In this chapter, extended relational databases are considered where some attribute values are imprecisely known. The need for imperfect data is more and more recognized and imprecise information can appear in diverse situations such as data warehouses, forecasts, incomplete archives, structured data extracted from texts, or systems where information issued from automated recognition procedures is stored. Different formalisms can be used to represent imprecise information (see  for instance), and the possibilistic setting is assumed in the rest of the chapter. A key question is to define a sound semantics for queries addressed to imprecise databases. Since imprecise data are represented as (possibly infinite) sets of acceptable candidates, an imprecise database can be seen as a set of regular databases, called worlds, associated with a choice for each attribute value. This approach provides a rational starting point for the definition of a query in the sense that its result is the set of the results obtained for each world (or interpretation). Unfortunately, such an approach is intractable, obviously in the case of an infinite number of worlds, but also due to the possibly huge number of worlds when it is finite. This observation leads to consider only specific queries which can be processed directly against the possibilistic database (the processing is then called “compact”), while delivering a result equivalent to the one defined in terms of worlds. The principle of the approach advocated is summarized in figure 1.
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