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.     

An extended algebra for constraint databases

Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. We extend the previously defined constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then, we introduce two distinct classes of constraint algebras, one based on the relational algebra, and one based on the nested relational algebra, and we present an algebra of the latter type. The algebra is proved equivalent to the generalized relational algebra when input relations are modified by introducing generalized tuple identifiers. However, from a user point of view, it is more suitable. Thus, the difference existing between such algebras is similar to the difference existing between the relational algebra and the nested relational algebra, dealing with only one level of nesting. We also show how external functions can be added to the proposed algebra     

Datalog extension for nested relations

The nested relational model allows relations that are not in first normal form. This paper gives an extension of Datalog rules for nested relations. In our approach, nested Datalog is a natural extension of Datalog introduced for the relational data model. A nested Datalog program has a hierarchical structure of rules and subprograms to manipulate relation values of nested relations. We introduce a new category of predicate symbols, the variable predicate symbols to refer to tuples of subrelations. The notion of soundness, safety and consistency is defined to avoid undesirable nested Datalog programs. The evaluation of nested Datalog is given in terms of the nested relational algebra. Finally, we relate the expressive power of nonrecursive nested Datalog to the power of nested relational algebra and safe nested tuple relational calculus.     

Fuzzy Rough Sets: The Forgotten Step

Traditional rough set theory uses equivalence relations to compute lower and upper approximations of sets. The corresponding equivalence classes either coincide or are disjoint. This behaviour is lost when moving on to a fuzzy T-equivalence relation. However, none of the existing studies on fuzzy rough set theory tries to exploit the fact that an element can belong to some degree to several "soft similarity classes" at the same time. In this paper we show that taking this truly fuzzy characteristic into account may lead to new and interesting definitions of lower and upper approximations. We explore two of them in detail and we investigate under which conditions they differ from the commonly used definitions. Finally we show the possible practical relevance of the newly introduced approximations for query refinement     

Domain-independent queries on databases with external functions

We study queries over databases with external functions, from a language-independent perspective. The input and output types of the external functions can be atomic values, flat relations, nested relations, etc. We propose a new notion of data-independence for queries on databases with external functions, which extends naturally the notion of generic queries on relational databases without external functions. In contrast to previous such notions, ours can also be applied to queries expressed in query languages with iterations. Next, we propose two natural notions of computability for queries over databases with external functions, and prove that they are equivalent, under reasonable assumptions. Thus, our definition of computability is robust. Finally, based on this equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines (Abiteboul and V. Vianu, 1991; Abiteboul et al., 1992) are complete on nested relations: they are known not to be complete on flat relations.     

A time bound on the materialization of some recursively defined views

A virtual relation (or view) can be defined with a recursive Horn clause that is a function of one or more base relations. In general, the number of times such a Horn clause must be applied in order to retrieve all the tuples in the virtual relation depends on the contents of the base relations of the definition. However, there exist Horn clauses for which there is an upper bound on the number of applications necessary to form the virtual relation, independent of the contents of the base relations. Considering a restricted class of recursive Horn clauses, we give necessary and sufficient conditions for members of the class to have this bound.     

Vague相似关系与Vague划分

通过对单位区间[0,1]的闭子区间集中的元素——Vague值的定义,引入二元Vague关系、关系运算、逆关系、关系的合成、λ-截关系等新的定义。从基于可能度的区间数序关系的概念以及Vague集投票模型的实际意义两个方面,引入闭子区间集中Vague值的偏序关系的定义,并利用偏序关系证明了Vague关系的一些主要性质。给出了满足sup-min传递性的Vague相似关系以及Vague划分的定义,建立了Vague相似关系与Vague划分一一对应性,进而以[0,1]上连续t模作为广义的“与”逻辑算子,引入Vague相似关系的特例——满足T-传递性的Vague T-相似关系与Vague T-划分新的定义。     

Ordered functional dependencies in relational databases

We extend the relational data model to incorporate linear orderings into data domains, which we call the ordered relational model. The conventional Functional Dependencies (FDs) are examined in the context of ordered relational databases by using the notion of System Ordering Independence (SOI), which refers to the desirable scenario that the ordering of tuples in a relation is independent of the implementation of the underlying DBMS. We also extend Armstrong's axiom system for FDs to object relations, which are a subclass of ordered relations that allow us to view tuples as objects. We formally define Ordered Functional Dependencies (OFDs) for the extended model by means of two possible extensions of domains, pointwise-orderings and lexicographical orderings. We first present a sound and complete axiom system for OFDs in the case of pointwise-orderings and then establish a sound and complete set of chase rules for OFDs in the case of lexicographical orderings. Our main result shows that the implication problems for both cases of OFDs are decidable, and that it is linear time for the case of pointwise-orderings.     

