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.     

Annotation Based Query Answer over Inconsistent Database

In this paper, we introduce a concept of Annotation Based Query Answer, and a method for its computation, which can answer queries on relational databases that may violate a set of functional dependencies. In this approach, inconsistency is viewed as a property of data and described with annotations. To be more precise, every piece of data in a relation can have zero or more annotations with it and annotations are propagated along with queries from the source to the output. With annotations, inconsistent da...     

The complexity of embedded axiomatization for a class of closed database views

It is well known that the complexity of testing the correctness of an arbitrary update to a database view can be far greater than the complexity of testing a corresponding update to the main schema. However, views are generally managed according to some protocol which limits the admissible updates to a subset of all possible changes. The question thus arises as to whether there is a more tractable relationship between these two complexities in the presence of such a protocol. In this paper, this question is addressed for closed update strategies, which are based upon the constant-complement approach of Bancilhon and Spyratos. The approach is to address a more general question – that of characterizing the complexity of axiomatization of views, relative to the complexity of axiomatization of the main schema. For schemata constrained by denial or consistency constraints, that is, statements which rule out certain situations, such as the equality-generating dependencies (EGDs) or, more specifically, the functional dependencies (FDs) of the relational model, a broad and comprehensive result is obtained in a very general framework which is not tied to the relational model in any way. It states that every such schema is governed by an equivalent set of constraints which embed into the component views, and which are no more complex than the original set. For schemata constrained by generating dependencies, of which tuple-generating dependencies (TGDs) in general and, more specifically, both join dependencies (JDs) and inclusion dependencies (INDs) are examples within the relational model, a similar result is obtained, but only within a context known as meet-uniform decompositions, which fails to recapture some important situations. To address the all-important case of relational schemata constrained by both FDs and INDs, a hybrid approach is also developed, in which the general theory regarding denial constraints is blended with a focused analysis of a special but very practical subset of the INDs known as fanout-free unary inclusion dependencies (fanout-free UINDs), to obtain results parallel to the above-mentioned cases: every such schema is governed by an equivalent set of constraints which embed into the component views, and which are no more complex than the original set. In all cases, the question of view update complexity is then answered via a corollary to this main result. Parts of this paper are based upon work reported in [21].     

基于模式图的规范化XML模式设计

在给定关系模式的属性集及其函数依赖最小覆盖集的基础上,提出一种基于模式图的规范化XML模式设计方法。定义了模式图,在模式图中增加了Keys的描述信息,给出由函数依赖集构造模式图的算法。该模式图独立于具体的XML模式语言,经分析证明,所设计的模式满足XNF。     

XML函数依赖及其推理规则

函数依赖在关系数据库和XML文档中都是一种重要的语义表达．通过分析函数依赖的表现形式在XML文档和关系数据库中的不同之处,提出了基于DTD中的路径表达式的XML函数依赖的概念．它不仅能表达元素的属性和元素的值之间的函数依赖,而且也能表达元素之间的函数依赖．给出了关于XML函数依赖的一组完备的推理规则集,这对解决XML函数依赖的蕴含问题具有重要的意义．     

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。     

Mapping DTDs to relational schemas with semantic constraints

XML is becoming a prevalent format and standard for data exchange in many applications. With the increase of XML data, there is an urgent need to research some efficient methods to store and manage XML data. As relational databases are the primary choices for this purpose considering their data management power, it is necessary to research the problem of mapping XML schemas to relational schemas. The semantics of XML schemas are crucial to design, query, and store XML documents and functional dependencies are very important representations of semantic information of XML schemas. As DTDs are one of the most frequently used schemas for XML documents in these days, we will use DTDs as schemas of XML documents here. This paper proposes the concept and the formal definition of XML functional dependencies over DTDs. A method to map XML DTDs to relational schemas with constraints such as functional dependencies, domain constraints, choice constraints, reference constraints, and cardinality constraints over DTDs is given, which can preserve the structures of DTDs as well as the semantics implied by the above constraints over DTDs. The concepts and method of mapping DTDs to relational schemas presented in the paper can be extended to the field of XML Schema just with some modifications in related formal definitions.     

