Domain independence and the relational calculus

Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here. It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power.Since the domain is potentially infinite, the answer to a relational calculus query is sometimes infinite (and hence not a relation). The following approaches which guarantee the finiteness of answers to queries are studied here:output-restricted unlimited interpretation, domain independent queries, output-restricted finite andcountable invention, andlimited interpretation. Of particular interest is the output-restricted unlimited interpretation—although the output is restricted to the active domain of the input and query, the quantified variables range over the infinite underlying domain. While this is close to the intuitive interpretation given to calculus formulas, the naive approach to evaluating queries under this semantics calls for the impossible task of examining infinitely many values. We describe here a constructiion which, given a queryQ under the output-restricted unlimited interpretation, yields a domain independent queryQ, with length no more than exponential in the length ofQ, such thatQ andQ (under their respective semantics) express the same function.This work supported in part by NSF grants IST-85-11541 and IRI-87-19875Work by this author was also supported in part by NSF grant IRI-9109520     

Pattern classification using fuzzy relational calculus

Our aim is to design a pattern classifier using fuzzy relational calculus (FRC) which was initially proposed by Pedrycz (1990). In the course of doing so, we first consider a particular interpretation of the multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. Subsequently, we introduce the notion of a fuzzy pattern vector to represent a population of training patterns in the pattern space and to denote the antecedent part of the said particular interpretation of the MFI. We introduce a new approach to the computation of the derivative of the fuzzy max-function and min-function using the concept of a generalized function. During the construction of the classifier based on FRC, we use fuzzy linguistic statements (or fuzzy membership function to represent the linguistic statement) to represent the values of features (e.g., feature F/sub 1/ is small and F/sub 2/ is big) for a population of patterns. Note that the construction of the classifier essentially depends on the estimate of a fuzzy relation /spl Rfr/ between the input (fuzzy set) and output (fuzzy set) of the classifier. Once the classifier is constructed, the nonfuzzy features of a pattern can be classified. At the time of classification of the nonfuzzy features of the testpatterns, we use the concept of fuzzy masking to fuzzify the nonfuzzy feature values of the testpatterns. The performance of the proposed scheme is tested on synthetic data. Finally, we use the proposed scheme for the vowel classification problem of an Indian language.     

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.     

Well-definedness and semantic type-checking for the nested relational calculus

The well-definedness problem for a programming language consists of checking, given an expression and an input type, whether the semantics of the expression is defined for all inputs adhering to the input type. A related problem is the semantic type-checking problem which consists of checking, given an expression, an input type, and an output type whether the expression always returns outputs adhering to the output type on inputs adhering to the input type. Both problems are undecidable for general-purpose programming languages. In this paper we study these problems for the Nested Relational Calculus, a specific-purpose database query language. We also investigate how these problems behave in the presence of programming language features such as singleton coercion and type tests.     

An interval-based temporal relational calculus for events with gaps

Abstract

Traditional interval-based representations of time assume interval convexity, i.e., that intervals are uninterrupted. This assumption makes it difficult to represent the common sense notion of a single event with ‘gaps’. Having a representation of this species of event contributes favorably to the ability of the human or machine to solve certain tasks, such as planning or database retrieval. This paper defines two kinds of discourse and knowledge object which comprise collections of convex intervals. Although other researchers have suggested the need for a relaxation of the assumption of convexity in event representation, there has been no attempt to offer a concise representation of gapped events. The formulation employed here to introduce gapped events is an extension of James Allen's interval-based approach to time representation. Allen's calculus of thirteen binary relations defined between two convex intervals is generalized to a matrix of binary relations between each pair of subintervals of pairs of non-convex intervals. A primary goal of this paper is to show that this extension of the interval-based approach increases the expressive power of the calculus, while retaining its computational advantages.     

A relational database integrity framework for access control policies

Access control is one of the most common and versatile mechanisms used for information systems security enforcement. An access control model formally describes how to decide whether an access request should be granted or denied. Since the role-based access control initiative has been proposed in the 90s, several access control models have been studied in the literature. An access control policy is an instance of a model. It defines the set of basic facts used in the decision process. Policies must satisfy a set of constraints defined in the model, which reflect some high level organization requirements. First-order logic has been advocated for some time as a suitable framework for access control models. Many frameworks have been proposed, focusing mainly on expressing complex access control models. However, though formally expressed, constraints are not defined in a unified language that could lead to some well-founded and generic enforcement procedures. Therefore, we make a clear distinction by proposing a logical framework focusing primarily on constraints, while keeping as much as possible a unified way of expressing constraints, policies, models, and reference monitors. This framework is closely tied to relational database integrity models. We then show how to use well-founded procedures in order to enforce and check constraints. Without requiring any rewriting previous to the inference process, these procedures provide clean and intuitive debugging traces for administrators. This approach is a step toward bridging the gap between general but hard to maintain formalisms and effective but insufficiently general ones.     

