Temporal association algebra: a mathematical foundation forprocessing object-oriented temporal databases

This paper describes an object-oriented temporal association algebra (called TA-algebra) which is intended to serve as a formal foundation for supporting a pattern-based query specification and processing paradigm. Different from the traditional table-and-attribute-based paradigm, the pattern-based paradigm views the intension of an object-oriented temporal database as a network of object classes interconnected by different association types and its extension as a network of associated temporal object instances. Consistent with this view, queries can be specified in terms of patterns of temporal object associations or nonassociations (i.e., linear, tree and network structures of object classes/objects with logical AND and OR branches). TA-algebra provides a set of algebraic operators for processing these patterns and allows the direct and/or indirect associations and/or nonassociations among temporal object instances to be more explicitly represented and maintained during processing than the traditional tabular representation of temporary or final query results. TA-algebra operators are based on time-interval and valid-time semantics and they preserve the closure property. The algebra is capable of operating on heterogeneous as well as homogeneous patterns of object associations. Both homogeneous and heterogeneous patterns are decomposed into a set of primitive temporal pattern instances for uniform treatment. This paper formally defines the TA-algebra operators and their mathematical properties. The applications of these operators in query decomposition and processing are illustrated by examples     

Foundations for object-oriented query processing

A minimal framework for an object-oriented query language standard should (1) include a formal definition of a high-level data model and the syntax and semantics of associated query languages, (2) provide the functionality of relational query languages, and (3) support proofs of correctness of transformations for logical query optimization. In this paper, a high-level conceptual model for object-oriented query processing is discussed; the model includes widely-used structural abstractions such as the isa relationship, associations (properties) between complex objects and complex objects/values, and inheritance of properties. A formal, algebraic query language for the model, inspired by relational algebra, is presented. Operators of the algebra allow queries based on values, queries that manipulate entire objects, and queries that construct new objects from existing objects/values. All queries retain connections to existing database objects, providing logical access paths to data. Each query result is a class, so the algebra has the closure property. The intensional and extensional results of query operators are summarized. Two forms of logical query optimization supported by the query algebra are outlined: algebraic transformations and classifier-based optimizations (optimizations which employ inclusion and exclusion dependencies between classes).     

An interface between object-oriented databases and relational databases

Currently relational databases are widely used, while object-oriented databases are emerging as a new generation of database technology. This paper presents a methodology to provide effective sharing of information in object-oriented databases and relational databases. The object-oriented data model is selected as a common data model to build an integrated view of the diverse databases. An object-oriented query language is used as a standard query language. A method is developed to transform a relational data definition to an equivalent object-oriented data definition and to integrate local data definitions. Two distributed query processing methods are derived. One is for general queries and the other for a special class of restricted queries. Using the methods developed, it is possible to access distributed object-oriented databases and relational databases such that the locations and the structural differences of the databases are transparent to users.     

An Object Algebra Approach to Multidatabase Query Decomposition in Donají

This paper presents an approach to query decomposition in a multidatabase environment. The unique aspect of this approach is that it is based on performing transformations over an object algebra that can be used as the basis for a global query language. In the paper, we first present our multidatabase environment and semantic framework, where a global conceptual schema based on the Object Data Management Group standard encompasses the information from heterogeneous data sources that include relational databases as well as object-oriented databases and flat file sources. The meta-data about the global schema is enhanced with information about virtual classes as well as virtual relationships and inheritance hierarchies that exist between multiple sources. The AQUA object algebra is used as the formal foundation for manipulation of the query expression over the multidatabase. AQUA is enhanced with distribution operators for dealing with data distribution issues. During query decomposition we perform an extensive analysis of traversals for path expressions that involve virtual relationships and hierarchies for access to several heterogeneous sources. The distribution operators defined in algebraic terms enhance the global algebra expression with semantic information about the structure, distribution, and localization of the data sources relevant to the solution of the query. By using an object algebra as the basis for query processing, we are able to define algebraic transformations and exploit rewriting techniques during the decomposition phase. Our use of an object algebra also provides a formal and uniform representation for dealing with an object-oriented approach to multidatabase query processing. As part of our query processing discussion, we include an overview of a global object identification approach for relating semantically equivalent objects from diverse data sources, illustrating how knowledge about global object identity is used in the decomposition and assembly processes.     

RQL: a recursive query language

Different classes of recursive queries in the relational databases are identified. It is shown that existing proposals to extend the relational query languages are either not powerful enough to express queries in many of these classes or use nonfirst normal form constructs. RQL, a recursive database query language that can be used to express recursive queries on all the classes identified, is presented. RQL is based on the relational algebra. In addition to functions that correspond to the standard and extended relational algebra operators, RQL supports functions required to express general recursive queries. The elements of RQL and the ways in which they are used to formulate complicated, but useful, recursive queries are described. The effects of the extensions embodied in RQL on the termination of recursive query evaluation are discussed     

A pattern-based object calculus

Several object-oriented database management systems have been implemented without an accompanying theoretical foundation for constraint, query specification, and processing. The pattern-based object calculus presented in this article provides such a theoretical foundation for describing and processing objectoriented databases. We view an object-oriented database as a network of interrelated classes (i.e., the intension) and a collection of time-varying object association patterns (i.e., the extension). The object calculus is based on first-order logic. It provides the formalism for interpreting precisely and uniformly the semantics of queries and integrity constraints in object-oriented databases. The power of the object calculus is shown in four aspects. First, associations among objects are expressed explicitly in an object-oriented database. Second, the nonassociation operator is included in the object calculus. Third, set-oriented operations can be performed on both homogeneous and heterogeneous object association patterns. Fourth, our approach does not assume a specific form of database schema. A proposed formalism is also applied to the design of high-level object-oriented query and constraint languages.     

