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Long-term data-driven studies have become indispensable in many areas ofscience. Often, the data formats, structures and semantics of data change overtime, the data sets evolve. Therefore, studies over several decades inparticular have to consider changing database schemas. The evolution of thesedatabases lead at some point to a large number of schemas, which have to bestored and managed, costly and time-consuming. However, in the sense ofreproducibility of research data each database version must be reconstructablewith little effort. So a previously published result can be validated andreproduced at any time.  Nevertheless, in many cases, such an evolution can not be fullyreconstructed. This article classifies the 15 most frequently used schemamodification operators and defines the associated inverses for each operation.For avoiding an information loss, it furthermore defines which additionalprovenance information have to be stored. We define four classes dealing withdangling tuples, duplicates and provenance-invariant operators. Each class willbe presented by one representative.  By using and extending the theory of schema mappings and their inverses forqueries, data analysis, why-provenance, and schema evolution, we are able tocombine data analysis applications with provenance under evolving databasestructures, in order to enable the reproducibility of scientific results overlonger periods of time. While most of the inverses of schema mappings used foranalysis or evolution are not exact, but only quasi-inverses, adding provenanceinformation enables us to reconstruct a sub-database of research data that issufficient to guarantee reproducibility.

Enhanced Inversion of Schema Evolution with Provenance