The Delta Logic Workshops aim to bring logicians from Mathematics, Philosophy, and Computer Science together. The Delta 16 Logic Workshop will hold at Sichuan University.
Delta_16 Logic Workshop
会议议程
2021年10月30日 星期六
会议地点：祥宇宾馆16楼会议室
线上会议：腾讯会议ID：582 679 472 密码：123456
第一场 9:10~10:50
主题：模糊逻辑
主持人：何家亮
发言人：2位
1.张德学（四川大学）：9:10~10:00
报告题目：Quantitative domain theory and many-valued logic
摘要：In this talk we present a brief introduction to quantitative domain theory and its connection with many-valued logic. With the Scott isomorphism between injective T0 spaces and continuous lattices as an example, we show that in the enriched context, validity of some mathematical statements may depend on the structure of truth values.
2.周红军（陕西师范大学）：10:00~10:50（线上）
报告题目：Overview on the centenary development and some new trends of mathematical fuzzy logics
摘要：In this talk we will provide first a short overview on the centenary developments of mathematical fuzzy logics from several perspectives including three development stages, three research levels, three axiomatic methods and three logical languages. As seen from the overview, mathematical fuzzy logics have gained substantial achievements, but most fuzzy logical systems are established based on the law of residuation (x Ä y £ z if and only if x £ y→ z, LR for short) between fuzzy conjunctions and fuzzy implications. The law of importation (LI, for short) x→(y→ z)=(x Ä y)→ z, which is much more general than (LR), is a new hot and difficult topic in mathematical fuzzy logics in recent decade. In the second part of this talk we will provide a survey on recent functional solving of (LI), where we will elaborate on the Massanet-Torrens’s (N, U)-implication solutions and two types of generator generated implication solutions proposed recently by the speaker. As an application of (LI), we will propose two new kinds of triple I methods based on our generator generated implications and associated t-norms to solve the generalized modus ponens problem in approximate reasoning. Finally, we will outline some further studies on this topic including the algebraic structures of importation algebras which can serve as an algebraic axiomatization of (LI).
茶歇，与会代表合影 10:50~11:20
第二场 11:20~12:10
主题：计算机
主持人：彭伟光
发言人：1位
刘江（中国科学院重庆智能绿色研究院）
1.报告题目：神经网络中的计算性能问题
摘要：从上个世纪60年代人工智能诞生以来，已经在工程应用领域取得了巨大成功。但是，到目前为止有两个基本问题困扰这个领域：第一，什么叫人工智能，它的形式化定义是什么？在数学中，希尔伯特曾经提出数学形式化并企图通过数学机械推理建立数学王国。这个雄心首先被哥德尔通过它的两个不完全性定理否定，后来又被图灵再次使用图灵机计算模型否定。这两个工作促成了递归论的诞生，同时表明基本概念的形式化定义对确立清晰研究对象以及严谨研究的至关重要性。神经网络是目前人工智能领域的一个通用模型，我们研究了神经网络模型中的激活函数对模型计算性能的影响，发现在不同激活函数下单个神经元的计算力——特别是逻辑问题的计算性能，表现出巨大差异。本报告抛砖引玉，讨论人工智能的形式化定义与神经网络计算性能，该报告提出更甚于解决问题，希望这些问题能引起逻辑学家对人工智能理论的兴趣，从根本上解决人工智能面临的瓶颈、促进人工智能与逻辑学交叉融合与发展。
午餐 12:20~14:00
第三场 14:10~15:50
主题：哲学逻辑
主持人：刘佶鑫
发言人：2位
1.徐召清（四川大学）：14:10~15:00
报告题目：知识限度的逻辑分析
摘要：知识限度中最有趣的现象是，有些真命题是不可知的。费奇有一个非常著名的论证表明：只要存在未知的真理，那就存在不可知的真理。这个论证常被称为“可知性
悖论”，但分析表明，费奇的论证在经典的模态认知逻辑中是可以辩护的。给定断言的知识规范，不可知的真理可以用来解释摩尔悖论、知识的封闭原则的反例以及知道者悖论等不可说的问题。将不可知性推广到相对的不可知性，不仅可以说明怀疑论问题中的困难，还可以对独断论悖论给出一种新的解释。知识限度的存在具有丰富的认识论价值，还有很多不可知的真理类型等待我们去探索。
2.石辰威（清华大学）：15:00~15:50（线上）
报告题目：论证（argumentation）、信念与知识的拓扑语义与逻辑
摘要：知识、信念与确证（justification）之间的关系一直是当代认识论的核心问题。认识逻辑（epistemic logic）中知识与信念的克里普克语义虽然简洁而有效，但是并没有直接将确证这一概念纳入对知识与信念的理解。逻辑学家们为了刻画确证概念还有它和知识与信念之间的关系已经做出了许多尝试。在本次报告中，我将介绍一种基于拓扑语义的尝试并以此为基础结合形式论证理论提出一个新的语义框架为分析理解确证、信念与知识这三个概念和它们之间的关系提供新的视角。
茶歇 15:50~16:10
第四场 16:10~17:50
主题：数理逻辑
主持人：喻良
发言人：2位
1.彭程（河北工业大学） ：16:10~17:00（线上）
报告题目：Title: Essential complexity of metrizable spaces
摘要：Let \Gamma be a class of subsets in all metrizable spaces and \Gamma(X) the collection of subsets of a metrizable space X in \Gamma. A metrizable space X is called essential \Gamma if f(X)\in\Gamma(Y) for any metrizable space Y and homeomorphism embedding f : X \rightarrow Y. In this report, we investigate the essential complexity of various classes, we also introduce the concept of \alpha-locally compact and study its essential complexity. This is joint work with Longyun Ding and Jiaming Li.
2. 姚宁远（复旦大学）：17:00~17:50
报告题目：On non-compact p-adic definable groups
摘要：Peterzil and Steinhorn proved in 2008 that if a group G definable in an o-minimal structure is not definably compact, then G contains a definable torsion-free subgroup of dimension one. In this talk, we will give a p-adic analogue of the Peterzil-Steinhorn theorem, in the special case of abelian groups. Let G be an abelian group definable in a p-adically closed field M. We will show that if G is not definably compact then there is a definable subgroup H of dimension one which is not definably compact. I will also discuss the strategies on how to classify the p-adic definable abelian groups based on this result. (Joint work with Will Johnson)
17:50~18:00 会议总结、闭幕
