Equational axiomatizability for coalgebra

A characterization result for equationally definable classes of certain coalgebras (including basic hidden algebra) shows that a class of coalgebras is definable by equations if and only if it is closed under coproducts, quotients, sources of morphisms and representative inclusions. The notions of equation and satisfaction are axiomatized in order to include the different approaches in the literature.     

一种基于进程代数的软件体系结构描述语言PEADL

对性能评价进程代数(PEPA)扩展,提出具有时序特征的随机进程代数(ESPA)。在此基础上进一步提出一种软件体系结构描述语言(PEADL)。介绍PEADL的语法和语义,并通过三层C/S结构应用系统展示PEADL的表述能力。     

计算机科学中的范畴数据类型的研究综述

范畴数据类型是指以范畴论为数学理论基础研究数据类型的描述、计算、语义和应用。早期的范畴数据类型研究以归纳数据类型为主,采用代数从归纳的角度研究有限数据类型的构造语义和递归性质。近年来,归纳数据类型的对偶概念——共归纳数据类型逐渐引起计算机科学工作者的关注与研究,他们采用共代数从观察的角度研究无限数据类型的行为语义和共递归性质。利用范畴论可以为数据类型研究提供统一的数学理论基础,并将代数和共代数中的各种重要研究成果有机地融合在一起,如语法构造与动态行为、递归与共递归、同余与互模拟等。目前,范畴数据类型已经在程序语言、计算描述、理论证明器和并行计算等领域得到广泛的应用。对范畴数据类型的基本概念、数学理论基础、逻辑基础及应用等方面的最新研究成果进行介绍,以引起国内外相关研究领域的学者对计算机科学中的范畴数据类型理论的关注。     

关系代数中除法运算的教学探讨

从关系代数中除法运算的定义出发,以实例分析和图表表示为工具,通过类比整数的除法运算阐明关系除法运算的本质含义,并给出关系代数中除法运算的基本运算表达式。解决以往除法运算的抽象定义难以被学生理解的不足,促进学生对知识点的透彻理解,取得较好的教学效果。     

基于条件事件代数的贝叶斯网的逻辑推理

条件事件代数理论在数据融合系统中有着重要的应用前景,该理论可用来解决不确定性、概率性和模糊性推理问题。条件事件代数是在确保规则与条件概率相容的前提下,把布尔代数上的逻辑运算推广到条件事件(规则)集合中的逻辑代数系统。对于一些特殊的贝叶斯网(如多树型网络)已经有了一些可行的概率推理的算法,但到目前为止,还没有可行的逻辑推理的算法。随着对不确定性知识研究的深入,迫切需要具有逻辑推理的算法。论文介绍了乘积空间条件事件代数的定义和基本性质,提出了基于乘积空间条件事件代数的贝叶斯网的逻辑推理的算法以及应用。     

进程代数及其在性能评价中的应用综述

进程代数是描述并发和通信系统的数学工具，形式化好、可操作性好，适合对复杂系统进行模型分析。本文从进程代数在计算机系统性能评价中的应用的角度对相关研究进行综述，对在此基础上开发新的形式化工具以及分析现有系统都具有指导意义。首先以CCS和PEPA为例介绍基本进程代数向随机进程代数的演进；然后阐述使用随机进程代数进行性能分析的方法，重点分析了模型简化的技术；比较了进程代数与其他性能评价方法的优缺点。     

数学软件MatLab在《线性代数》教学中的应用研究

《线性代数》是大学数学课程的一个重要组成部分,是大学的一门公共基础课,而且是考研的必考课程之一。如何很好地完成这门课程的教学任务而且学生能学有所用,这是每个大学数学教师面临的主要问题。在教学过程中适当地引入数学软件,不仅可以提高学生的学习兴趣,也可以使学生在以后的学习工作中真正地使用这门课程的一些基本的方法。     

Structure from Motion Using Bio-Inspired Intelligence Algorithm and Conformal Geometric Algebra

Structure from Motion algorithms offer good advantages, such as extract 3D information in monocular systems and structures estimation as shown in Hartley & Zisserman for numerous applications, for instance; augmented reality, autonomous navigation, motion capture, remote sensing and object recognition among others. Nevertheless, this algorithm suffers some weaknesses in precision. In the present work, we extent the proposal in Arana-Daniel, Villaseñor, López-Franco, & Alanís that presents a new strategy using bio-inspired intelligence algorithm and Conformal Geometric Algebra, based in the object mapping paradigm, to overcome the accuracy problem in two-view Structure form motion algorithms. For this instance, we include two new experiments and the inclusion of the circle entity; the circle carries stronger information about its motion than other geometric entities, as we will show.     

