活动类别：“Workshop on Order, Topology and Logic”系列学术报告
活动时间：9:00
活动日期：2018-4-14
地点：长安校区 数学与信息科学学院学术报告厅
主办单位：数学与信息科学学院
讲座题目1：Regularity vs. constructive complete (co) distributivity
讲座时间：9:00-10:00
讲座日期：2018-4-14
报告人：赖洪亮教授
讲座内容简介：
It is well known that a relation ϕ between sets is regular if and only if Kϕ is completely distributive (cd), where Kϕ is the complete lattice consisting of fixed points of the Kan adjunction induced by ϕ. For a small quantaloid Q, we investigate the Q-enriched version of this classical result, i.e., the regularity of Q-distributors versus the constructive complete distributivity (ccd) of Q-categories, and prove that “the dual of Kϕ is (ccd) ⇒ϕ is regular ⇒Kϕ is (ccd)” for any Q-distributor ϕ. Although the converse implications do not hold in general, in the case that Q is a commutative integral quantale, we show that these three statements are equivalent for any ϕ if and only if Q is a Girard quantale.
讲座人简介：
赖洪亮，四川大学数学学院教授。主要从事序、拓扑和范畴论相关领域的研究。主持国家自然科学基金3项，主要工作发表在Topology and its Applications, Theory and Applications of Categories, Journal of Pure and Applied Algebra, Fuzzy Sets and Systems等杂志上。
讲座题目2：On fuzzy differentiability of fuzzy-number-valued functions
讲座时间：10:00-11:00
讲座日期：2018-4-14
报告人：邱东 教授
讲座内容简介：
The importance of the derivative of a function in the study of analysis is well-known. For fuzzy functions, the Hukuhara difference and its generalized differences are used to define the differentiability. These generalized derivatives are motivated by their usefulness in a very quickly developing area at the intersection of set-valued analysis and fuzzy sets, namely, the area of fuzzy analysis and fuzzy differential equations. But in many applications they appear to have own imperfections and to be very restrictive.
In this talk, on the one hand, I will give an improved characterization for the g-derivative which is the most general of those existing generalized H-derivatives. On the other hand, I will define the differentiability from a totally new point of view. I also show connections to the ideas of generalized H-derivatives. Finally, some potential applications will be discussed.
讲座人简介：
邱东，教授，博士生导师，重庆邮电大学文峰高端省部级后备人才项目获得者，重庆邮电大学模糊数学与人工智能创新团队负责人。2009年博士毕业于电子科技大学应用数学专业。主要从事不确定性的数学理论及其在自然语言处理中的应用研究，研究工作主要集中在模糊分析理论和自然语言的语义分析研究。在FSS、INS、JMAA等国际学术期刊发表论文50余篇，其中SCI检索40余篇。主持和参与国家和省部级项目10余项。
讲座题目3：模糊系统的互模拟理论
讲座时间：11:00-12:00
讲座日期：2018-4-14
报告人：吴恒洋 博士
讲座内容简介：
迁移系统是描述系统行为的重要数学模型。互模拟是系统行为比较的科学方法和状态空间约简技术，也是并发系统和模态逻辑模型论的核心概念之一，它在并发系统的规范与验证中扮演重要角色。本报告重点阐述模糊迁移系统互模拟的基础理论。主要内容包括：（1）互模拟的背景介绍；（2）状态互模拟的概念、算法、余代数、以及逻辑刻画；（3）分布互模拟；（4）基于状态/分布的行为距离的概念、算法、以及逻辑刻画；（5）可进一步研究的问题。
讲座人简介：
吴恒洋，华东师范大学计算机科学与软件工程学院副教授。主要研究领域是形式化方法，包括形式语义学、Domain理论等。近年来，主要研究兴趣是模糊系统的互模拟理论。相关工作发表在IEEE Transitions on Fuzzy Systems, Information Sciences, Fuzzy Sets and Systems, Frontiers of Computer Science以及计算机学报等杂志上。
讲座题目4：On some open problems in domain theory
讲座时间：14:30-15:30
讲座日期：2018-4-14
报告人：奚小勇 博士
讲座内容简介：
In this talk, we will talk about some open problems in domain theory, which is the intersection between mathematics (especially topology) and theoretical computer science. Some problems are hard, some are relatively easy ones.