Object-oriented query language access to relational databases: A semantic framework for query translation

This research investigates and approach to query processing in a multidatabase system that uses an objectoriented model to capture the semantics of other data models. The object-oriented model is used to construct a global schema, defining an integrated view of the different schemas in the environment. The model is also used as a self-describing model to build a meta-database for storing information about the global schema. A unique aspect of this work is that the object-oriented model is used to describe the different data models of the multidatabase environment, thereby extending the meta database with semantic information about the local schemas. With the global and local schemas all represented in an object-oriented form, structural mappings between the global schema and each local schema are then easily supported. An object algebra then provides a query language for expressing global queries, using the structural mappings to translate object algebra queries into SQL queries over local relational schema. The advantage of using an object algebra is that the object-oriented database can be viewed as a blackboard for temporary storage of local data and for establishing relationships between different databases. The object algebra can be used to directly retrieve temporarily-stored data from the object-oriented database or to transparently retrieve data from local sources using the translation process described in this paper.     

Fuzzy database query languages and their relational completenesstheorem

Two fuzzy database query languages are proposed. They are used to query fuzzy databases that are enhanced from relational databases in such a way that fuzzy sets are allowed in both attribute values and truth values. A fuzzy calculus query language is constructed based on the relational calculus, and a fuzzy algebra query language is also constructed based on the relational algebra. In addition, a fuzzy relational completeness theorem such that the languages have equivalent expressive power is proved     

Efficient Querying and Animation of Periodic Spatio-Temporal Databases

We propose a representation of spatio-temporal objects with continuous and cyclic or acyclic periodic movements. We also describe an extended relational algebra query language for databases with such objects. We show that the new spatio-temporal databases are closed under the extended relational algebra queries, and each fixed relational algebra query can be evaluated in PTIME in the size of the input database.     

Fuzzy rough set techniques for uncertainty processing in a relational database

This paper concerns the modeling of imprecision, vagueness, and uncertainty in databases through an extension of the relational model of data: the fuzzy rough relational database, an approach which uses both fuzzy set and rough set theories for knowledge representation of imprecise data in a relational database model. The fuzzy rough relational database is formally defined, along with a fuzzy rough relational algebra for querying. Comparisons of theoretical properties of operators in this model with those in the standard relational model are discussed. An example application is used to illustrate other aspects of this model, including a fuzzy entity–relationship type diagram for database design, a fuzzy rough data definition language, and an SQL‐like query language supportive of the fuzzy rough relational database model. This example also illustrates the ease of use of the fuzzy rough relational database, which often produces results that are better than those of conventional databases since it more accurately models the uncertainty of real‐world enterprises than do conventional databases through the use of indiscernibility and fuzzy membership values. ©2000 John Wiley & Sons, Inc.     

Object query optimization through detecting independent subqueries

The problem of query optimization in object-oriented databases is addressed. We follow the Stack-Based Approach to query languages, which employs the naming-scoping-binding paradigm of programming languages rather than traditional database concepts such as relational/object algebras or calculi. The classical environment stack is a semantic basis for definitions of object query operators, such as selection, projection/navigation, dependent join, and quantifiers. We describe a general object data model and define a formalized OQL-like query language SBQL. Optimization by rewriting concerns queries containing so-called independent subqueries. It consists in detecting them and then factoring outside loops implied by query operators. The idea is based on the formal static analysis of scoping rules and binding names occurring in a query. It is more general than the classical pushing selections/projections before joins.     

Export database derivation in object-oriented wrappers

Wrappers export the schema and data of existing heterogeneous databases and support queries on them. In the context of cooperative information systems, we present a flexible approach to specify the derivation of object-oriented (OO) export databases from local relational databases. Our export database derivation consists of a set of extent derivation structures (EDS) which defines the extent and deep extent of export classes. Having well-defined semantics, the EDS can be readily used in transforming wrapper queries to local queries. Based on the EDS, we developed a wrapper query evaluation strategy which handles OO queries on the export databases. The strategy is unique in that it considers the limited query processing capabilities of local database systems as well as the language constraints on the local query languages.     

一个实现对象查询语言的形式化基础

在基于CORBA(common object request broker)的面向对象多数据库系统SCOPE/CIMS中，作者选择了对象数据库管理组ODMG(object database management group)提出的对象数据库标准ODMG-93的OQL(object query language)作为全局查询语言.为此，提出了一种实现OQL的形式化基础,包括适合建模OQL的一种对象演算和一种对象代数；对象演算的规范化规则和规范化步骤；对象演算与对象代数的等价映射规则及转换策略.     

