Distance-Based Repairs of Databases

Abstract

Abstract. We introduce a general framework for repairing inconsistent databases by distance-based considerations. The uniform way of representing repairs and their semantics clarifies the essence behind various approaches to consistency restoration in database systems, helps to compare the underlying formalisms, and relates them to existing methods of defining belief revision operators, merging data sets, and integrating information systems.

Distance semantics for database repair

“…3 That is, d f is obtained by applying f on the distances among matched elements and on the distances among non-matched elements and the other set. c) A matching m between sets A and B is called…”

“…That is, the function value is non-decreasing when an element in the multiset is replaced by a larger element 3. Alternatively, one could define, for a nonempty set S, d(e, S) = 1 2 max{d(e, s) | s ∈ S}.…”

“…The rest of this paper, which is a revised and extended version of the paper in [3], is organized as follows: In Section 2 we give a general representation of consistency restoration in database systems as a distance minimization problem. In Section 3 we consider different distance-based approaches to database repairing, and incorporate the notion of optimal matching (between the spoiled and the recovered data) for generalizing some existing repairing methods and defining several new ones.…”

Commonsense reasoning by distance semantics

“…Indeed, reasoning with distance semantics is a cornerstone behind many formalisms for maintaining uncertainty, such as operators for modelling belief revision (e.g., [7,16,18,24,29]), methodologies for merging independent datasources [20,21,25], consistent query answering in database systems [1,3,4,9,10,26], and several areas in the context of social choice theory, such as group decision making [22], preference representation [23], and judgment aggregation [17,27].…”