Querying fuzzy relational databases through fuzzy domain calculus

In this paper we present a definition of a domain relational calculus for fuzzy relational databases using the GEFRED model as a starting point. It is possible to define an equivalent fuzzy tuple relational calculus and consequently we achieve the two query language levels that Codd designed for relational databases but these are extended to fuzzy relational databases: Fuzzy relational algebra (defined in the GEFRED model) and the fuzzy relational calculus which is put forward in this paper. The expressive power of this fuzzy relational calculus is demonstrated through the use of a method to translate any algebraic expression into an equivalent expression in fuzzy domain relational calculus. Furthermore, we include a useful system so that the degree to which each value has satisfied the query condition can be measured. Some examples are also included in order to clarify the definition. ©1999 John Wiley & Sons, Inc.     

基于关系演算的Java模式识别

分析了面向对象类与对象间的关系,在此基础上建立了对应的属性模型并且以关系演算的方法进行捕获模型的对象关系;讨论并实现了动、静态相结合的基于Java语言的经典设计模式检查工具,并以该工具为基础做实验对一些设计模式进行了验证。     

A structure-based model of semantic integrity constraints for relational data bases

Data base management systems (DBMSs) are in widespread use because of the ease and flexibility with which users access large volumes of data. Ensuring data accuracy through integrity constraints is a central aspect of DBMS use. However, many DBMSs still lack adequate integrity support. In addition, a comprehensive theoretical basis for such support—the role of a constraint classification system—has yet to be developed. This paper presents a formalism that classifies semantic integrity constraints based on the structure of the relational model. Integrity constraints are characterized by the portion of the data base structure they access, whether one or more relations, attributes, or tuples. Thus, the model is completely general, allowing the arbitrary specification of any constraint. Examples of each type of constraint are illustrated using a small engineering data base, and various implemention issues are discussed.     

A logic-based mechanism for integrity maintenance of engineering databases

The semantics of engineering data can be represented in terms of constraints and can be maintained via constraint checking and enforcement. Conventional databases (e.g. Relational Databases) are inadequate for maintaining engineering data semantics because they have no effective means for representing and checking/enforcing constrains. As an extension of relational databases, deductive databases overcome this inadequacy by enabling constraint representation and checking. However, they too lack the constraint enforcement ability. a logic-based mechanism for enforcing constrainst in deductive databases is presented in this paper. The mechanism is composed of two operators: a truth enforcement operator and a falsity enforcement operator. The mechanics of these operators and their use for integrity enfocement are described herein.     

Minimal-change integrity maintenance using tuple deletions

We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [in: ACM Symposium on Principles of Database Systems (PODS), 1999, 68] (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable cases. We consider denial constraints, general functional and inclusion dependencies, as well as key and foreign key constraints. Our results shed light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance.     

Optimizing the evaluation of calculus expressions in a relational database system

There is an interesting search strategy (due to James B. Rothnie) for efficient implementation of a limited kind of selection criterion for a relational database. This strategy is here generalized to arbitrary relational calculus expressions, and an analysis of the resulting improvement of performance is given. The strategy is used in a relational database system TGR and an overview of the architecture of this system is presented. TGR uses microprogrammed database primitives for searching the database. This approach is very similar to the use of a database processor although it also allows flexible change of processor design. The behaviour of TGR in evaluating typical queries is analyzed and the results are used for pointing out the bottlenecks in a relational database system with a particular type of structure. As a conclusion the construction of a database processor with the database primitives from TGR as instruction set is recommended. This would be a step towards getting acceptable performance in a relational database system.     

A relational calculus with set operators, its safety, andequivalent graphical languages

The authors propose a relational calculus (RC/S) which uses set comparison and set manipulation operators to replace universal quantifiers and negations. It is argued that compared to the Codd relational calculus (RC), RC/S queries are easier to construct and comprehend. It is proved that the expressive power of RC is equivalent to the expressive power of RC/S, and algorithms for translating an RC query into an RC/S query and vice versa are given. A safe RC/S query is defined as one that has finite output and can be evaluated in finite time. Then a subset of RC/S queries, called RC/S* is defined, and it is proved that RC/S* is safe. RC/S* is compared to the existing largest safe subsets of RC, i.e. the evaluable formulas and the allowed formulas. Algorithms are given to transform any evaluable formula into an RC/S* query, and some RC/S* formulas that are not evaluable are given. RC/S* queries can be directly implemented using a graphical language similar to Query-by-Example (QBE). Two different graphical languages are described that are equivalent to the RC/S* in expressive power, and these languages are compared to QBE     

