面向对象程序设计中的类型理论

一、什么是类型理论?类型理论是研究类型的定义、模型和推导规律的形式化理论,它和逻辑、代数、计算机程序设计语言、软件开发都有着密切的联系。类型理论起源于对数学悖论的研究,脱胎于带类型的λ-演算及其与逻辑的对应关系的探讨,在计算机科学中找到了其广阔应用领域。如果从研究对象和侧重点上来划分,类型理论可粗略地分为两类:代数类型理论和逻辑类型理论。代数类型理论主要研究类型的代数结构和模型,所使用的工具主要是多类代数、范畴论,Topoes 理论等。程序设     

苹果树稀果的好处及方法

最近，嵌套关系模型语言及复杂对象语言的研究已引起人们的广泛重视。这些语言有些是代数结构的，有些是基于演算的，还有的是面向逻辑程序设计的。本文将介绍这些语言的发展概况、最新研究结果以及语言的表达能力，并就其完备性问题进行了讨论。     

具有面向对象特征的知识库系统

本文讨论了具有面向对象特征的知识库系统KBASE~ 的数据模型、语言及实现。KBASE~ 的数据模型可以方便地支持对象标识、类层次、多继承等面向对象概念。描述性查询语言KBL是DATALOG针对于非一范式关系模型的扩充。本文重构了KBL的语义理论框架,提出了通过计算相关类的下确界来解决属性继承中的冲突问题,通过在KBL程序中添加规则来实现实例继承的方案,本文说明了KBL程序可以转换成语义等价的DATALOG程序,描述了这种转换的基本思想,探索了知识库和面向对象数据库有机结合的可行途径。     

概念知识表示和推理

Nilsson教授首先提出了代数格应用于概念知识表示的思想．其优点在于知识表示的代数特性和图示特性，在此基础上．表文把代数格与PROLOG相结合．定义了一种基于概念的逻辑编程语言．其语言具有比PROLOG更抽象、更方便的编程风格．此外．给出了该逻辑编程语言的匹配算法．     

SQL在递归查询和逻辑谓词上的扩充

本文讨论了对ＳＱＬ语言的递归查询和逻辑谓词功能上的扩充方法，给出了递归查询的关系代数表达式，并就考虑路径的递归查询和不考虑路径的递归查询两方面对ＳＱＬ在句法和算法上，对ＳＱＬ中逻辑谓词扩充的理论，句法和算法进行了讨论。     

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。     

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。     

动态模糊逻辑的格结构及其应用研究

当前非经典逻辑的一个重要的研究方向是其代数结构的研究,动态模糊逻辑理论作为一种处理动态性、模糊性问题的重要工具,其代数结构尚不够完善和成熟.通过选择适合动态模糊逻辑的逻辑代数表示系统,建立了动态模糊逻辑的格结构,最后研究动态模糊逻辑格结构的特性及其在组织结构中的应用.     

数据树——一种用于异构数据源集成的公共数据模型

文中提出一种异构数据源集成的公共数据模型－附有元数据的数据树。数据树的元数据附在数据上，便于表达没有稳定模式的数据、自描述的数据、非结构化和半结构化的数据以及从各种异构数据源集成的数据。作为数据树操纵语言的数学基础，文中提出了数据树代数，它提供了八种操作，比关系代数具有更大的灵活性和较强的功能。     

人工智能应用中基于区间代数的时态推理

时态表示和推理是人工智能领域的重要研究内容之一,它的应用范围分布很广,从逻辑基础研究到知识系统的应用。区间代数是一种独立的与领域无关的时态理论。用区间代数能表示不确定的时态关系,可以很方便的用于时态推理,表达能力强;时态关系的区间表示比较直观,可理解性强;同时区间代数可以进一步扩展到二维空间领域,即将区间代数拓展为矩阵代数,实现二维空间推理。在一维时态推理中,将时态的区间表示和矩阵表示相结合,在提高计算效率的同时,保持了形象直观的时态表示。     

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.     

