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。     

ON TEMPORAL DEDUCTIVE DATABASES

This article introduces a temporal deductive database system featuring a logic programming language and an algebraic front-end. The language, called Temporal DATALOG, is an extension of DATALOG based on a linear-time temporal logic in which the flow of time is modeled by the set of natural numbers. Programs of Temporal DATALOG are considered as temporal deductive databases, specifying temporal relationships among data and providing base relations to the algebraic front-end. The minimum model of a given Temporal DATALOG program is regarded as the temporal database the program models intensionally. The algebraic front-end, called TRA, is a point-wise extension of the relational algebra upon the set of natural numbers. When needed during the evaluation of TRA expressions, slices of temporal relations over intervals can be retrieved from a given temporal deductive database by bottom-up evaluation strategies.
A modular extension of Temporal DATALOG is also proposed, through which temporal relations created during the evaluation of TRA expressions may be fed back to the deductive part for further manipulation. Modules therefore enable the algebra to have full access to the deductive capabilities of Temporal DATALOG and to extend it with nonstandard algebraic operators. This article also shows that the temporal operators of TRA can be simulated in Temporal DATALOG by program clauses.     

满足TNF的历史关系数据库的代数结构

建立了满足TNF的历史关系数据库的代数结构,在保持标准关系代数的基础上,实现了不同时间属性值的比较,从而能通过代数运算实现属性动态变化情况的查询。     

数据仓库中时态视图的维护

数据仓库的一个重要用途是利用时态视图向用户提供历史信息.因为在传统关系数据模型中增加了对时间的支持,而且时态视图的更新不仅来自于基表更新,还包括时间前进,所以,目前对非时态视图维护的研究成果不适用于时态视图,并且已有的一些时态视图维护算法也不适用于数据仓库.以历史关系模式为对象,根据增量式维护方法的原理,采用纯删除、纯插入的计算方法,用代数语言给出了5种基本历史关系代数运算的更新传播算法,由这5种历史关系代数组合定义的时态视图都可用迭代方法得到其增量维护计算式.所采用的纯删除、纯插入思想也可移用于其他历史     

A complete temporal relational algebra

Various temporal extensions to the relational model have been proposed. All of these, however, deviate significantly from the original relational model. This paper presents a temporal extension of the relational algebra that is not significantly different from the original relational model, yet is at least as expressive as any of the previous approaches. This algebra employs multidimensional tuple time-stamping to capture the complete temporal behavior of data. The basic relational operations are redefined as consistent extensions of the existing operations in a manner that preserves the basic algebraic equivalences of the snapshot (i.e., conventional static) algebra. A new operation, namely temporal projection, is introduced. The complete update semantics are formally specified and aggregate functions are defined. The algebra is closed, and reduces to the snapshot algebra. It is also shown to be at least as expressive as the calculus-based temporal query language TQuel. In order to assess the algebra, it is evaluated using a set of twenty-six criteria proposed in the literature, and compared to existing temporal relational algebras. The proposed algebra appears to satisfy more criteria than any other existing algebra. Edited by Wesley Chu. Received February 1993 / Accepted April 1995     

The Semijoin Algebra and the Guarded Fragment

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin” operator, then the resulting “semijoin algebra” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to μGF.This author has been partially supported by the European Community Research Training Network “Games and Automata for Synthesis and Validation” (GAMES), contract HPRN-CT-2002-00283.     

Expressiveness of temporal query languages: on the modelling of intervals, interval relationships and states

Storing and retrieving time-related information are important, or even critical, tasks on many areas of computer science (CS) and in particular for artificial intelligence (AI). The expressive power of temporal databases/query languages has been studied from different perspectives, but the kind of temporal information they are able to store and retrieve is not always conveniently addressed. Here we assess a number of temporal query languages with respect to the modelling of time intervals, interval relationships and states, which can be thought of as the building blocks to represent and reason about a large and important class of historic information. To survey the facilities and issues which are particular to certain temporal query languages not only gives an idea about how useful they can be in particular contexts, but also gives an interesting insight in how these issues are, in many cases, ultimately inherent to the database paradigm. While in the area of AI declarative languages are usually the preferred choice, other areas of CS heavily rely on the extended relational paradigm. This paper, then, will be concerned with the representation of historic information in two well known temporal query languages: Templog in the context of temporal deductive databases, and TSQL2 in the context of temporal relational databases. We hope the results highlighted here will increase cross-fertilisation between different communities. This article can be related to recent publications drawing the attention towards the different approaches followed by the Databases and AI communities when using time-related concepts.     

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     

EXTENSION OF THE RELATIONAL DATABASE AND ITS ALGEBRA WITH ROUGH SET TECHNIQUES

This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain. There are several obvious applications for which the rough relational database model can more accurately model an enterprise than does the standard relational model. These include systems involving ambiguous, imprecise, or uncertain data. Retrieval over mismatched domains caused by the merging of one or more applications can be facilitated by the use of indiscernibility, and naive system users can achieve greater recall with the rough relational database. In addition, applications inherently “rough” could be more easily implemented and maintained in the rough relational database.     

