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Lossless Selection Views under Constraints

The problem of updating a database through a set of views consists in propagating updates of the views to the base relations over which the view relations are defined, so that the changes to the database reflect exactly those to the views. This is a classical problem in database research, known as the view update problem [1], which in recent years has received renewed attention. View updates can be consistently propagated in an unambiguous way under the condition that the mapping between database and view relations is lossless, and that each database relation can be expressed in terms of the view relations by means of a query, in much the same way the latter are defined from the former [3]. In such a context, database decompositions play an important role, in that their losslessness is associated with the existence of an explicit reconstruction operator that prescribes how a database relation can be rebuilt from the pieces into which it has been decomposed. In the case of horizontal decomposition, in which a relation is split into sub-relations containing each a subset of its rows, the reconstruction operator is the union. The study of horizontal decomposition in the literature has mostly focused on settings where data values can only be compared for equality. However, most realworld applications make use of data values coming from domains with a richer structure (e.g., ordering) on which a variety of other restrictions besides equality can be expressed (e.g., that of being within a range or above a threshold). It is therefore of practical interest to consider a scenario where some of the attributes in the database schema are interpreted over a specific domain, such as the reals or the integers, on which a set of special predicates (e.g., smaller/greater than) and functions (e.g., addition/subtraction) are defined, according to a first-order language C. We consider horizontal decomposition in such a setting and investigate its losslessness in the presence of integrity constraints. The only restriction we impose on the language C is that of being closed under negation.