统计与科学数据库上的代数操作

针对统计与科学数据库的应用要求,本文以语义数据模型MICSUM2为基础,以C—关系、原子统计表和复合统计表为操作对象,定义了统计与科学数据库上的操作。这些操作构成了C—关系、原子统计表和统计表集合上的代数,简称MS代数。MS代数从两个方面扩展了关系代数,一是MS代数操作具有更丰富的语义和更广泛的操作对象;二是MS代数包括很多支持统计分析查询的新代数操作,MS代数是构造对用户友好的统计与科学数据库查询语言的理论基础。     

A graphical query language: VISUAL and its query processing

This paper describes VISUAL, a graphical icon-based query language with a user-friendly graphical user interface for scientific databases and its query processing techniques. VISUAL is suitable for domains where visualization of the relationships is important for the domain scientist to express queries. In VISUAL, graphical objects are not tied to the underlying formalism; instead, they represent the relationships of the application domain. VISUAL supports relational, nested, and object-oriented models naturally and has formal basis. For ease of understanding and for efficiency reasons, two VISUAL semantics are introduced, namely, the interpretation and execution semantics. Translations from VISUAL to the Object Query Language (for portability considerations) and to an object algebra (for query processing purposes) are presented. Concepts of external and internal queries are developed as modularization tools.     

A data model and a query languagefor multimedia documents databases

A multimedia application involves information that may be in a form of video, images, audio, text and graphics, need to be stored, retrieved and manipulated in large databases. In this paper, we propose an object-oriented database schema that supports multimedia documents and their temporal, spatial and logical structures. We present a document example and show how the schema can adress all the structures described. We also present a multimedia query specification language that can be used to describe a multimedia content portion to be retrieved from the database. The language provides means by which the user can specify the information on the media as well as the temoral and spatial relationships among these media.     

关系代数派生算子语义表达式间等价性证明

关系代数的派生算子在关系数据库查询语言中得到了广泛应用。它们的语义有两种常见的表示方式,一种是基于原始算子的表达式,一种是基于一阶逻辑的表达式。但有关的文献资料都没有给出这两种表达式等价性的严格证明。文章尝试通过一系列等价变换,证明派生算子语义的这两种表达式间的等价性。从派生算子(主要是除算子)语义的原始算子表达式出发,根据关系代数表达式的特点,通过一步步的等价变换,得到派生算子语义的一阶逻辑表达式。所使用的变换方法能为关系代数表达式的正确性证明打下基础。     

Aggregation of imprecise and uncertain information in databases

Information stored in a database is often subject to uncertainty and imprecision. Probability theory provides a well-known and well understood way of representing uncertainty and may thus be used to provide a mechanism for storing uncertain information in a database. We consider the problem of aggregation using an imprecise probability data model that allows us to represent imprecision by partial probabilities and uncertainty using probability distributions. Most work to date has concentrated on providing functionality for extending the relational algebra with a view to executing traditional queries on uncertain or imprecise data. However, for imprecise and uncertain data, we often require aggregation operators that provide information on patterns in the data. Thus, while traditional query processing is tuple-driven, processing of uncertain data is often attribute-driven where we use aggregation operators to discover attribute properties. The aggregation operator that we define uses the Kullback-Leibler information divergence between the aggregated probability distribution and the individual tuple values to provide a probability distribution for the domain values of an attribute or group of attributes. The provision of such aggregation operators is a central requirement in furnishing a database with the capability to perform the operations necessary for knowledge discovery in databases     

How to Comprehend Queries Functionally

Compilers and optimizers for declarative query languages use some form of intermediate language to represent user-level queries. The advent of compositional query languages for orthogonal type systems (e.g., OQL) calls for internal query representations beyond extensions of relational algebra. This work adopts a view of query processing which is greatly influenced by ideas from the functional programming domain. A uniform formal framework is presented which covers all query translation phases, including user-level query language compilation, query optimization, and execution plan generation. We pursue the type-based design—based on initial algebras—of a core functional language which is then developed into an intermediate representation that fits the needs of advanced query processing. Based on the principle of structural recursion we extend the language by monad comprehensions (which provide us with a calculus-style sublanguage that proves to be useful during the optimization of nested queries) and combinators (abstractions of the query operators implemented by the underlying target query engine). Due to its functional nature, the language is susceptible to program transformation techniques that were developed by the functional programming as well as the functional data model communities. We show how database query processing can substantially benefit from these techniques.     

Query languages for relational multidatabases

With the existence of many autonomous databases widely accessible through computer networks, users will require the capability to jointly manipulate data in different databases. A multidatabase system provides such a capability through a multidatabase manipulation language, such as MSQL. We propose a theoretical foundation for such languages by presenting a multirelational algebra and calculus based on the relational algebra and calculus. The proposal is illustrated by various queries on an example multidatabase. It is shown that properties of the multirelational algebra may be used for optimization and that every multirelational algebra query can be expressed as a multirelational calculus query. The connection between the multirelational languages and MSQL, the multidatabase version of SQL, is also investigated.