On the expressive power of the relational algebra with partially ordered domains

Assuming data domains are partially ordered, we define the partially ordered relational algebra (PORA) by allowing the ordering predicate ? to be used in formulae of the selection operator σ. We apply Paredaens and Bancilhon's Theorem to examine the expressiveness of the PORA, and show that the PORA expresses exactly the set of all possible relations which are invariant under order-preserving automorphisms of databases. The extension is consistent with the two important extreme cases of unordered and linearly ordered domains. We also investigate the three hierarchies of: (1) computable queries, (2) query languages and (3) partially ordered domains, and show that there is a one-to-one correspondence between them.     

Toward Practical Query Evaluation for Constraint Databases

Linear constraint databases (LCDBs) extend relational databases to include linear arithmetic constraints in both relations and queries. A LCDB can also be viewed as a powerful extension of linear programming (LP) where the system of constraints is generalized to a database containing constraints and the objective function is generalized to a relational query containing constraints. Our major concern is query optimization in LCDBs. Traditional database approaches are not adequate for combination with LP technology. Instead, we propose a new query optimization approach, based on statistical estimations and iterated trials of potentially better evaluation plans. The resulting algorithms are not only effective on LCDBs, but also applicable to existing query languages. A number of specific constraint algebra algorithms are also developed: select-project-join for two relations, constraint sort-join and constraint multi-join.     

Relational theory of queries

In this paper a new presentation of the relational theory of queries will be given. Both the relational algebra and the (domain) relational calculus will be systematically derived from first-order logic. The connections between logic, algebra and calculus will become extremely simple: e.g. the relational algebra will be isomorphic with a subset of relational calculus. Also some theoretical results about the completeness of the relational query languages will be presented. Both the relational calculus and the relational algebra will be extended to contain aggregate functions.     

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。     

基于BCDM的双时态关系代数

双时态概念数据模型BCDM是一种重要的时态数据库模型，基于BCDM模型，建立了一种双时态关系代数．首先，对时态数据库事务时间和有效时间进行规范化的定义，给出BCDM中时间元素的规范化定义和演算描述；而后，定义时态映射，用以描述BCDM中的双时态元组，并形式描述时态映射的演算；最后，用时态映射定义的元组对双时态关系进行定义，并由此给出双时态关系代数运算的形式化描述．     

Extending a multi-set relational algebra to a parallel environment

Parallel database systems will very probably be the future for high-performance data-intensive applications. In the past decade, many parallel database systems have been developed, together with many languages and approaches to specify operations in these systems. A common background is still missing, however. This paper proposes an extended relational algebra for this purpose, based on the well-known standard relational algebra. The extended algebra provides both complete database manipulation language features, and data distribution and process allocation primitives to describe parallelism. It is defined in terms of multi-sets of tuples to allow handling of duplicates and to obtain a close connection to the world of high-performance data processing. Due to its algebraic nature, the language is well suited for optimization and parallelization through expression rewriting. The proposed language can be used as a database manipulation language on its own, as has been done in the PRISMA parallel database project, or as a formal basis for other languages, like SQL.Recommended by: Patrick Valduriez     

Adding time dimension to relational model and extending relational algebra

A methodology for adding the time dimension to the relational model is proposed and relational algebra is extended for this purpose. We propose time-stamping attributes instead of adding time to tuples. Each attribute value is stored along with a time interval over which it is valid. Non-first normal form realations are used. A relation can have atomic, set-valued, triplet-valued, or set triplet-valued attributes. The last two types of attributes preserve the time (history). Furthermore, new algebraic operations are defined to extract information from historical relations. These operations convert one attribute type to another and do selection over the time dimension. Algebraic rules and identities for the new operations are also included.     

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.     

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     

A functional processor for the relational algebra on a microcomputer

We have built on the U.C.S.D. P-system (running on an IBM Personal Computer) a relational algebra processor, MRDS/FS, which is extremely powerful and which supports a functional syntax for the programmer-user. The relational algebra is provided in the extended operators μ-join, σ-join, project and select. The domain algebra is fully implemented for the first time, giving operations on attributes: arithmetic, logic, comparison and four different categories of aggregation of these. A strictly functional syntax is provided, permitting user-defined functions using the relational and domain algebras as primitive operations. An interactive editor permits the creation, copying and changing of both relations and user-defined functions.     

SPARQL查询的关系代数表示与转换方法

为解决基于本体的数据集成系统中的查询转换问题,提出SPARQL查询的关系代数表示和转换方法。引入RDF图模式的关系代数,定义了五种基本的关系运算,给出了SPARQL查询的关系代数表示;提出了SPARQL到SQL的查询转换方法,将基于本体的SPARQL查询转换为可在关系数据库上直接执行的SQL查询,从而实现关系数据库的集成。系统实现表明,该方法能够有效地实现查询语言的转换。