The Semiring Framework for Database Provenance.

Imagine a computational process that uses a complex input consisting of multiple \"items\" (e.g.,files, tables, tuples, parameters, configuration rules) The provenance analysis of such a process allows us to understand how the different input items affect the output of the computation. It can be used, for example, to derive confidence in the output (given confidences in the input items), to derive the minimum access clearance for the output (given input items with different classifications), to minimize the cost of obtaining the output (given a complex input item pricing scheme). It also applies to probabilistic reasoning about an output (given input item distributions), as well as to output maintenance, and to debugging. Provenance analysis for queries, views, database ETL tools, and schema mappings is strongly influenced by their declarative nature, providing mathematically nice descriptions of the output-inputs correlation. In a series of papers starting with PODS 2007 we have developed an algebraic framework for describing such provenance based on commutative semirings and semimodules over such semirings. So far, the framework has exploited usefully the observation that, for database provenance, data use has two flavors: joint and alternative. Here, we have selected several insights that we consider essential for the appreciation of this framework's nature and effectiveness and we also give some idea of its applicability.