Using Computer Algebra techniques for the specification,verification and synthesis of recursive programs

We describe an innovative method for proving total correctness of tail recursive programs having a specific structure, namely programs in which an auxiliary tail recursive function is driven by a main nonrecursive function, and only the specification of the main function is provided. The specification of the auxiliary function is obtained almost fully automatically by solving coupled linear recursive sequences with constant coefficients. The process is carried out by means of CA (Computer Algebra) and AC (Algorithmic Combinatorics) and is implemented in the Theorema system (using Mathematica). We demonstrate this method on an example involving polynomial expressions. Furthermore, we develop a method for synthesis of recursive programs for computing polynomial expressions of a fixed degree by means of “cheap” operations, e.g., additions, subtractions and multiplications. For a given polynomial expression, we define its recursive program in a schemewise manner. The correctness of the synthesized programs follows from the general correctness of the synthesis method, which is proven once for all, using the verification method presented in the first part of this paper.     

形式代数在空间网格结构中的应用

文章依据形式代数（ＦｏｒｍｅｘＡｌｇｅｂｒａ）理论，采用ＦＯＲＴＲＡＮ语言编制了实用程序，使外形比较简单的平板网架、筒壳和外形较复杂的球壳、双曲抛物面形和马鞍形等网格结构都能够自动成形，避免了以往繁琐且易于出错的结构成形工作，与计算机辅助图形相结合，既直观又便于修改和检查。文章通过实例来说明形式代数在空间结构的自动成形中的应用。     

新型前馈网络学习算法在语音识别中的应用

简要介绍一种全新的前馈神经网络学习算法--代数算法,以该理论提出者针对这一算法做出的多方面的理论证明为基础,将此算法与传统BP算法相比较,利用其在网络结构和获取全局最优点方面具有传统BP算法不可比拟的优点,在matlab7.0实验平台上,分别把传统BP算法和此种新型学习算法应用于语音识别,通过仿真实验说明了新型算法的有效性,语音识别的精度在一定程度上得到了改善.     

针对信息安全专业《近世代数》课程改革的探讨

针对信息安全专业的《近世代数》教学,分析信息安全专业学生与数学专业学生在《近世代数》学习上存在的差异性,并因此提出如何调整《近世代数》的教学内容使其更适合信息安全专业学生的学习,探讨针对信息安全专业《近世代数》学习的教学方法改革,从而提高信息安全专业学生学习《近世代数》的积极性和效果。     

基于关系代数的模糊综合评判算法的研究和实现

模糊综合评判有着广泛的实际应用背景。关系代数是数据库技术的一个非常重要的理论基础,SQL语言是关系代数在数据库技术中的表现形式。把关系代数与模糊综合评判结合起来,有着重要的实践意义。基于关系代数的RFCE就是关系代数与模糊综合评判结合的结晶。     

A computer-verified monadic functional implementation of the integral

We provide a computer-verified exact monadic functional implementation of the Riemann integral in type theory. Together with previous work by O’Connor, this may be seen as the beginning of the realization of Bishop’s vision to use constructive mathematics as a programming language for exact analysis.     

Categorical proof theory of classical propositional calculus

We investigate semantics for classical proof based on the sequent calculus. We show that the propositional connectives are not quite well-behaved from a traditional categorical perspective, and give a more refined, but necessarily complex, analysis of how connectives may be characterised abstractly. Finally we explain the consequences of insisting on more familiar categorical behaviour.     

Institution Morphisms

Institutions formalise the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasises the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of different notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is uniform and informative to replace the current chaotic nomenclature; another goal is to investigate the properties and interrelations of these notions in a systematic way. Following brief expositions of indexed categories, diagram categories, twisted relations and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the ‘plain maps’ of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories. Because of this duality, we prefer the name ‘comorphism’ over ‘plain map’; moreover, we argue that morphisms are more natural than comorphisms in many cases. We also consider ‘theoroidal’ morphisms and comorphisms, which generalise signatures to theories, based on a theoroidal institution construction, finding that the ‘maps’ of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We introduce ‘forward’ and ‘semi-natural’ morphisms, and develop some of their properties. Appendices discuss institutions for partial algebra, a variant of order sorted algebra, two versions of hidden algebra, and a generalisation of universal algebra; these illustrate various points in the main text. A final appendix makes explicit a greater generality for the institution concept, clarifies certain details and proves some results that lift institution theory to this level. Received December 2000 / Accepted in revised form January 2002     

基于范畴论的形式化地理本体对齐和集成研究

本体对齐可解决本体间的异构,而范畴论可屏蔽本体间的异构性并为本体集成提供统一的方法框架。将范畴论引入本体对齐研究领域中,在范畴论的基础上,结合地理本体特征,对态射进行了重新定义,构造了一个更复杂的范畴。其中范畴中的对象为地理本体,而态射不仅能表达相等关系,也可以描述地理本体间的多种语义关系。在态射定义的基础上,根据态射的特性定义了本体对齐和本体对齐的复合,最后对本体集成进行了阐述。     

Towards a Formal Account of Reasoning about Evidence: Argumentation Schemes and Generalisations

This paper studies the modelling of legal reasoning about evidence within general theories of defeasible reasoning and argumentation. In particular, Wigmore's method for charting evidence and its use by modern legal evidence scholars is studied in order to give a formal underpinning in terms of logics for defeasible argumentation. Two notions turn out to be crucial, viz. argumentation schemes and empirical generalisations.