A survey of fuzzy implication algebras and their axiomatization

The theory of fuzzy implication algebras was proposed by Professor Wangming Wu in 1990. The present paper reviews the following two aspects of studies on FI-algebras: concepts, properties and some subclasses of FI-algebras; axiomatization of the class of FI-algebras and some of its important subclasses. The main results are summarized in the current paper, the relationships between FI-algebras and several classes of important fuzzy algebras are discussed, such as BL-algebras, MTL-algebras, and residuated lattices, and propositional calculus systems of several special classes of FI-algebras are shown.     

Traces of fuzzy binary relations

In this paper the right and left trace of a fuzzy binary relation is defined and investigated. Basic properties of a fuzzy relation (such as reflexivity, different kinds of transitivity, linearity, etc.) are characterized by means of its traces.     

蕴涵格的滤子及同余关系

在蕴涵格中引和了蕴涵滤子的概念，讨论了蕴涵滤子的一些基本性质，并由此建立了由素蕴涵滤子决定的同余关系及其商蕴涵格，以便为Fuzz推理建立了严格的逻辑基础作些必要的准备。     

格值命题逻辑系统LP(X)的闭包算子

In this paper, closure operators of lattice-valued propositional logic LP(X) are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP(X) is investigated. At the same time, a tool for checking compactness of LP(X) is given.     

新手-熟手高中化学教师PCK个案比较研究* ——以“氧化还原反应”主题为例

采用访谈法与质性资料分析法,测查了6名(3名新手与3名熟手)高中化学教师关于氧化还原反应主题的PCK。结果表明:(1)新手教师与熟手教师在CTO,KoL与KoS组分上存在较明显的差异。新手教师倾向于采用“教师-传授”教学取向,对学生知识的把握相对不足,更强调使用习题巩固策略;而熟手教师倾向于采用“学生-建构”教学取向,对学生知识的把握更为全面,更强调学生自主建构知识的过程。(2)新手教师与熟手教师在KoC与KoA组分上存在较明显的相似之处。在课程知识方面,教师对课程标准与教材中氧化还原反应主题内容具有较好的理解,但对化学基本观念、学科核心素养认识尚浅;在评价知识方面,教师偏向于传统的评价方式,且集中在形成性评价和总结性评价,但相对缺乏对学生的课前诊断性评价。文末据此对我国化学教师教育及其研究提出相关建议。     

The simplest protoalgebraic logic

The logic is the sentential logic defined in the language with just implication → by the axiom of reflexivity or identity “” and the rule of Modus Ponens “from φ and to infer ψ”. The theorems of this logic are exactly all formulas of the form . We argue that this is the simplest protoalgebraic logic, and that in it every set of assumptions encodes in itself not only all its consequences but also their proofs. In this paper we study this logic from the point of view of abstract algebraic logic, and in particular we use it as a relatively natural counterexample to settle some open problems in this theory. It appears that this logic has almost no properties: it is neither equivalential nor weakly algebraizable; it does not have an algebraic semantics; it does not satisfy any form of the Deduction Theorem, other than the most general parameterized and local one that all protoalgebraic logics satisfy; it is not filter‐distributive; and so on. It satisfies some forms of the interpolation property but in a rather trivial way. Very few things are known about its algebraic counterpart, save that its intrinsic variety is the class of all algebras of the similarity type.     

A computational algebraic-geometry method for conditional-independence inference

We consider the problems of semi-graphoid inference and of independence implication from a set of conditional-independence statements. Based on ideas from R. Hemmecke et al. [Combin. Probab. Comput., 2008, 17: 239–257], we present algebraic-geometry characterizations of these two problems, and propose two corresponding algorithms. These algorithms can be realized with any computer algebra system when the number of variables is small.     

教育实习经历对化学职前教师PCKg发展的影响——以高中化学实习教师的个案研究为例

基于学科教学识知PCKg理论,以一位化学职前教师(即高等师范院校的化学教育硕士)为个案,在长达5个月的研究期中,藉由教学观察、教案文件、导师访谈以及量表问卷等方式收集资料,探讨个案职前教师在实习历程中PCKg的建构与发展情形,及高中教学现场和师资培育高校的协助对实习教师的教学专业成长的影响,并建构“师培高校与中学现场协同培育以促进职前教师专业成长”的实习模式。研究结果可为未来规划师资培育工作及职前教师实习制度提供案例参考和研究建议。     

国外科学教师信念的理论与实证研究评述

评述国外科学教师信念的理论与实证研究,前者主要包括信念的定义内涵与理论框架,后者主要涵盖信念的测评方式、以及信念与实践的关系等;并据此探讨这类研究对我国化学教师教育的启示,以期对我国化学教师信念研究与化学教师发展提供有益思路。     

Fuzzy蕴涵代数与MV代数

本文讨论Ｆｕｚｚｙ蕴涵代数与ＭＶ代数之间的关系，并证明了在一定的条件下Ｆｕｚｚｙ蕴函代数是剩余格。