Symbolic user-defined periodicity in temporal relational databases

Calendars and periodicity play a fundamental role in many applications. Recently, some commercial databases started to support user-defined periodicity in the queries in order to provide "a human-friendly way of handling time" (see, e.g., TimeSeries in Oracle 8). On the other hand, only few relational data models support user-defined periodicity in the data, mostly using "mathematical" expressions to represent periodicity. In this paper, we propose a high-level "symbolic" language for representing user-defined periodicity which seems to us more human-oriented than mathematical ones, and we use the domain of Gadia's temporal elements in order to define its properties and its extensional semantics. We then propose a temporal relational model which supports user-defined "symbolic" periodicity (e.g., to express "on the second Monday of each month") in the validity time of tuples and also copes with frame times (e.g., "from 1/1/98 to 28/2/98"). We define the temporal counterpart of the standard operators of the relational algebra, and we introduce new temporal operators and functions. We also prove that our temporal algebra is a consistent extension of the classical (atemporal) one. Moreover, we define both a fully symbolic evaluation method for the operators on the periodicities in the validity times of tuples, which is correct but not complete, and semisymbolic one, which is correct and complete, and study their computational complexity.     

Extensions to SQL for historical databases

A historical management system (HDBMS) is described which uses an extended relational data model with state-oriented, instead of `cubic', conceptualization. Two types of historical relations, called state and event relations, are provided for modeling real-world objects. The query language SQL has been extended for definition, retrieval, and update of historical relations. The extended SQL, called HSQL, is a superset of SQL. The author defines a few primitive algebra operations for historical relations, and uses them as a basis for extensions to SQL. In this way, HSQL retains the elegant structural and algebraic framework of SQL. HSQL contains a few new clauses, many operations and built-in functions on time domain, and facilities for retrospective updates and time-rollback     

A relational language with deductions,functions and recursions

We propose here a .relational algebra capable of deducing tuples from a premise expressed in an extended relational form: it also supports user-defined and recursive functions in the form of parameterised views, and provides a facility for easier specification of queries. The paper shows the power of the language in dealing with problems such as ancestors, part explosions and connected tours.This language, called DEAL, is an enhanced version of the PRECI Algebraic Language (PAL) but presented here in a SQL-like syntax.     

Numerical operations on a relational database

The problem is discussed of defining numerical operations on a relational database to accommodate the statistical analyses associated with a bivariate frequency table. An attempt has been made to extend Codd's relational algebra to include simple bivariate statistical operations preserving the closure of Codd's algebra. This extended algebra is applied to bivariate relational data structures needed for real-time automatic statistical quality control of a manufacturing process. Also discussed are some new category-numeric operations on relational tables     

HIFUN - a high level functional query language for big data analytics

We present a high level query language, called HIFUN, for defining analytic queries over big datasets, independently of how these queries are evaluated. An analytic query in HIFUN is defined to be a well-formed expression of a functional algebra that we define in the paper. The operations of this algebra combine functions to create HIFUN queries in much the same way as the operations of the relational algebra combine relations to create algebraic queries. The contributions of this paper are: (a) the definition of a formal framework in which to study analytic queries in the abstract; (b) the encoding of a HIFUN query either as a MapReduce job or as an SQL group-by query; and (c) the definition of a formal method for rewriting HIFUN queries and, as a case study, its application to the rewriting of MapReduce jobs and of SQL group-by queries. We emphasize that, although theoretical in nature, our work uses only basic and well known mathematical concepts, namely functions and their basic operations.     

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     

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.     

Temporal relational data model

This paper incorporates a temporal dimension to nested relations. It combines research in temporal databases and nested relations for managing the temporal data in nontraditional database applications. A temporal data value is represented as a temporal atom; a temporal atom consists of two parts: a temporal set and a value. The temporal atom asserts that the value is valid over the time duration represented by its temporal set. The data model allows relations with arbitrary levels of nesting and can represent the histories of objects and their relationships. Temporal relational algebra and calculus languages are formulated and their equivalence is proved. Temporal relational algebra includes operations to manipulate temporal data and to restructure nested temporal relations. Additionally, we define operations to generate a power set of a relation, a set membership test, and a set inclusion test, which are all derived from the other operations of temporal relational algebra. To obtain a concise representation of temporal data (temporal reduction), collapsed versions of the set-theoretic operations are defined. Procedures to express collapsed operations by the regular operations of temporal relational algebra are included. The paper also develops procedures to completely flatten a nested temporal relation into an equivalent 1 NF relation and back to its original form, thus providing a basis for the semantics of the collapsed operations by the traditional operations on 1 NF relations     

A data model and algebra for probabilistic complex values

We present a probabilistic data model for complex values. More precisely, we introduce probabilistic complex value relations, which combine the concept of probabilistic relations with the idea of complex values in a uniform framework. We elaborate a model-theoretic definition of probabilistic combination strategies, which has a rigorous foundation on probability theory. We then define an algebra for querying database instances, which comprises the operations of selection, projection, renaming, join, Cartesian product, union, intersection, and difference. We prove that our data model and algebra for probabilistic complex values generalizes the classical relational data model and algebra. Moreover, we show that under certain assumptions, all our algebraic operations are tractable. We finally show that most of the query equivalences of classical relational algebra carry over to our algebra on probabilistic complex value relations. Hence, query optimization techniques for classical relational algebra can easily be applied to optimize queries on probabilistic complex value relations.     