Incremental computation of set difference views

Views can be computed by means of recomputation or they can be computed incrementally. Incremental view computation outperforms view recomputation in many situations. This is particularly true in distributed database environments such as data warehousing environments. The authors present and analyze two algorithms for the incremental computation of relational set difference views. Set differences occur naturally in the definition of the set-division operator and in rewritten nested queries. The I/O efficiency of the incremental algorithms is compared to each other and to efficient recomputation algorithms. The cost analysis strongly indicates that incremental computation of set difference views outperforms recomputation of set difference views in many situations     

A time bound on the materialization of some recursively defined views

A virtual relation (or view) can be defined with a recursive Horn clause that is a function of one or more base relations. In general, the number of times such a Horn clause must be applied in order to retrieve all the tuples in the virtual relation depends on the contents of the base relations of the definition. However, there exist Horn clauses for which there is an upper bound on the number of applications necessary to form the virtual relation, independent of the contents of the base relations. Considering a restricted class of recursive Horn clauses, we give necessary and sufficient conditions for members of the class to have this bound.This research was supported by the National Science Foundation under Grant ECS-8300463.     

A comparative study of various nested normal forms

As object-relational databases (ORDBs) become popular in the industry, it is important for database designers to produce database schemes with good properties in these new kinds of databases. One distinguishing feature of an ORDB is that its tables may not be in first normal form. Hence, ORDBs may contain nested relations along with other collection types. To help the design process of an ORDB, several normal forms for nested relations have recently been defined, and some of them are called nested normal forms. In this paper, we investigate four nested normal forms, which are NNF [20], NNF [21], NNF [23], and NNF [25], with respect to generalizing 4NF and BCNF, reducing redundant data values, and design flexibility. Another major contribution of this paper is that we provide an improved algorithm that generates nested relation schemes in NNF [20] from an a-acyclic database scheme, which is the most general type of acyclic database schemes. After presenting the algorithm for NNF [20], the algorithms of all of the four nested normal forms and the nested database schemes that they generate are compared. We discovered that when the given set of MVDs is not conflict-free, NNF [20] is inferior to the other three nested normal forms in reducing redundant data values. However, in all of the other cases considered in this paper, NNF [20] is at least as good as all of the other three nested normal forms     

The integrity constraints for similarity-based fuzzy relational databases

This paper first introduces a new definition for the conformance of tuples existing in a similarity-based fuzzy database relation. Then the formal definitions of fuzzy functional and multivalued dependencies are given on the basis of the conformance values presented here. These dependencies are defined to represent relationships between domains of the same relation that exist. The definitions of the fuzzy dependencies presented in this study allow a sound and complete set of inference rules. In this paper, we include examples to demonstrate how the integrity constraints imposed by these dependencies are enforced whenever a tuple is to be inserted or to be modified in a fuzzy database relation. © 1998 John Wiley & Sons, Inc.     

Rough集理论中知识与运算的矩阵表示

同一问题在不同知识表示下算法难度不同。Rough集理论把知识定义为对对象的分类能力,并提供了一套基于代数系统的知识表达和处理方法。然而在代数表示下,知识的本质以及运算直观性较差,不易于理解。同济大学苗夺谦教授建立了知识与信息之间的关系,在此基础上给出了Rough集理论中概念和运算的信息表示,并给出了知识约简在代数和信息两种表示下的等价性证明。现进一步将知识及其运算表示成粒矩阵形式,继而给出了知识约简在代数、信息和粒矩阵3种表示下的等价性证明。     

An ASN.1 Model and Integration Approach for Structured Text

A language for manipulating ASN.1 print files is defined as an addition to the ASN.1 data definition language as specified in the ISO standards 8824 and 8825. The language has syntax similar in spirit to SQL, and provides analogous operations. Together, ASN.1 and the manipulation language define a model that can represent attribute hierarchies, multivalued attributes, optional attributes, both ordered and unordered attributes and tuples, and unnamed attributes—constructs that are absent in the traditional relational model. In addition, the proposed model allows the semantics of order, homogeneity, optionality, choosability, and uniqueness to be attached to constructs and construct elements. The approach is well suited for modeling data where form is important, such as text and flat file databases having ad hoc formats. It also supports modeling relations. The primary motivation for developing this language is to provide a common model for a database integration approach where some of the databases are in the form of formatted flat file text, while others are relational. Although the approach is general and can be applied in many different areas, scientific database and tool integration was the primary motive for its development.     