讲座人简介：
奚小勇，江苏师范大学副教授，四川大学博士。主要从事拓扑学与Domain理论的研究，发表论文20多篇，完全或部分解决了Domain理论领域内若干公开问题，如Amadio-Curien问题，Ho-Zhao问题等
讲座题目5：Diagonals between distance distributions
讲座时间：15:30-16:30
讲座日期：2018-4-14
报告人：申力立 博士
讲座内容简介：
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the quantaloid of diagonals between distance distributions, which is expected to establish the categorical foundation of probabilistic partial metric spaces. Observing that the quantale of distance distributions w.r.t. an arbitrary continuous t-norm is non-divisible, we precisely characterize diagonals between distance distributions, and prove that one-step functions are the only distance distributions on which the set of diagonals coincides with the generated down set.
讲座人简介：
申力立，2014年6月毕业于四川大学数学学院，获博士学位。2014年7月至2016年4月在加拿大约克大学从事博士后研究。现为四川大学数学学院副教授，主要研究方向为范畴论及其应用。个人主页：http://math.mickeylili.com/
讲座题目6：Weak algebraic information systems and a new equivalent category of DOM of domains
讲座时间：16:30-17:30
讲座日期：2018-4-14
报告人：何青玉 博士
讲座内容简介：
In this topic, concepts of generalized algebraic information system (in short, GA-inf) and weak algebraic information system (in short, wA-inf) are introduced. Relationships among several algebraicities of information systems are explored. Main results are:
(1) A dcpo D is an algebraic domain iff D is represented by an algebraic information system (in short, A-inf), and iff D is represented by a GA-inf;
(2) every A-inf is a GA-inf and a wA-inf;
(3) every C-inf S(D, B) induced by a domain with a basis B is a wA-inf;
(4) the category WAINF of wA-infs and approximable mappings is equivalent to the category DOM of domains and Scott continuous functions.
讲座人简介：
何青玉，扬州大学数学科学学院讲师。主要从事Domain理论与一般拓扑学的研究，主要工作发表在Topology and its Applications, Algebra Universalis, Order等杂志上。主持国家自然科学基金2项，江苏省自然科学基金1项。
讲座题目7：Some research progress on (L,M)-fuzzy convergence theory
讲座时间：9:15-10:15
讲座日期：2018-4-15
报告人：庞斌 博士
讲座内容简介：
With the development of fuzzy topology, various types of fuzzy convergence structures have been investigated in different frameworks of fuzzy topological spaces. In this talk, we mainly focus on three types of fuzzy convergence structures in the framework of (L,M)-fuzzy topological spaces, including stratified (L,M)-fuzzy Q-convergence structures, enriched (L,M)-fuzzy convergence structures and stratified (L,M)-ordered convergence structures. Generally, we call them (L,M)-fuzzy convergence structures. Concretely, we will study their Cartesian-closedness and their categorical relations with stratified (L,M)-fuzzy topological spaces.
讲座人简介：
庞斌，北京理工大学数学与统计学院副研究员。2015年6月，在北京理工大学获得博士学位。2015年7月至 2017年8月在哈尔滨工业大学从事博士后研究。主要研究方向为模糊拓扑学与模糊凸空间理论。主持1项国家自然科学基金，1项博士后基金和1项广东省自然科学基金。主要工作发表在Fuzzy Sets and Systems, IEEE Transactions on Fuzzy Systems, Journal of Intelligent and Fuzzy Systems, Iranian Journal of Fuzzy Systems等杂志上。
讲座题目8：Aggregation Functions: Uninorms
讲座时间：10:15-11:15
讲座日期：2018-4-15
报告人：苏勇 博士
讲座内容简介：
This report is a brief survey on uninorms as a mixed aggregation functions. Firstly, research backgrounds concerning uninroms are presented. Then, present research situations on the characterizations of several most studied classes of uninorms are given. Finally, present research situations on equations involving uninorms, including distributivity equations, migrativity equations and modularity equations are stated.
讲座人简介：
苏勇，江南大学理学院副教授。主要从事模糊系统算子与函数方程的研究。主要工作发表在IEEE Transactions on Fuzzy Systems, Fuzzy Sets and Systems, Information Sciences, International Journal of Approximate Reasoning等杂志上。
