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This paper presents a framework for data integration currently under development in the Squirrel project. The framework is based on a special class of mediators, called Squirrel integration mediators. These mediators can support the traditional virtual and materialized approaches, and also hybrids of them.In the Squirrel mediators, a relation in the integrated view can be supported as (a) fully materialized, (b) fully virtual, or (c) partially materialized (i.e., with some attributes materialized and other attributes virtual). In general, (partially) materialized relations of the integrated view are maintained by incremental updates from the source databases. Squirrel mediators provide two approaches for doing this: (1) materialize all needed auxiliary data, so that data sources do not have to be queried when processing the incremental updates; or (2) leave some or all of the auxiliary data virtual, and query selected source databases when processing incremental updates.The paper presents formal notions of consistency and "freshness" for integrated views defined over multiple autonomous source databases. It is shown that Squirrel mediators satisfy these properties.