Unique Solutions in Data Exchange

Data exchange is the problem of transforming data structured according to a source schema into data structured according to a target schema, via a mapping specified by rules in the form of source-to-target tuple generating dependencies. In this context, given a source instance and a mapping, there might be more than one valid target instance that satisfies the mapping. This issue contradicts the main goal of exchanging data, namely to have a materialised target instance that can be used to answer queries over the target schema without reference to the original source instance. In this paper we introduce and solve the novel problem of definability abduction, which aims at finding extensions to the initial schema mappings to guarantee the uniqueness of the materialised target instance. We consider several semantic criteria to select reasonable extensions and provide provably sound and complete algorithms to generate these additions. We also do a complexity analysis in different data exchange settings, also with source and target dependencies.