Armstrong axioms and Boyce-Codd-Heath Normal Form under bag semantics

The theory of functional dependencies is based on relations, i.e. sets of tuples. Over relations, the class of functional dependencies subsumes the class of keys. Commercial database systems permit the storage of bags of tuples where duplicate tuples can occur. Over bags, keys and functional dependencies interact differently from how they interact over relations.We establish finite ground axiomatizations of keys and functional dependencies over bags, and show a strong correspondence to goal and definite clauses in classical propositional logic. We define a syntactic Boyce-Codd-Heath Normal Form condition, and show that the condition characterizes schemata that will never have any redundant data value occurrences in their instances. The results close the gap between the existing set-based theory of data dependencies and database practice where bags are permitted.     

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.     

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.     

Semantic sampling of existing databases through informative Armstrong databases

Functional dependencies (FDs) and inclusion dependencies (INDs) convey most of data semantics in relational databases and are very useful in practice since they generalize keys and foreign keys. Nevertheless, FDs and INDs are often not available, obsolete or lost in real-life databases. Several algorithms have been proposed for mining these dependencies, but the output is always in the same format: a simple list of dependencies, hard to understand for the user. In this paper, we define informative Armstrong databases (IADBs) from databases as being small subsets of an existing database, satisfying exactly the same FDs and INDs. They are an extension of the classical notion of Armstrong databases, but more suitable for the understanding of dependencies, since tuples are real-world tuples. The main result of this paper is to bound the size of an IADB in the case of non-circular INDs. A constructive proof of this result is given, from which an algorithm has been devised. An implementation and experiments against a real-life database were performed; the obtained database contains 0.6% of the initial database tuples only. More importantly, such semantic sampling of databases appear to be a key feature for the understanding of existing databases at the logical level.     

Performance of VIDEBAS in an operational environment

VIDEBAS is a relational database management system in which a database consists of two parts, namely a “real-only” and an “update” part. The first part remains unmodified until the next reorganization and exploits redundancy to achieve fast access to data. A prototype of VIDEBAS has been built. In this paper a performance comparison between this relational system and a DBTG-system (UDS) is made. The used external memory and the number of page accesses to retrieve and update tuples is estimated. Although it is commonly assumed that in an operational environment relational systems are slower than network systems the opposite appears. On the other hand UDS needs less external memory.     

模糊关系数据库中的非对称冗余元组

在现实世界中,有些对象比其它的更具有一般性,两个对象的相似度可能不对称。两个对象之间的相似关系可能既不对称又不传递,我们用弱相似关系来表示。本文提出了非对称冗余元组来处理模糊关系数据库中的弱相似关系。非对称冗余元组的概念是模糊关系数据库的冗余概念的推广,它用来删除一些冗余信息,表示更精确的信息。     

具有多时间粒度的时态数据库初等关键字、简单范式分解问题研究

一个好的数据库逻辑设计目标是消除数据冗余以及插入、删除和更新异常．对于时态数据库也是如此．提出了时态初等函数依赖、时态初等关键字、时态简单关键字等概念,在此基础上利用具有多时间粒度的时态函数依赖（TFD）约束对时态数据库进行了规范化研究,提出了规范程度高于时态三范式低于时态Boyce—Code范式的时态初等关键字范式（TEKNF）及时态简单范式（TSNF）,并研究了时态初等关键字范式和时态简单范式的分解问题,给出了相关分解算法,并对算法的可终止性、正确性进行了证明,对时间复杂度进行了分析．     

具有多时间粒度的时态多值依赖及时态模式分解方法研究

一个好的数据库逻辑设计目标是消除数据冗余以及插入、删除和更新异常.对于时态数据库,通过具有多时间粒度的时态函数依赖约束对时态数据库进行规范化已有大量研究.基于时态函数依赖和多值依赖理论提出了多时间粒度约束的时态多值依赖(TMVD)等概念,并给出了时态多值依赖的推理规则,对其有效性、完备性进行了证明.由于包含有限个TMVD的TMVD集通常蕴含着无限个TMVD,给出了TMVD的有限推理规则,对其有效性、完备性进行了证明.最后,基于时态多值依赖集提出了时态第四范式,并给出了时态模式的T4NF的无损分解算法,对算法的可终止性、正确性进行了证明,并对时间复杂度进行了分析.     

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”     

实例分析关系模式的规范化与反规范化

规范化是减少数据冗余、设计合理的数据库的重要手段,是数据库课程的重点。由于涉及到关系数学理论,仅做理论讲解,很难使学生理解,尤其是高职层次的学生。本文通过一个关系模式不断分解、规范化的实例,采用逐步深入的方法解决数据库设计中存在的问题,使学生既掌握数据库设计的技能,也加深对函数依赖、规范化理论的理解。     

RRDB与FRDB关系的系统研究

以粗糙集理论(Rough Set Theory)和关系数据库理论为基础,从函数依赖、范式理论、Armstrong公理等方面系统地研究了粗糙关系数据库(Rough Relational DataBase,简称RRDB)与模糊关系数据库(Fuzzy Relational DataBase,简称FRDB)之间的关系。结果表明,模糊函数依赖与粗糙函数依赖均为经典函数依赖的泛化,模糊范式理论为经典范式的扩充,而粗糙范式理论自成体系,从推理规则上看,它们都不同程度地符合Armstrong公理。     

Dependency-preserving normalization of relational and XML data

Having a database design that avoids redundant information and update anomalies is the main goal of normalization techniques. Ideally, data as well as constraints should be preserved. However, this is not always achievable: while BCNF eliminates all redundancies, it may not preserve constraints, and 3NF, which achieves dependency preservation, may not always eliminate all redundancies. Our first goal is to investigate how much redundancy 3NF tolerates in order to achieve dependency preservation. We apply an information-theoretic measure and show that only prime attributes admit redundant information in 3NF, but their information content may be arbitrarily low. Then we study the possibility of achieving both redundancy elimination and dependency preservation by a hierarchical representation of relational data in XML. We provide a characterization of cases when an XML normal form called XNF guarantees both. Finally, we deal with dependency preservation in XML and show that like in the relational case, normalizing XML documents to achieve non-redundant data can result in losing constraints.     

