A New Approach to Database Auto-Design by Logic

The database auto-design is an important problem in database research.In this paper we propose some new ideas and an approach called “logic approach” to implement the database auto-design.Given a relational scheme and a set of the functional dependencies for the relation we can obtain all of the functional dependencies and key for the relation and determine the normal form the relation satisfies.     

An Infornation-Theoretic Analysis of Relational Databases—Part I: Data Dependencies and Information Metric

Database design is based on the concept of data dependency, which is the interrelationship between data contained in various sets of attributes. In particular, functional, multivalued and acyclic join, dependencies play an essential role in the design of database schemas. The basic definition of an information metric and how this notion can be used in relational database are discussed in this paper. We use Shannon entropy as an information metric to quantify the information associated with a set of attributes. Thus, we prove that data dependencies can be formulated in terms of entropies. These formulas make the numerical computation and testing of data dependencies feasible. Among the different types of data dependencies, the acyclic join dependency is most important to the design of a relational database schema. The acyclic join dependency, with multivalued dependency as a special case, impose a constraint on the information-preserving decomposition of a relation. It is interesting that this constraint on a relation is similar to Gibbs' condition for separating physical systems in statistical mechanics. They both assert that entropy is preserved during the decomposition process. That is, the entropies of the corresponding set of attributes must satisfy the inclusion–exclusion identity.     

Normalization and lossless join decomposition of similarity‐based fuzzy relational databases

Fuzzy relational database models generalize the classical relational database model by allowing uncertain and imprecise information to be represented and manipulated. In this article, we introduce fuzzy extensions of the normal forms for the similarity‐based fuzzy relational database model. Within this framework of fuzzy data representation, similarity, conformance of tuples, the concept of fuzzy functional dependencies, and partial fuzzy functional dependencies are utilized to define the fuzzy key notion, transitive closures, and the fuzzy normal forms. Algorithms for dependency preserving and lossless join decompositions of fuzzy relations are also given. We include examples to show how normalization, dependency preserving, and lossless join decomposition based on the fuzzy functional dependencies of fuzzy relation are done and applied to some real‐life applications. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 885–917, 2004.     

Representative Instances and ?-Acyclic Relational Schemes

In this paper, we study under what conditions will a pairwise inconsistent relational database ≪R,r≫ have a universal/representative instance L. If R is ?-acyclic and r satisfies all existence constraints, then it is possible to construct a universal instance L, using unmarked nulls, whose total projections onto R yield exactly the relations in r. We show that L would actually be a representative instance under a set of functional dependencies if R satisfies the additional mild condition: for any functional dependency X ? A where A is a single attribute, whenever XA is contained in two relation schemes R and R' of R, it follows that R ?R' is a relation scheme of R, having X as one of its keys.     

Relational database schema design for uncertain data

Driven by the dominance of the relational model, we investigate how the requirements of applications on the certainty of functional dependencies can improve the outcomes of relational database schema design. For that purpose, we assume that tuples are assigned a degree of possibility with which they occur in a relation, and that functional dependencies are assigned a dual degree of certainty which says to which tuples they apply. A design theory is developed for functional dependencies with degrees of certainty, including efficient axiomatic and algorithmic characterizations of their implication problem. Naturally, the possibility degrees of tuples bring forward different degrees of data redundancy, caused by functional dependencies with the dual degree of certainty. Variants of the classical syntactic Boyce–Codd and Third Normal Forms are established. They are justified semantically in terms of eliminating data redundancy and update anomalies of given degrees, and minimizing data redundancy of given degrees across all dependency-preserving decompositions, respectively. As a practical outcome of our results, designers can simply fix the degree of certainty they target, and then apply classical decomposition and synthesis to the set of functional dependencies whose associated degree of certainty meets the target. Hence, by fixing the certainty degree a designer controls which integrity requirements will be enforced for the application and which data will be processed by the application. The choice of the certainty degree also balances the classical trade-off between query and update efficiency on future database instances. Our experiments confirm the effectiveness of our control parameter, and provide original insight into classical normalization strategies and their implementations.     

从DTD映射到关系模式:一种保持数据依赖的映射方法

XML正迅速成为互联网上数据表示和交换的标准．用关系数据库存储XML数据是XML存储策略之一．为了将XML数据存储到关系数据库中，人们研究了从DTD到关系模式的映射方法．提出了一种保持数据依赖的映射方法PDD．与已有的Shared—Inlining方法相比，PDD方法充分考虑了DTD蕴涵的数据依赖关系，保证了XML文档的完整性．通过对泛关系进行模式分解，得到的关系模式保持函数依赖，并且满足2NF．可以证明，这种方法是有效的．     

