To promote interdisciplinary interaction between different faculty members and students on the campus, a weekly meeting has been organized by our postdoc Yinlin Guan since September 2020, called Tsing Ch’a Sessions (清茶会). Its slogan “know thyself and let others know you better.”
■Schedule for 2021-2022 Spring Semester
|2022 Feb 24||Zhenkun Hu 胡振坤 (Tsinghua University)|
|2022 Mar 03||Mingliang Chu 储明亮 (Tsinghua University)|
|2022 Mar 10||Qian Chen 陈谦 (Tsinghua University)|
|2022 Mar 17||Penghao Du 杜鹏昊 (Tsinghua University)|
|2022 Mar 24||Qingyu He 何清瑜 (Tsinghua University)|
|2022 Mar 31||Yuqi Liu 刘雨琦 (Tsinghua University)|
|2022 Apr 07||Fengxiang Cheng 成凤祥 (Tsinghua University)|
|2022 Apr 14||Lingyuan Ye 叶凌远 (Tsinghua University)|
|2022 May 12||Haoxuan Yin 尹昊萱 (Tsinghua University)|
|2022 May 19||Haotian Tong 童昊天 (Tsinghua University)|
|2022 May 26||Dazhu Li 李大柱 (Chinese Academy of Science)|
|2022 Jun 02||Chenwei Shi 石辰威 (Tsinghua University)|
|2022 Jun 09||Yinlin Guan 管银霖 (Tsinghua University)|
|2022 Jun 16||Kaibo Xie 谢凯博 (Tsinghua University)|
2022 May 26 14:00-15:30 Dazhu Li 李大柱 (Chinese Academy of Science): A Logical Analysis of Dynamic Dependence ntuitionistic Logic
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. In this talk, we study temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic. The talk is based on recent joint work with Alexandru Baltag and Johan van Benthem.
2022 May 19 14:00-15:30 Haotian Tong 童昊天 (Tsinghua University): Carnap’s Problem in Intuitionistic Logic
Carnap’s problem asks whether we can uniquely fix the semantics from a given consequence relation via a reversed Tarski-Bolzano function. Here we introduce and formulate this problem and quickly recapitulate the results in propositional and first-order logic. Then we briefly review the Hilbert system and Kripke semantics of intuitionistic propositional logic (IPC) and some intermediate logics (ICs) and formalize Carnap’s problem in IPC. Finally, we show much of IPC to be categorical, that is, fixed by the appropriate syntactic rules. However, implication remains elusive, so we show preliminary attempts at fixing it, including a limiting principle and the result in a logic above IPC, i.e., Dummett logic (LC).
2022 May 12 14:00-15:30 Haoxuan Yin 尹昊萱 (Tsinghua University): A New Proof Method for Lyndon’s Theorem in Variations of First-Order Logic
Lyndon’s homomorphism theorem shows the equivalence between the semantic notion of monotonicity and the syntactic notion of positive occurrence. Existing proof methods either take a detour from Lyndon’s interpolation theorem, or involve complicated model constructions. In this talk, we will give a new proof method that greatly simplifies the process of model construction. In some variations of first-order logic e.g. monadic first-order logic with the infinity quantifier, a sentence upward monotonic in P is equivalent to a P-positive sentence of the same depth. Therefore, we only need to consider sentences up to a certain level of distinguishability, and have a more relaxed requirement on the models that we construct. We will show our successful attempts in monadic first-order logic with the infinity quantifier and modal logic, and analyze the difficulty we face in their combination i.e. graded modal logic.
2022 Apr 14 14:00-15:30 Lingyuan Ye 叶凌远 (Tsinghua University): Towards a Unification of Semantics of Modal Logic
In this talk, I’ll introduce a new framework to provide a unifying description of different types of semantics for modal logic found in the literature and discuss their relations, using the language of topological categories. Common structures of this type include relational ones like Kripke frames, preorders, equivalence relations, etc., topological spaces, neighbourhood frames, or various other algebraic models.
From a philosophical perspective, the project can be viewed as giving a precise description of the “landscape of information”, if we identify different types of semantic models of modal logic as different ways of representing information structure. Our framework would provide a solid mathematical language to study the interplay between different information structures.
Form a technical perspective, we will provide a detailed study of the correspondence between the syntactical structure of (various extensions of) the modal language on one hand, and semantic structures of topological categories on the other hand, just like the way categorical logic does for first-order and higher-order theories. This is will allow us to obtain a conceptual understanding of the abstract structure of modal logic.
