In this paper we consider the problem of the logical characterization of the notion of consistent answer in a relational database that may violate given integrity constraints. This notion is captured in terms of the possible repaired versions of the database. A rnethod for computing consistent answers is given and its soundness and completeness (for some classes of constraints and queries) proved. The method is based on an iterative procedure whose termination for several classes of constraints is proved as well.

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The handling of user preferences is becoming an increasingly important issue in present-day information systems. Among others, preferences are used for information filtering and extraction to reduce the volume of data presented to the user. They are also used to keep track of user profiles and formulate policies to improve and automate decision making. We propose here a simple, logical framework for formulating preferences as preference formulas. The framework does not impose any restrictions on the preference relations, and allows arbitrary operation and predicate signatures in preference formulas. It also makes the composition of preference relations straightforward. We propose a simple, natural embedding of preference formulas into relational algebra (and SQL) through a single winnow operator parameterized by a preference formula. The embedding makes possible the formulation of complex preference queries, for example, involving aggregation, by piggybacking on existing SQL constructs. It also leads in a natural way to the definition of further, preference-related concepts like ranking. Finally, we present general algebraic laws governing the winnow operator and its interactions with other relational algebra operators. The preconditions on the applicability of the laws are captured by logical formulas. The laws provide a formal foundation for the algebraic optimization of preference queries. We demonstrate the usefulness of our approach through numerous examples.

We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We identify two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [ABC99] (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable. We consider denial constraints, general functional and inclusion dependencies, as well as key and foreign key constraints. Our results shed light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance.Given a database instance r, the set Σ(r) of facts of r is the set of ground atomic formulas {P (ā) | r P (ā)}, where P is a relation name andā a ground tuple. Definition 2The distance ∆ − (r, r ′ ) between data-base instances r and r ′ is defined as ∆ − (r, r ′ ) = (Σ(r) − Σ(r ′ )).Definition 3 For the instances r, r ′ , r ′′ , r ′ ≤ r r ′′ if ∆ − (r, r ′ ) ⊆ ∆ − (r, r ′′ ), i.e., if the distance between r and r ′ is less than or equal to the distance between r and r ′′ .Definition 4 Given a set of integrity constraints IC and database instances r and r ′ , we say that r ′ is a repair of r w.r.t. IC if r ′ IC and r ′ is ≤ r -minimal in the class of database instances that satisfy IC.If r ′ is a repair of r, then Σ(r ′ ) is a maximal consistent subset of Σ(r). We denote by Repairs IC (r) the set of repairs of r w.r.t. IC. This set is nonempty, since the empty database instance satisfies every set of FDs and INDs.