are expressed in languages over alphabets composed of symbols for each of their respective relations. The mapping consists of assertions between queries over and queries over . When users pose queries over the data integration system, they pose queries over and the mapping then asserts connections between the elements in the global schema and the source schemas. A database over a schema is defined as a set of sets, one for each relation (in a relational database). The database corresponding to the source schema would comprise the set of sets of tuples for each of the heterogeneous data sources and is called the source database. Note that this single source database may actually represent a collection of disconnected databases. The database corresponding to the virtual mediated schema is called the global database. The global database must satisfy the mapping with respect to the source database. The legality of this mapping depends on the nature of the correspondence between and . Two popular ways to model this correspondence exist: Global as View or GAV and Local as View or LAV. GAV systems model the global database as a set of views over . In this case associates to each element of a query over . Query processing becomes a straightforward operation due to the well-defined associations between and . The burden of complexity falls on implementing mediator code instructing the data integration system exactly how to retrieve elements from the source databases. If any new sources join the system, considerable effort may be necessary to update the mediator, thus the GAV approach appears preferable when the sources seem unlikely to change. In a GAV approach to the example data integration system above, the system designer would first develop mediators for each of the city information sources and then design the global schema around these mediators. For example, consider if one of the sources served a weather website. The designer would likely then add a corresponding element for weather to the global schema. Then the bulk of effort concentrates on writing the proper mediator code that will transform predicates on weather into a query over the weather website. This effort can become complex if some other source also relates to weather, because the designer may need to write code to properly combine the results from the two sources. On the other hand, in LAV, the source database is modeled as a set