of views over . In this case associates to each element of a query over . Here the exact associations between and are no longer well-defined. As is illustrated in the next section, the burden of determining how to retrieve elements from the sources is placed on the query processor. The benefit of an LAV modeling is that new sources can be added with far less work than in a GAV system, thus the LAV approach should be favored in cases where the mediated schema is less stable or likely to change. In an LAV approach to the example data integration system above, the system designer designs the global schema first and then simply inputs the schemas of the respective city information sources. Consider again if one of the sources serves a weather website. The designer would add corresponding elements for weather to the global schema only if none existed already. Then programmers write an adapter or wrapper for the website and add a schema description of the website's results to the source schemas. The complexity of adding the new source moves from the designer to the query processor. Query processing The theory of query processing in data integration systems is commonly expressed using conjunctive queries and Datalog, a purely declarative logic programming language. One can loosely think of a conjunctive query as a logical function applied to the relations of a database such as " where ". If a tuple or set of tuples is substituted into the rule and satisfies it (makes it true), then we consider that tuple as part of the set of answers in the query. While formal languages like Datalog express these queries concisely and without ambiguity, common SQL queries count as conjunctive queries as well. In terms of data integration, "query containment" represents an important property of conjunctive queries. A query contains another query (denoted ) if the results of applying are a subset of the results of applying for any database. The two queries are said to be equivalent if the resulting sets are equal for any database. This is important because in both GAV and LAV systems, a user poses conjunctive queries over a virtual schema represented by a set of views, or "materialized" conjunctive queries. Integration seeks to rewrite the queries represented by the views to make their results equivalent or maximally contained by our user's query. This corresponds to