Database Repairs and Analytic Tableaux

In this article, we characterize in terms of analytic tableaux the repairs of inconsistent relational databases, that is databases that do not satisfy a given set of integrity constraints. For this purpose we provide closing and opening criteria for branches in tableaux that are built for database instances and their integrity constraints. We use the tableaux based characterization as a basis for consistent query answering, that is for retrieving from the database answers to queries that are consistent with respect to the integrity constraints.     

Processing negation and disjunction in logic programs through integrity constraints

Integrity constraints were initially defined to verify the correctness of the data that is stored in a database. They were used to restrict the modifications that can be applied to a database. However, there are many other applications in which integrity constraints can play an important role. For example, the semantic query optimization method developed by Chakravarthy, Grant, and Minker for definite deductive databases uses integrity constraints during query processing to prevent the exploration of search space that is bound to fail. In this paper, we generalize the semantic query optimization method to apply to negated atoms. The generalized method is referred to assemantic compilation. This exploration has led to two significant results. First, semantic compilation provides an alternative search space for negative query literals. The alternative search space can find answers in cases for which negation-as-finite-failure and constructive negation cannot. Second, we show how semantic compilation can be used to transform a disjunctive database with or without functions and denial constraints without negation into a new disjunctive database that complies with the integrity constraints.     

Disjunctive databases for representing repairs

This paper addresses the problem of representing the set of repairs of a possibly inconsistent database by means of a disjunctive database. Specifically, the class of denial constraints is considered. We show that, given a database and a set of denial constraints, there exists a (unique) disjunctive database, called canonical, which represents the repairs of the database w.r.t. the constraints and is contained in any other disjunctive database with the same set of minimal models. We propose an algorithm for computing the canonical disjunctive database. Finally, we study the size of the canonical disjunctive database in the presence of functional dependencies for both subset-based repairs and cardinality-based repairs.     

Prioritized repairing and consistent query answering in relational databases

A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how conflicts should be resolved. We investigate here the framework of preferred consistent query answers, in which user preferences are used to narrow down the set of repairs to a set of preferred repairs. We axiomatize desirable properties of preferred repairs. We present three different families of preferred repairs and study their mutual relationships. Finally, we investigate the complexity of preferred repairing and computing preferred consistent query answers.     

Model theoretic approach to view updates in deductive databases

The view update problem for deductive databases has been defined as the problem of accomplishing the update of an intensional predicate by modifying appropriately the extensional database. A previous paper by Grant, Horty, Lobo, and Minker developed algorithms for the insertion and the deletion of an intensional predicate in certain important classes of stratified disjunctive deductive databases. This paper introduces a model theoretic approach which encompasses a wide class of Herbrand semantics, including the perfect model and stable model semantics, for disjunctive databases including negation. This generalizes the earlier results: now the intensional database may contain disjunctive and denial rules, and the database may be required to satisfy integrity constraints. As in the previous paper, the algorithms are proved to be correct and best according to the criterion of causing minimal change to the database, where the first priority is to minimize deletions.     

Active Integrity Constraints for Database Consistency Maintenance

This paper introduces active integrity constraints (AICs), an extension of integrity constraints for consistent database maintenance. An active integrity constraint is a special constraint whose body contains a conjunction of literals which must be false and whose head contains a disjunction of update actions representing actions (insertions and deletions of tuples) to be performed if the constraint is not satisfied (that is its body is true). The AICs work in a domino-like manner as the satisfaction of one AIC may trigger the violation and therefore the activation of another one. The paper also introduces founded repairs, which are minimal sets of update actions that make the database consistent, and are specified and “supported” by active integrity constraints. The paper presents: 1) a formal declarative semantics allowing the computation of founded repairs and 2) a characterization of this semantics obtained by rewriting active integrity constraints into disjunctive logic rules, so that founded repairs can be derived from the answer sets of the derived logic program. Finally, the paper studies the computational complexity of computing founded repairs.     

Study on consistent query answering in inconsistent databases

Consistent query answering is an approach to retrieving consistent answers over databases that might be inconsistent with respect to some given integrity constraints. The approach is based on a concept of repair. This paper surveys several recent researches on obtaining consistent information from inconsistent databases, such as the underlying semantic model, a number of approaches to computing consistent query answers and the computational complexity of this problem. Furthermore, the work outlines potential research directions in this area.     