Justification for inclusion dependency normal form

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. In this paper, we address the issue of normalization in the presence of FDs and INDs and, in particular, the semantic justification for an inclusion dependency normal form (IDNF), which combines the Boyce-Codd normal form with the restriction on the INDs that they be noncircular and key-based. We motivate and formalize three goals of database design in the presence of FDs and INDs: noninteraction between FDs and INDs, elimination of redundancy and update anomalies, and preservation of entity integrity. We show that (as for FDs), in the presence of INDs, being free of redundancy is equivalent to being free of update anomalies. Then, for each of these properties, we derive equivalent syntactic conditions on the database design. Individually, each of these syntactic conditions is weaker than IDNF and the restriction that an FD is not embedded in the right-hand side of an IND is common to three of the conditions. However, we also show that, for these three goals of database design to be satisfied simultaneously, IDNF is both a necessary and a sufficient condition     

A note on approximation measures for multi-valued dependencies in relational databases

We consider the problem of defining a normalized approximation measure for multi-valued dependencies in relational database theory. An approximation measure is a function mapping relation instances to real numbers. The number to which an instance is mapped, intuitively, describes the strength of the dependency in that instance. A normalized approximation measure for functional dependencies has been proposed previously: the minimum number of tuples that need be removed for the functional dependency to hold divided by the total number of tuples. This leads naturally to a normalized measure for multi-valued dependencies: the minimum number of tuples that need be removed for the multi-valued dependency to hold divided by the total number of tuples.The measure for functional dependencies can be computed efficiently, O(|r|log(|r|)) where |r| is the relation instance. However, we show that an efficient algorithm for computing the analogous measure for multi-valued dependencies is not likely to exist. A polynomial time algorithm for computing the measure would lead to a polynomial time algorithm for an NP-complete problem (proven by a reduction from the maximum edge biclique problem in graph theory). Hence, we argue that it is not a good measure. We propose an alternate measure based on the lossless join characterization of multi-valued dependencies. This measure is efficiently computable, O(|r|²).     

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.     

Exploring into programs for the recovery of data dependenciesdesigned

Data dependencies play an important role in the design of a database. Many legacy database applications have been developed on old generation database management systems and conventional file systems. As a result, most of the data dependencies in legacy databases are not enforced in the database management systems. As such, they are not explicitly defined in database schema and are enforced in the transactions, which update the databases. It is very difficult and time consuming to find out the designed data dependencies manually during the maintenance and reengineering of database applications. In software engineering, program analysis has long been developed and proven as a useful aid in many areas. With the use of program analysis, this paper proposes a novel approach for the recovery of common data dependencies, i.e., functional dependencies, key constraints, inclusion dependencies, referential constraints, and sum dependencies, designed in a database from the behavior of transactions, which update the database. The approach is based on detecting program path patterns for implementing most commonly used methods to enforce these data dependencies     

Semantic foundations of 4NF in relational database design

The issue of providing a formal justification for the use of fourth normal form (4NF) in relational database design is investigated. The motivation and formal definitions for three goals of database design are presented. These goals are the elimination of: redundancy, key-based update anomalies and fact-based replacement anomalies. It is then shown that, depending on the type of constraints permitted, either Boyce-Codd normal form (BCNF) or 4NF are the exact conditions needed to ensure most of the design goals. However, it is also shown that the conditions required to ensure the absence of a particular class of key-based update anomaly are new normal forms which have not previously been identified. In particular, for the case where the only constraints are functional dependencies (FDs), it is shown that the required normal form is a new normal form that is stronger than third normal form (3NF) yet weaker than BCNF. Similarly, in the more general case where both FD and multivalued dependencies (MVDs) are present, the required normal form is a new normal form that is weaker than 4NF. Received: 7 July 1995 / 28 December 1998     

数据库逻辑设计中消除规范化处理问题

关系数据库设计要求规范化处理的过程以消除数据冗余和更新异常问题. 范式化理论的算法与数据依赖有着直接的联系, 数据依赖中最重要的是函数依赖, 识别该依赖既耗时又复杂. 讨论如何在采用ER模型的数据库逻辑设计步骤中消除规范化处理过程, 在概念结构设计过程中遵循一组规则将产生满足3NF范式的初始关系模式集, 以节省数据库设计者在导出初始关系模式集后的规范化处理步骤.     

Approximate dependencies in database systems

Functional dependencies are the most commonly used approach for capturing real-word integrity constraints which are to be reflected in a database. There are, however, many useful kinds of constraints, especially approximate ones, that cannot be represented correctly by functional dependencies and therefore are enforced via programs which update the database, if they are enforced at all. This tends to make such constraints invisible since they are not an explicit part of the database, increasing maintenance problems and the likelihood of inconsistencies. We propose a new approach, cluster dependencies, as a way to enforce approximate dependencies. By treating equality as a fuzzy concept and defining appropriate similarity measures, it is possible to represent a broad range of approximate constraints directly in the database by storing and accessing cluster definitions. We discuss different interpretations of cluster dependencies and describe the additional data structures needed to enforce them. We also contrast them with an existing approach, fuzzy functional dependencies, which are much more limited in the kind of approximate constraints they can represent.