Research has deeply investigated several issues related to the use of integrity constraints on relational databases. In particular, a great deal of attention has been devoted to the problem of extracting "reliable" information from databases containing pieces of information inconsistent with regard to some integrity constraints. In this manuscript, the problem of extracting consistent information from relational databases violating integrity constraints on numerical data is addressed. Aggregate constraints defined as linear inequalities on aggregate-sum queries on input data are considered. The notion of repair as consistent set of updates at attribute-value level is exploited, and the characterization of several data-complexity issues related to repairing data and computing consistent query answers is provided. Moreover, a method for computing reasonable repairs of inconsistent numerical databases is introduced, for a restricted but expressive class of aggregate constraints. An extension of this method for dealing with the data repairing problem in the presence of weak aggregate constraints which are expected to be satisfied, but not required to, is presented. Furthermore, a technique for computing consistent answers of aggregate queries in the presence of a wide form of aggregate constraints is provided. Finally, extensions of the framework as well as several open problems are discussed.

Autorentext
Francesco Parisi is a Professor of Law at the University of Minnesota Law School and a Professor of Economics at the University of Bologna, Department of Economics. In 2002, he was appointed Professore Ordinario per Chiara Fama at the University of Milan (Statale) where he held a Chair in Private Law. From 1993 to 2006, he taught at George Mason University where he served as Professor of Law & Director of the Law and Economics Program and as an Associate Director of the J.M. Buchanan Center for Political Economy. Professor Parisi received his D.Jur. degree from the University of Rome "La Sapienza", an LL.M., a J.S.D. and an M.A. degree in Economics from the University of California at Berkeley and a Ph.D in Economics from George Mason University. Professor Parisi currently serves as Editor-in-Chief of the Review of Law and Economics and the Supreme Court Economic Review.

Inhalt
Introduction.- Preliminaries.- Repairing and Querying: the Fundamental Decision Problems.- Computing Card-minimal Repairs.- Consistent Answers to Aggregate Queries.- Possible Extensions and Open Problems.- References.