A three-valued semantics for querying and repairing inconsistent databases

The problem of managing and querying inconsistent databases has been deeply investigated in the last few years. As the problem of consistent query answering is hard in the general case, most of the techniques proposed so far have an exponential complexity. Polynomial techniques have been proposed only for restricted forms of constraints (such as functional dependencies) and queries. In this paper, a technique for computing “approximate” consistent answers in polynomial time is proposed, which works in the presence of a wide class of constraints (namely, full constraints) and Datalog queries. The proposed approach is based on a repairing strategy where update operations assigning an undefined truth value to the “reliability” of tuples are allowed, along with updates inserting or deleting tuples. The result of a repair can be viewed as a three-valued database which satisfies the specified constraints. In this regard, a new semantics (namely, partial semantics) is introduced for constraint satisfaction in the context of three-valued databases, which aims at capturing the intuitive meaning of constraints under three-valued logic. It is shown that, in order to compute “approximate” consistent query answers, it suffices to evaluate queries by taking into account a unique repair (called deterministic repair), which in some sense “summarizes” all the possible repairs. The so obtained answers are “approximate” in the sense that are safe (true and false atoms in the answers are, respectively, true and false under the classical two-valued semantics), but not complete.     

First-order query rewriting for inconsistent databases

We consider the problem of retrieving consistent answers over databases that might be inconsistent with respect to a set of integrity constraints. In particular, we concentrate on sets of constraints that consist of key dependencies, and we give an algorithm that computes the consistent answers for a large and practical class of conjunctive queries. Given a query q, the algorithm returns a first-order query Q (called a query rewriting) such that for every (potentially inconsistent) database I, the consistent answers for q can be obtained by evaluating Q directly on I.     

Distance semantics for database repair

In many scenarios, a database instance violates a given set of integrity constraints. In such cases, it is often required to repair the database, that is, to restore its consistency. A primary motif behind the repairing approaches is the principle of minimal change, which is the aspiration to keep the recovered data as faithful as possible to the original (inconsistent) database. In this paper, we represent this qualitative principle quantitatively, in terms of distance functions and some underlying metrics, and so 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 several 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.      

Probabilistic query answering over inconsistent databases

This paper presents a framework for querying inconsistent databases in the presence of functional dependencies. Most of the works dealing with the problem of extracting reliable information from inconsistent databases are based on the notion of repair, a minimal set of tuple insertions and deletions which leads the database to a consistent state (called repaired database), and the notion of consistent query answer, a query answer that can be obtained from every repaired database. In this work, both the notion of repair and query answer differ from the original ones. In the presence of functional dependencies, tuple deletions are the only operations that are performed in order to restore the consistency of an inconsistent database. However, deleting a tuple to remove an integrity violation potentially eliminates useful information in that tuple. In order to cope with this problem, we adopt a notion of repair, based on tuple updates, which allows us to better preserve information in the source database. A drawback of the notion of consistent query answer is that it does not allow us to discriminate among non-consistent answers, namely answers which can be obtained from a non-empty proper subset of the repaired databases. To obtain more informative query answers, we propose the notion of probabilistic query answer, that is query answers are tuples associated with probabilities. This new semantics of query answering over inconsistent databases allows us to give a measure of uncertainty to query answers. We show that the problem of computing probabilistic query answers is FP ^#P -complete. We also propose a technique for computing probabilistic answers to arbitrary relational algebra queries.     

基于空值修复的数据库一致性查询方法*

完整性约束常用来定义数据库的数据语义,违反约束的数据库实例为不一致数据库,返回含有不一致结果的查询称为不一致查询。一致性查询目的在于不修改数据库实例而从不一致数据库获取满足约束的查询结果,已有方法因其支持的约束类型有限或计算复杂度高而影响其应用范围。提出了一种基于空值修复的数据库一致性查询方法,首先将原始完整性约束转换为与查询相关的统一约束,然后根据统一约束对原SQL查询进行查询重写,重写后的查询将不一致属性值当做空值来处理以获得满足完整性约束的结果。系统实现与实验证明,该方法在多种完整性约束类型与SQL     

Minimal-change integrity maintenance using tuple deletions

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 focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [in: ACM Symposium on Principles of Database Systems (PODS), 1999, 68] (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 cases. 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.     

