Abstract

The two fundamental operators of schema mappings, composition and inversion, are discussed. The goal of composition operator is to generate a mapping M13 has the same effect as applying successively two given mappings M12 andM23. The proposals for inverting mappings including Fagin-inverse based on the idea that a mapping composed with its inverse should be equal to the identity schema mapping. Quasi-inverses are based on the idea to relax the notion of Fagin-inverse by not differentiating between source instances that have the same space of solutions. Maximum recovery is a mapping that brings back the maximum amount of sound information. For every mapping M that is total and closed-down if quasi-invertible, then M has a maximum recovery and, furthermore, every maximum recovery of M is also a quasi-inverse of M. One of the features of algorithm maximum recovery is the use of query rewriting allowing reusing in the computation of an inverse the large number of techniques for query rewriting.