Query containment under bag and bag-set semantics

Conjunctive queries (CQs) are at the core of query languages encountered in many logic-based research fields such as AI, or database systems. The majority of existing work assumes set semantics but often in real applications the manipulation of duplicate tuples is required. One of the major problems that arises as part of advanced features of query optimization, data integration, query reformulation and many other research topics is testing for containment of such queries. In this work, we investigate the complexity of query containment problem for CQs under bag semantics (i.e. duplicate tuples are allowed in both the database and the results of queries) and under bag-set semantics (i.e. duplicates are allowed in the result of the queries but not in the database). We derive complexity results for these problems for five major subclasses of CQs; and we also find necessary conditions for CQ query containment. The general case of these problems remains open.     

基于不确定理论的不确定性数据Top-k查询计算

在不确定性数据集中,基于参数化排名函数的Top-k查询研究近年来备受关注。给出了一种新的解决方法,该方法将不确定性数据集中的元组建模为不确定网络,将有序元组的Top-k查询等价转化为相应样本图中边的不确定测度关系,并对样本图依据所包含边的排序位置进行分类,从而 将不确定性数据中基于参数化排名函数的Top-k查询等价转换为依Top-k值不同的有限查询。本算法避免了计算所有元组在样本图中的排名不确定测度值,提高了不确定图的Top-k查询计算效率。 理论分析和实验结果表明,提出的Top-k查询算法能够从非确定角度解决不确定性数据的Top-k查询计算问题。     

基于嵌套语义的约束代数

1 引言约束数据库近期被Kanellakis等提出作为处理空间数据的一般性框架。约束数据库用约束来建模和检索数据。在数据层,约束能用有限的形式来表示可能是无限的关系元组集。例如,约束x~2 y~2≤9表示中心在点(0,0)处,半径为3的圆。在查询语言层,约束通过允许数学计算而增强了简单关系语言的表达能力,同时约束查询语言保留了关系查询语言的所有特征,如封闭性和自底向上求值。关系代数能被扩充来处理约束关系,这个新的代数叫做约束代数CALG。     

XML多值依赖的推理规则集问题

XML多值依赖的推理规则集问题是解决XML数据依赖的蕴涵问题的基础，是XML规范化理论的关键问题之一。该文对XML树、树元组等进行了重新定义，与Vincent等人不同，提出了基于DTD的XML多值依赖的概念，通过对XML的关系化表示给出了其形式化定义，定义了XML多值依赖集的闭包、XML多值依赖路径依赖基以及XML多值依赖路径集的闭包等概念，给出了一个有效且完备的推理规则集，并对其有效性及完备性进行了证明。     

Equivalence and Normal Forms for the Restricted and Bounded Fixpoint in the Nested Algebra

The nested model is an extension of the traditional, “flat” relational model in which relations can also have relation-valued entries. Its “default” query language, the nested algebra, is rather weak, unfortunately, since it is only a conservative extension of the traditional, flat relational algebra, and thus can express only a small fraction of the polynomial-time queries. Therefore, it was proposed to extend the nested algebra with a fixpoint construct, but the resulting language turned out to be too powerful: many inherently exponential queries could also be expressed. Two polynomial-time restrictions of the fixpoint closure of the nested algebra were proposed: the restricted fixpoint closure (by Gyssens and Van Gucht) and the bounded fixpoint closure (by Suciu). Here, we prove two results. First we show that both restrictions are equivalent in expressive power. The proof technique relies on known encodings of nested relations into flat ones, and on a novel technique, called type substitution, by which we reduce the equivalence of the two restrictions to its obvious counterpart in the flat relational model. Second we prove that both the bounded fixpoint queries and the restricted fixpoint queries admit normal forms, in which the fixpoint occurs exactly once. The proof technique relies on a novel encoding method of nested relations into flat ones.     

On the equivalence between FDs in XML and FDs in relations

With the growing use of the eXtensible Markup Language (XML) in database technology as a format for the permanent storage of data, the topic functional dependencies in XML (XFDs) has assumed increased importance because of its central role in database design. Recently, two different approaches have been proposed for defining an XFD. The first uses the concept of a ‘tree tuple’, whereas the second uses the concept of a ‘closest node’. In general, the two approaches are not comparable, but are comparable when a Document Type Definition is present and there is no missing information in the XML document. The first contribution of this article shows that when the two XFD definitions are comparable, the definitions are equivalent, and so there is essentially a common definition of an XFD in complete XML documents. The second contribution is to provide justification for the definition of a ‘closest node’ XFD. We show that if a complete flat relation is mapped to an XML document by an arbitrary sequence of nest operations, the XML document satisfies a ‘closest node’ XFD if and only if the relation satisfies the corresponding functional dependency. The class of XML documents generated in this fashion is a subset of the class of XML documents for which the two definitions of XFDs coincide. Hence ‘tree tuple’ and ‘closest node’ XFDs both capture the semantics of FDs when a complete relation is mapped to an XML document via arbitrary nesting.