt a data integration system. The proposed model allows for natural extensions, like considering data quality predicates, and even more expressive ontologies for data quality assessment.