2022 Apr 07 14:00-15:30 Fengxiang Cheng 成凤祥 (Tsinghua University): The Problem of Logical Omniscience
In the paper ‘The Problem of Logical Omniscience, written by Robert C. Stalnaker, the author first defends the deductive omniscience of an agent as a kind of idealization and explains why we need it. This work aims to clarify what the problem of logical omniscience is, which is discussed from the perspective of the sentence storage model and the question-answer machine respectively. In my presentation, I will introduce four different motivations of idealization and illustrate how the author attributes this problem to the concepts of knowledge and belief.
2022 Mar 31 14:00-15:30 Yuqi Liu 刘雨琦 (Tsinghua University): Formalizing Explanatory Dialogues
In the paper ‘Formalizing Explanatory Dialogues’ written by Abdallah Arioua and Madalina Croitoru, the authors develop an argumentation framework based on Walton’s CE system on explanatory dialogue. They define the explanation in a goal-directed dialogue system governed by a set of rules. My presentation is to introduce the two main concerns in their work: the commitment stores in the dialogue and dialectical shifts. The former guarantees the success of an explanatory dialogue and the latter aims at incorporating the explanation into a wider range of different dialogues.
Ref. Arioua, M. Croitoru, Formalizing explanatory dialogues, in: International Conference on Scalable Uncertainty Management, Springer, 2015, pp. 282–297.
2022 Mar 24 14:00-15:30 Qingyu He 何清瑜 (Tsinghua University): A Topological Perspective on Causal Inference
In the paper ‘A Topological Perspective on Causal Inference’ written by Duligur Ibeling and Thomas Icard, the authors put forward a general framework for topologizing spaces of causal models and characterized levels of the causal hierarchy topologically as an illustration. This work demonstrates that topologizing causal models helps clarify the scope and limits of causal inference under different assumptions. Since causal inference is the central issue for causality, I will focus on the technical results of causal inference. The proof of topological causal hierarchy theorem and some advantages of the framework will also be showed in this presentation.
2022 Mar 17 14:00-15:30 Penghao Du 杜鹏昊 (Tsinghua University): An introduction of the paper ‘The Logic of Public Announcements, Common Knowledge, and Private Suspicions’
In the paper ‘The Logic of Public Announcements, Common Knowledge, and Private Suspicions’ by Alexandru Baltag, Lawrence S. Moss, and Slawomir Solecki, the authors put forward a new logical system that extends the epistemic logic with dynamic modalities of actions. This system is further extended with a notion of common knowledge. In my presentation, I will introduce various types of actions, such as public announcements, announcements to groups privately, announcements with suspicious outsiders, etc. I will illustrate their difference with a few examples. Finally, I will show some technical results from the paper.
2022 Mar 10 14:00-15:30 Qian Chen 陈谦 (Tsinghua University): Modal Language and Bounded Fragments of Predicate Logic
This is a work where guarded fragment was first introduced. The aim of this work is to find natural fragments of predicate logic extending the modal one which inherit nice properties such as finite axiomatizability, Beth definability and decidability. The so-called guarded fragment enjoys nice properties.
2022 Mar 03 14:00-15:30 Mingliang Chu 储明亮 (Tsinghua University): 斯佩德对中世纪指代理论中“上升”和“下降”问题的研究
保罗·文森特·斯佩德（Paul Vincent Spade）在‘The Logic of Categorical: The Medieval Theory of Descent and Ascent’ 一文中基于 T. K. Scott（1966）对十四世纪早期指代理论的划分，着重就第二种划分，即指代模式原则 (‘the doctrine of modes of supposition’)，给出了语义解释，语法定义，以及相应的推理规则，并就“指代模式原则”所适用的句型做了一系列规定，同时借助现代逻辑已有的结果，论证了指代模式原则中包含的三个内定理。由此进一步得出，Burley，Ockham 和 Buridan 这三位在十四世纪极具影响力的逻辑学家对于指代模式原则的语法定义本质上是一致的。
2022 Feb 24 14:00-15:30 Zhenkun Hu 胡振坤 (Tsinghua University): 瓦格纳对“夫”在中国古代论证性文本中作用的研究
著名汉学家瓦格纳(Rudolf G. Wagner)在《A Building Block of Chinese Argumentation: Initial Fu夫 as a Phrase Status Marker》一文指出，中国古代的分析和论证性文本中，各种修辞可以用来标记语句的身份地位，如果缺失对这方面问题的研究，我们便无法准确理解中国古代的论证。与其他语言相比，文言文中作为身份地位标记的词汇在关于论证的研究中长期被忽视。瓦格纳认为，“夫”这个词是古代哲学文本中重要的语句身份标记，他从魏晋玄学文本尤其是王弼对《周易》《老子》的注释中寻找“夫”的规范性意义。他的研究分为两个步骤，第一步是用定性和定量方法研究历史文本中业已形成的关于句首之“夫”用法的普遍意义，第二步是试图刻画出“夫”的意义、使用在历史中的发展脉络和时间线索。
Click HERE to check the past sessions.