Integrating Data from Possibly Inconsistent Databases

We address the problem of data inconsistencies while integrating data sets from multiple autonomous relational databases. We start by arguing that the semantics of integrating possibly inconsistent data is naturally captured by the maximal consistent subsets of the set of all information contained in the collected data. Based on this idea, we propose a simple and intuitive semantical framework, called the integrated relational calculus which is an extension of the classical relational calculus, for manipulating and querying possibly inconsistent data. We then show that our model generalizes the recently proposed model of flexible relational algebra of Agarwal, Keller, Wiederhold and Saraswat in the sense that the latter can be embedded into the former. We also shows that the flexible relational model is not capable to integrate correctly relations with more than one keys. We further argue that flexible relational model provides a rather weak query language. We then proves that for the databases with only one key the flexible model provides a correct integration of inconsistent data.