Techniques of integrating Datalog with PROLOG

Since extending DATALOG to a general-purpose programming language seems very difficult,many projects have embedded a DATALOG-based query laguage into a procedural host language,such as CORAL,Glue-Nail,etc.Although DATALOG can be consideed as function-free PROLOG,they are very different in many aspects.For instance,DATALOG is declarative while PROLOG isn‘t,DATALOG takes “a-set-at-a-time” mode of evaluation but PROLOG takes “a-tuple-at-a-time”one,DATALOG is only a query language whereas PROLOG is a general-purpose programming language.It is thought that integrating DATALOG with PROLOG may take their advantages.KBASEP is such a language.It uses KBASE as the query language and PROLOG as its procedural host language,where KBASE is a ne extemsion of DATALOG with negation and function.This paper introduces the integration techniques used in KBASE-P system.     

Default logic as a query language

Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI formalisms as relational database query languages has been investigated to a much smaller extent. In this work, we propose a novel application of Reiter's default logic by introducing a default query language (DQL) for finite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO_∃∀ the existential-universal fragment of second-order logic. This result is not only of theoretical importance: We exhibit queries-which are useful in practice-that can be expressed with DQL and cannot with other query languages based on nonmonotonic logics such as DATALOG with negation under the stable model semantics. In particular, we show that DQL is well-suited for diagnostic reasoning     

Time-based operators for relational algebra query languages

We present a new approach for historical relational algebra languages based upon generalized logic for Boolean and comparison operators and a temporal modification of the standard relational algebra operators. Historical versions of standard (snapshot) relational algebra operators based upon this generalized logic are presented. The temporal modification employs a logic that operates on sets of value/time-interval pairs and which can be applied to snapshot as well as historical databases. Our emphasis is that the generalized operators can be used to enrich existing historical query languages and to provide an easier and more natural time-based interface. Using the generalized operators, users can express their queries more naturally, succinctly and elegantly. Examples are presented which illustrate that the modified operators offer a good degree of flexibility in expressing different temporal requirements.     

Using FP as a query language for relational data-bases

FP is the programming language defined by J. Backus to demonstrate the virtues of functional programming as opposed to conventional programming in Von Neumann-like languages.In this paper we investigate the use of FP in the framework of relational data bases. In particular, we show how the language can be used to define base relations, to derive views from a collection of relations, and to express complex database queries.The language provides all capabilities of pure algebraic relational languages, but is considerably more powerful. As such, it can be used as a formal specification language to describe the semantics of queries expressed in relational languages, such as Query-By-Example. In addition the algebra of FP programs allows one to formally prove properties of such queries.     

ERL: Logic for entity-relationship databases

We develop a logic for entity-relationship databases, ERL, that is a generalization of database logic. ERL provides advantages to the ER model much as FOL (first-order logic) does to the relational model: a uniform language for expressing database schema, integrity constraints, and database manipulation; clearly defined semantics; the capability to express database transformations; and deductive capabilities. We propose three query languages for ER databases called ERRC, ERSQL, and ERQBE, which are generalizations of the relational calculus, SQL, and QBE, respectively. We use example queries and updates to demonstrate the capabilities of these languages. We apply database transformations to introduce the notion of views and to show that both ERRC and ERSQL are relationally complete.Research sponsored in part by the National Science Foundation under grant IRI-8921951 and by Towson State University.     

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.     

The equational theory of Kleene lattices

Languages and families of binary relations are standard interpretations of Kleene algebras. It is known that the equational theories of these interpretations coincide and that the free Kleene algebra is representable both as a relation and as a language algebra. We investigate the identities valid in these interpretations when we expand the signature of Kleene algebras with the meet operation. In both cases, meet is interpreted as intersection. We prove that in this case, there are more identities valid in language algebras than in relation algebras (exactly three more in some sense), and representability of the free algebra holds for the relational interpretation but fails for the language interpretation. However, if we exclude the identity constant from the algebras when we add meet, then the equational theories of the relational and language interpretations remain the same, and the free algebra is representable as a language algebra, too. The moral is that only the identity constant behaves differently in the language and the relational interpretations, and only meet makes this visible.     

Proceduralism and parallelism in specification languages

We discuss the advantages and limitations of the “nonprocedural” mode of expression, in the context of languages for programming, system specification, and database access. A language is introduced which has some relevance to all three of the above processes. The syntax of LEGOL is based on the relational algebra, but incorporates procedural control structures for use when the underlying application logic demands. Using this language, solutions can be suggested for some example stock-control problems which are difficult to handle in a purely non-procedural way.     

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