An inverse of a schema mapping M is intended to "undo" what M does, thus providing a way to perform "reverse" data exchange. In recent years, three different formalizations of this concept have been introduced and studied, namely, the notions of an inverse of a schema mapping, a quasi-inverse of a schema mapping, and a maximum recovery of a schema mapping. The study of these notions has been carried out in the context in which source instances are restricted to consist entirely of constants, while target instances may contain both constants and labeled nulls. This restriction on source instances is crucial for obtaining some of the main technical results about these three notions, but, at the same time, limits their usefulness, since reverse data exchange naturally leads to source instances that may contain both constants and labeled nulls. We develop a new framework for reverse data exchange that supports source instances that may contain nulls, thus overcoming th...
Ronald Fagin, Phokion G. Kolaitis, Lucian Popa, Wa