Views and Updates over Distributed Databases

This contribution deals with systematic exploitation of logical reduction techniques to databases. The particular applications are views and updates over distributed databases. Logical reduction techniques come in two favors. The first one: the syntactically defined translation schemes, which describe transformations of database schemes. They give rise to two induced maps, translations and transductions. Transductions describe the induced transformation of database instances and the translations describe the induced transformations of queries. The second one: Feferman-Vaught reductions, which are applied in situations, where a relational structure is pieced together from a set of sub-structures. The reduction describes how the queries over the structure can be computed from queries over the components and queries over the index set. Combination and development of these techniques allow us to generalize the propagation technique for relational algebra and the incremental re-computation technique for some kinds of Data log programs to cases of definable sets of tuples to be deleted or inserted.