Interval-based temporal functional dependencies: specification and verification

In the temporal database literature, every fact stored in a database may be equipped with two temporal dimensions: the valid time, which describes the time when the fact is true in the modeled reality, and the transaction time, which describes the time when the fact is current in the database and can be retrieved. Temporal functional dependencies (TFDs) add valid time to classical functional dependencies (FDs) in order to express database integrity constraints over the flow of time. Currently, proposals dealing with TFDs adopt a point-based approach, where tuples hold at specific time points, to express integrity constraints such as “for each month, the salary of an employee depends only on his role”. To the best of our knowledge, there are no proposals dealing with interval-based temporal functional dependencies (ITFDs), where the associated valid time is represented by an interval and there is the need of representing both point-based and interval-based data dependencies. In this paper, we propose ITFDs based on Allen’s interval relations and discuss their expressive power with respect to other TFDs proposed in the literature: ITFDs allow us to express interval-based data dependencies, which cannot be expressed through the existing point-based TFDs. ITFDs allow one to express constraints such as “employees starting to work the same day with the same role get the same salary” or “employees with a given role working on a project cannot start to work with the same role on another project that will end before the first one”. Furthermore, we propose new algorithms based on B-trees to efficiently verify the satisfaction of ITFDs in a temporal database. These algorithms guarantee that, starting from a relation satisfying a set of ITFDs, the updated relation still satisfies the given ITFDs.     

An Extension of "Representative Instances and γ-Acyclic Relational Schemes"

Let R be a γ-acyclic relational scheme, and let F be the set of functional dependencies (FD's) embodied in R. Given an existence constrained database r over R, it was shown in [1] that it is possible to connect tuples from different relations in r and construct a universal instance L, possibly containing null values δ, such that the total projection of L onto R yields exactly the set r. Moreover, conditions were given which guarantee that this L would satisfy the functional dependency with nulls (NFD) counterparts of FD's, in F. The purpose of this note is to generalize the latter result and show that under the same conditions, L actually satisfies NFD counterparts of FD's in the closure F+ of F.     

Functional dependencies with null values, fuzzy values, and crispvalues

Based on the concepts of the semantic proximity, we present a definition of the fuzzy functional dependency, We show that the inference rules for fuzzy functional dependencies, which are the same as Armstrong's axioms for the crisp case, are correct and complete. We also show that dependent constraints with dull values constitute a lattice. Functional dependencies in classical relational databases and null functional dependencies can be viewed as a special case of fuzzy functional dependencies. By applying the unified functional dependencies to the relational database design, we can represent the data with fuzzy values, null values and crisp values under relational database management systems, By using fuzzy functional dependencies, we can compress the range of a fuzzy value and make this fuzzy value “clearer”     

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.     

Propagating XML constraints to relations

We present a technique for refining the design of relational storage for XML data. The technique is based on XML key propagation: given a set of keys on XML data and a mapping (transformation) from the XML data to relations, what functional dependencies must hold on the relations produced by the mapping? With the functional dependencies one can then convert the relational design into, e.g. 3NF, BCNF, and thus develop efficient relational storage for XML data. We provide several algorithms for computing XML key propagation. One algorithm is to check whether a functional dependency is propagated from a set of XML keys via a predefined mapping; this allows one to determine whether or not the relational design is in a normal form. The others are to compute a minimum cover for all functional dependencies that are propagated from a set of XML keys and hold on a universal relation; these provide guidance for how to design a relational schema for storing XML data. These algorithms show that XML key propagation and its associated minimum cover can be computed in polynomial time. Our experimental results verify that these algorithms are efficient in practice. We also investigate the complexity of propagating other XML constraints to relations. The ability to compute XML key propagation is a first step toward establishing a connection between XML data and its relational representation at the semantic level.     

NF-NR: A practical normal form for nested relations

We propose a normal form for nested relations, called NF-NR, which removes undesirable anomalies from a nested relational database schema. Both functional dependencies and multivalued dependencies are considered. NF-NR reduces to 3NF/4NF if the nested relation considered is actually a flat relation. Especially, NF-NR removes global redundancies among a set of nested relations. Two approaches to NF-NR database design, namely the restructuring rules approach and the ER approach, are discussed. We relate NF-NR to ER-NF, a normal form of ER defined earlier, by defining a simple mapping from an ERD in ER-NF to a set of nested relations in NF-NR. This approach effectively removes ambiguitics and redundancies on a semantic level and hence gives a set of nested relations with clean semantics and yet in good normal form. A set of desirable properties for any normal form for nested relations are described and an evaluation of several existing normal forms is given based on this set of properties. The evaluation shows that NF-NR improves over previously proposed normal forms in various aspects and is a more practical normal form for nested relations.     

A new method for computing fuzzy functional dependencies in relational database systems

In this paper, we present a new method for computing fuzzy functional dependencies between attributes in fuzzy relational database systems. The method is based on the use of fuzzy implications. A literature analysis has shown that there is no algorithm that would enable the identification of attribute relationships in fuzzy relational schemas. This fact was the motive for development a new methodology in the analysis of fuzzy functional dependencies over a given set of attributes. Solving this, not so new problem, is not only research challenge having theoretical importance, but it also has practical significance. Possible applications of the proposed methodology include GIS, data mining, information retrieval, reducing data redundancy in fuzzy relations through implementation of logical database model, estimation of missing values etc.     