OO代数——一个面向对象的数据库的基本查询模型

本文提出了一个面向对象的数据库系统的基本查询模型－ＯＯ代数，它具有关系代数相似的形式，具有封闭性和远比关系代数强得多的表达能力。文中首先给出了面向对象的数据库系统的数据结构的一种形式化描述－ＯＳＧ，然后ＯＯ代数的五种基本运算：并、差、类间连接、类内选择及广义投影被一一定义，并说明了用关系代数实现这五种运算的方法。     

Temporal probabilistic object bases

There are numerous applications where we have to deal with temporal uncertainty associated with objects. The ability to automatically store and manipulate time, probabilities, and objects is important. We propose a data model and algebra for temporal probabilistic object bases (TPOBs), which allows us to specify the probability with which an event occurs at a given time point. In explicit TPOB-instances, the sets of time points along with their probability intervals are explicitly enumerated. In implicit TPOB-instances, sets of time points are expressed by constraints and their probability intervals by probability distribution functions. Thus, implicit object base instances are succinct representations of explicit ones; they allow for an efficient implementation of algebraic operations, while their explicit counterparts make defining algebraic operations easy. We extend the relational algebra to both explicit and implicit instances and prove that the operations on implicit instances correctly implement their counterpart on explicit instances.     

Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries

This paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes. Precise as well as partial (imprecise, uncertain) knowledge concerning the value of the attributes are represented by means of [0,1]-valued possibility distributions in Zadeh's sense. Thus, we have to manipulate ordinary relations on Cartesian products of sets of fuzzy subsets rather than fuzzy relations. Besides, vague queries whose contents are also represented by possibility distributions can be taken into account. The basic operations of relational algebra, union, intersection, Cartesian product, projection, and selection are extended in order to deal with partial information and vague queries. Approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation. Then, the main features of a query language based on the extended relational algebra are presented. An illustrative example is provided. This approach, which enables a very general treatment of relational databases with fuzzy attribute values, makes an extensive use of dual possibility and necessity measures.     

基于关系代数的XML数据查询

XML渐已成为Web上数据表示和交换的通用语言。为了有效地利用大量的XML文档,需要研究XML数据查询技术。提出了基于关系代数的XML数据查询方法。XML子句可以用关系代数表达式表示,并通过关系代数操作得到查询结果。该方法为查询XML数据提供了一种简洁和有效的手段。     

Fuzzy relational algebra for possibility-distribution-fuzzy-relational model of fuzzy data

In the real world, there exist a lot of fuzzy data which cannot or need not be precisely defined. We distinguish two types of fuzziness: one in an attribute value itself and the other in an association of them. For such fuzzy data, we propose a possibility-distribution-fuzzy-relational model, in which fuzzy data are represented by fuzzy relations whose grades of membership and attribute values are possibility distributions. In this model, the former fuzziness is represented by a possibility distribution and the latter by a grade of membership. Relational algebra for the ordinary relational database as defined by Codd includes the traditional set operations and the special relational operations. These operations are classified into the primitive operations, namely, union, difference, extended Cartesian product, selection and projection, and the additional operations, namely, intersection, join, and division. We define the relational algebra for the possibility-distribution-fuzzy-relational model of fuzzy databases.     

基于BCDM的含有变量的双时态关系代数研究*

在BCDM(双时态概念数据模型)中,时间变元Now和UC的存在解决了时态记录的频繁更新问题;但是时态变元的存在又给数据库的操作带来某种不确定性甚至是错误,同时引起关系代数运算的歧义。基于BCDM,通过绑定时间变元,用时态映射的集合定义时态关系,由此建立了一种含有时间变元的双时态关系代数体系。该关系代数体系在双时态运算下是封闭的。     

The power of languages for the manipulation of complex values

Various models and languages for describing and manipulating hierarchically structured data have been proposed. Algebraic, calculus-based, and logic-programming oriented languages have all been considered. This article presents a general model for complex values (i.e., values with hierarchical structures), and languages for it based on the three paradigms. The algebraic language generalizes those presented in the literature; it is shown to be related to the functional, style of programming advocated by Backus (1978). The notion of domain independence (from relational databases) is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated to guarantee domain independence. The main results are: The domain-independent calculus, the safe calculus, the algebra, and the logic-programming oriented language have equivalent expressive power. In particular, recursive queries, such as the transitive closure, can be expressed in each of the languages. For this result, the algebra needs the powerset operation. A more restricted version of safety is presented, such that the restricted safe calculus is equivalent to the algebra without the powerset. The results are extended to the case where arbitrary functions and predicates are used in the languages.     

Algebraic decomposition of discrete functions

Consideration was given to the functional decomposition of the discrete systems which is reducible to the functional decomposition of the discrete functions, where by the decomposition is meant the representation of a function by a formula in the basis of unary and binary operations. The algebraic decomposition in an algebra consisting of two binary operations and functions of two variables was studied. A procedure of formula design on the basis of composition of repetition-free subformulas was substantiated. Both exact and asymptotic complexity estimates of the designed formulas were given.     

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．     

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 Generalized Implementation Method for Relational Data Sublanguages

A set of primitive operations on tuples is derived; it is shown that these operations are necessary and sufficient for the implementation tion of any language equivalent in power to the relational algebra. The translation of queries from a variety of relational languages into these tuple operations is discussed and illustrated with several examples. A method is given for the conversion of such a translated query into a network of processes and files. An optimization algorithm which operates on this network is described and demonstrated. Using this method, many different relational languages can be implemented using the same data management software; furthermore, the underlying software can be changed without requiring any changes at the user interface. This approach should yield great benefits in reduced cost and increased flexibility of implementation.