Controlled generation of intensional answers

Intensional answers are conditions that tuples of values must satisfy to belong to the usual extensional answer of a query addressed to a deductive database. The authors review the concept of intensional answers and introduce a general method for generating them as logical consequences of the query and of deduction rules. The authors show how integrity constraints can filter out inadequate answers and produce simpler and more informative answers. An efficient organization for the combination of answers and constraints is described. The introduction of negation in queries and in the body of deduction rules is discussed. Beyond the mechanics of answer generation, the interest of the approach also depends on a strategy for selecting answers to a user submitting a query. This requires techniques for user modeling and dialogue management similar to those required for expert systems     

Consistent data for inconsistent XML document

XML document may contain inconsistencies that violate predefined integrity constraints, which causes the data inconsistency problem. In this paper, we consider how to get the consistent data from an inconsistent XML document. There are two basic concepts for this problem: Repair is the data consistent with the integrity constraints, and also minimally differs from the original one. Consistent data is the data common for every possible repair. First we give a general constraint model for XML, which can express the commonly discussed integrity constraints, including functional dependencies, keys and multivalued dependencies. Next we provide a repair framework for inconsistent XML document with three basic update operations: node insertion, node deletion and node value modification. Following this approach, we introduce the concept of repair for inconsistent XML document, discuss the chase method to generate repairs, and prove some important properties of the chase. Finally we give a method to obtain the greatest lower bound of all possible repairs, which is sufficient for consistent data. We also implement prototypes of our method, and evaluate our framework and algorithms in the experiment.     

View updates in stratified disjunctive databases

The view update problem is considered in the context of deductive databases where the update of an intensional predicate is accomplished by modifying appropriately the underlying relations in the extensional database. Two classes of disjunctive databases are considered. The first class contains those disjunctive databases which allow only definite rules in the intensional database and disjunctive facts in the extensional database. The second class contains stratified disjunctive databases so that in addition to the first class, negation is allowed in the bodies of the rules, but the database must be stratified. Algorithms are given both for the insertion of an intensional predicate into and the deletion of an intensional predicate from the database. The algorithms use SLD resolution and the concept of minimal models of the extensional database. The algorithms are proved to be correct and best according to the criterion of causing minimal change to the database, where we give first priority to minimizing deletions.Research supported by the National Science Foundation under grant numbers IRI-8916059, IRI-8921591, IRI-9200898, and IRI-9210220.     

Computational methods for database repair by signed formulae*

We introduce a simple and practical method for repairing inconsistent databases. Given a possibly inconsistent database, the idea is to properly represent the underlying problem, i.e., to describe the possible ways of restoring its consistency. We do so by what we call signed formulae, and show how the ‘signed theory’ that is obtained can be used by a variety of off-the-shelf computational models in order to compute the corresponding solutions, i.e., consistent repairs of the database. *This paper is a revised and extended version of [9].     

Inferring negative information from disjunctive databases

We propose criteria that any rule for inferring negative information from disjunctive databases should satisfy, and examine existing rules from this viewpoint. We then present a new inference rule, the ‘disjunctive database rule’ (DDR), and compare it to the existing rules with respect to the criteria. In particular, the DDR is equivalent to the CWA for definite databases, it infers no more negative information than the GCWA, and it interprets disjunction inclusively rather than exclusively. We generalize the DDR to a class of layered databases, describe an implementation of the DDR, ‘negation as positive failure’, and study its soundness and completeness properties.     

Implementing temporal integrity constraints using an active DBMS

The paper proposes a general architecture for implementing temporal integrity constraints by compiling them into a set of active DBMS rules. The modularity of the design allows easy adaptation to different environments. Both differences in the specification languages and in the target rule systems can be easily accommodated. The advantages of this architecture are demonstrated on a particular temporal constraint compiler. This compiler allows automatic translation of integrity constraints formulated in Past Temporal Logic into rules of an active DBMS (in the current version of the compiler two active DBMS are supported: Starburst and INGRES). During the compilation the set of constraints is checked for the safe evaluation property. The result is a set of SQL statements that includes all the necessary rules needed for enforcing the original constraints. The rules are optimized to reduce the space overhead introduced by the integrity checking mechanism. There is no need for an additional runtime constraint monitor. When the rules are activated, all updates to the database that violate any of the constraints are automatically rejected (i.e., the corresponding transaction is aborted). In addition to straightforward implementation, this approach offers a clean separation of application programs and the integrity checking code