基于近似函数依赖的关系数据属性权重评估方法

在现实应用中,一些关系数据的规范化程度不高,往往存在数据冗余和不一致现象。为了有效评估此类数据 中的属性重要程度,提出了一种基于近似函数依赖的属性权重评估方法。该方法基于一致集的概念导出最大集,生成 最小非平凡函数依赖集,从而找出属性之间的近似函数依赖关系,进而求出近似候选码和近似关键字,在此基础上根 据属性支持度计算属性权重。实验结果和分析表明,提出的属性权重评估方法能够合理地获取关系数据中的属性重 要程度,算法具有较好的稳定性和较高的执行效率。     

An analysis of multivalued and join dependencies based on the entity-relationship approach

In this paper, we show that multivalued dependencies and join dependencies are not very viable for certain cases of relational database design; they are sometimes difficult to be identified; they are relation sensitive; and we are unable to talk about these types of dependencies without referring to some specific relation. We also show that the entity-relationship approach can be used for relational database design without any of the above mentioned undesirable properties of multivalued dependencies and join dependencies.     

Functional dependencies among Boolean dependencies

In this paper, we consider functional dependencies among Boolean dependencies (BDs, for short). Armstrong relations are defined for BDs (called BD-Armstrong relations). For BDs, two necessary and sufficient conditions for the existence of BD-Armstrong relations are given. A necessary and sufficient condition for the existence of Armstrong relations for functional dependencies (FDs, for short) is given, which in some sense is more convenient than the condition given in [3]. We give an algorithm that solves the problem of deciding if two BDs imply the same set of functional dependencies. If the BDs are given in perfect disjunctive normal form, then the algorithm requires only polynomial time. Although Mannila and Räihä have shown that for some relations exponential time is needed for computing any cover of the set of FDs defined in this relation, as a consequence, we show that the problem of deciding if two relations satisfy the same set of FDs can be solved in polynomial time. Another consequence is a new correspondence of the families of functional dependencies to the families of Sperner systems. By this correspondence, the estimate of the number of databases given previously in [6] is improved. It is shown that there is a one-to-one correspondence between the closure of the FDs that hold in a BD and its so-calledbasic cover. As applications of basic covers, we obtain a representation of a key, the family of minimal keys and a representation of canonical covers.This research was supported by the Hungarian Foundation for Scientific Research, Grant Nos. OTKA 2575, 2149.     

Database sampling with functional dependencies

During the development of information systems, there is a need to prototype the database that the applications will use when in operation. A prototype database can be built by sampling data from an existing database. Including relevant semantic information when extracting a sample from a database is considered invaluable to support the development of data-intensive applications. Functional dependencies are an example of semantic information that could be considered when sampling a database. This paper investigates how a database relation can be sampled so that the resulting sample satisfies precisely a given set of functional dependencies (and its logical consequences), i.e. is an Armstrong relation.     

A top-down proof procedure for generalized data dependencies

Data dependencies are well known in the context of relational database. They aim to specify constraints that the data must satisfy to model correctly the part of the world under consideration. The implication problem for dependencies is to decide whether a given dependency is logically implied by a given set of dependencies. A proof procedure for the implication problem, called “chase”, has already been studied in the generalized case of tuple-generating and equality-generating dependencies. The chase is a bottom-up procedure: from hypotheses to conclusion, and thus is not goal-directed. It also entails in the case of TGDs the dynamic creation of new constants, which can turn out to be a costly operation. This paper introduces a new proof procedure which is top-down: from conclusion to hypothesis, that is goal-directed. The originality of this procedure is that it does not act as classical theorem proving procedures, which require a special form of expressions, such as clausal form, obtained after Skolemization. We show, with our procedure, that this step is useless, and that the notion of piece allows infering directly on dependencies, thus saving the cost of Skolemizing the dependencies set and, morever, that the inference can be performed without dynamically creating new constants. Although top-down approaches are known to be less efficient in time than bottom-up ones, the notion of piece cuts down irrelevant goals usually generated, leading to a usable top-down method. With the more recent introduction of constrained and ordered dependencies, some interesting perspectives also arise. Received: 16 October 2000 / 11 May 2002     

Impurity measures in databases

We introduce purity dependencies as generalizations of functional dependencies in relational databases starting from the notion of impurity measure. The impurity measure of a subset of a set relative to a partition of that set and the relative impurity of two partitions allow us to define the relative impurity of two attribute sets of a table of a relational database and to introduce purity dependencies. We discuss properties of these dependencies that generalize similar properties of functional dependencies and we highlight their relevance for approximate classifications. Finally, an algorithm that mines datasets for these dependencies is presented. Received: 4 July 2000 / 16 November 2001