XML函数依赖及其与键的关系

通过分析函数依赖的表现形式在XML文档和关系数据库中的不同之处，提出了基于DTD中的路径表达式的XML函数依赖的概念．并且给出了XML函数依赖的XML表示方法，研究了XML函数依赖和XML键的关系．     

The Relational Structure of Belief Networks

This paper demonstrates the relational structure of belief networks by establishing an extended relational data model which can be applied to both belief networks and relational applications. It is demonstrated that a Markov network can be represented as a generalized acyclic join dependency (GAJD) which is equivalent to a set of conflict-free generalized multivalued dependencies (GMVDs). A Markov network can also be characterized by an entropy function, which greatly facilitates the manipulation of GMVDs. These results are extensions of results established in relational theory. It is shown that there exists a complete set of inference rules for the GMVDs. This result is important from a probabilistic perspective. All the above results explicitly demonstrate that there is a unified model for relational database and probabilistic reasoning systems. This is not only important from a theoretical point of view in that one model has been developed for a number of domains, but also from a practical point of view in that one system can be implemented for both domains. This implemented system can take advantage of the performance enhancing techniques developed in both fields. Thereby, this paper serves as a theoretical foundation for harmonizing these two important information domains.     

On data dependency structures of relational databases

The properties of the set of all functional dependencies (which is defined to be FD sub-structure), derivable from a given set of functional dependencies (FD's) and multivalued dependencies (MVD's) for a relational database, are studied. A necessary and sufficient condition that a set of FD's is a cover for the FD sub-structure is proved, which can be tested for validity by an efficient algorithm. An algorithm of generating a cover for the FD substructure is presented. It can be shown, however, that in at least one instance, the number of FD's in the cover may actually increase more than exponentially as the number of MVD's increases.     

Fuzzy functional dependencies and Bayesian networks

Bayesian networks have become a popular technique for representing and reasoning with probabilistic information.The fuzzy functional dependency is an important kind of data dependencies in relational databases with fuzzy values,The purpose of this paper is to set up a connection between these data dependencies and Bayesian networks.The connection is done through a set of methods that enable pepople to obtain the most information of independent conditions from fuzzy functional dependencies.     

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     

Decomposition for a new kind of imprecise information system

In this paper, we first propose a new kind of imprecise information system, in which there exist conjunctions (∧’s), disjunctions (∨’s) or negations (¬’s). Second, this paper discusses the relation that only contains ∧’s based on relational database theory, and gives the syntactic and semantic interpretation for ∧ and the definitions of decomposition and composition and so on. Then, we prove that there exists a kind of decomposition such that if a relation satisfies some property then it can be decomposed into a group of classical relations (relations do not contain ∧) that satisfy a set of functional dependencies and the original relation can be synthesized from this group of classical relations. Meanwhile, this paper proves the soundness theorem and the completeness theorem for this decomposition. Consequently, a relation containing ∧’s can be equivalently transformed into a group of classical relations that satisfy a set of functional dependencies. Finally, we give the definition that a relation containing ∧’s satisfies a set of functional dependencies. Therefore, we can introduce other classical relational database theories to discuss this kind of relation.     

Appropriate inferences of data dependencies in relational databases

We study inference systems for the combined class of functional and full hierarchical dependencies in relational databases. Two notions of implication are considered: the original notion in which a dependency is implied by a given set of dependencies and the underlying set of attributes, and the alternative notion in which a dependency is implied by a given set of dependencies alone. The first main result establishes a finite axiomatisation for the original notion of implication which clarifies the role of the complementation rule in the combined setting. In fact, we identify inference systems that are appropriate in the following sense: full hierarchical dependencies can be inferred without use of the complementation rule at all or with a single application of the complementation rule at the final step of the inference only; and functional dependencies can be inferred without any application of the complementation rule. The second main result establishes a finite axiomatisation for the alternative notion of implication. We further show how inferences of full hierarchical dependencies can be simulated by inferences of multivalued dependencies, and vice versa. This enables us to apply both of our main results to the combined class of functional and multivalued dependencies. Furthermore, we establish a novel axiomatisation for the class of non-trivial functional dependencies.     

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.     

Controlling FD and MVD inferences in multilevel relational databasesystems

The authors investigate the inference problems due to functional dependencies (FD) and multivalued dependencies (MVD) in a multilevel relational database (MDB) with attribute and record classification schemes, respectively. The set of functional dependencies to be taken into account in order to prevent FD-compromises is determined. It is proven that incurring minimum information loss to prevent compromises is an NP-complete problem. An exact algorithm to adjust the attribute levels so that no compromise due to functional dependencies occurs is given. Some necessary and sufficient conditions for MVD-compromises are presented. The set of MVDs to be taken into account for controlling inferences is determined. An algorithm to prevent MVD-compromises in a relation with conflict-free MVDs is given     

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.     

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     

XML的函数依赖

通过分析函数依赖的表现形式在XML文档和关系数据库中的不同之处，提出了基于DTD中的路径表达式的XML函数依赖的概念．它不仅能表达元素的属性和元素的值之间的函数依赖，而且也能表达元素之间的函数依赖．给出了关于XML函数依赖的一组推理规则集．     

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．