DFL: A dataflow language based on Petri nets and nested relational calculus

In this paper we propose DFL—a formal, graphical workflow language for dataflows, i.e., workflows where large amounts of complex data are manipulated, and the structure of the manipulated data is reflected in the structure of the workflow. It is a common extension of (1) Petri nets, which are responsible for the organization of the processing tasks, and (2) nested relational calculus, which is a database query language over complex objects, and is responsible for handling collections of data items (in particular, for iteration) and for the typing system. We demonstrate that dataflows constructed in a hierarchical manner, according to a set of refinement rules we propose, are semi-sound, i.e., initiated with a single token (which may represent a complex scientific data collection) in the input node, terminate with a single token in the output node (which represents the output data collection). In particular they never leave any “debris data” behind and an output is always eventually computed regardless of how the computation proceeds.     

A graph-based approach for rule integrity and maintainability in expert system maintenance

Just as conventional software systems have maintenance costs far exceeding development costs, so too do rule-based expert systems. They are frequently developed by an incremental and iterative method, where knowledge and decision rules are extracted and added to the system in a piecemeal manner throughout system evolution. Thus, ensuring the correctness and consistency of the rule base (RB) becomes an important, though challenging task. However, most research work in expert systems has focused on building and validating rule bases, leaving the maintenance issue unexplored. We propose a graph-based approach, called the object classification model (OCM), as a methodology for RB maintenance. An experiment was conducted to compare the OCM with traditional RB maintenance methods. The results show that the OCM helps knowledge engineers retain rule-base integrity and, thus, increase rule-base maintainability.     

基于Hadoop的时态信息存储与时态关系演算问题研究

面对海量的非结构化时态信息,构建了在分布式环境下的数据存储模型,并在此基础上提出一种基本的时态数据处理方法。使用Hadoop平台下的分布式、非结构化数据库HBase对海量时态数据进行存储,构造以时态集合为时态存储单元的时态数据存储模型;针对分布式处理特征和时态集合数据类型,提出一种在Map/Reduce编程计算模式下进行海量时态信息关系演算的实现方法;通过扩展时态区间关系运算,实现以时态集合为基本时态数据操作对象的交、并等关系运算。以医疗时态数据作为研究实例,表明了所提出的时态数据存储模型和关系演算方案在分布式应用系统下的适用性。     

Differential calculus of interval-valued q-rung orthopair fuzzy functions and their applications

The interval-valued q-rung orthopair fuzzy set (IVq-ROFS) provides an extension of Yager's q-rung orthopair fuzzy set (q-ROFS), where membership and nonmembership degrees are subsets of the closed interval $\left[0,1\right]$. In such a situation, it is more superior for decision makers to provide their judgments by intervals instead of crisp numbers due to the uncertainty and vagueness in real life. In this paper, we study the calculus theories of IVq-ROFS from the microscopic. In particular, we first introduce the elementary arithmetic of interval-valued q-rung orthopair fuzzy values (IVq-ROFVs), including addition, multiplication, and their inverse. They are the basis for analysis and calculation throughout the work. In addition, we discuss and prove in detail the operation properties and aggregation operators of IVq-ROFVs. Then, we introduce the concept of interval-valued q-rung orthopair fuzzy functions (IVq-ROFFs), which is the main research object of this paper. After that, we further discuss the continuity, derivatives and differentials of IVq-ROFFs. We also find that the derivatives of IVq-ROFFs are closely related to elasticity, which is an important concept in economics. Finally, we provide some application examples to verify the feasibility and effectiveness of the derived results.     

Semantic integrity support in SQL:1999 and commercial (object-)relational database management systems

The correctness of the data managed by database systems is vital to any application that utilizes data for business, research, and decision-making purposes. To guard databases against erroneous data not reflecting real-world data or business rules, semantic integrity constraints can be specified during database design. Current commercial database management systems provide various means to implement mechanisms to enforce semantic integrity constraints at database run-time. In this paper, we give an overview of the semantic integrity support in the most recent SQL-standard SQL:1999, and we show to what extent the different concepts and language constructs proposed in this standard can be found in major commercial (object-)relational database management systems. In addition, we discuss general design guidelines that point out how the semantic integrity features provided by these systems should be utilized in order to implement an effective integrity enforcing subsystem for a database. Received: 14 August 2000 / Accepted: 9 March 2001 / Published online: 7 June 2001     

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.