Initiated by the center’s students and researchers in 2019, the Tsinghua Logic Salon has quickly grown into a lively platform for try-outs and exchanges of new ideas. Researchers in various fields of logic are invited to present their latest research, as well as the challenges that they see. Every participant is encouraged to engage in discussions and exchange of perspectives. Each session lasts for 2 hours in total, with 30 minutes of discussion included.
2021-12-17 15:30-17:30 申国桢 武汉大学
An application of lattice theory to non-well-ordered cardinals
Using a special kind of Birkhoff lattices, we construct a permutation model in which there exists a finite-to-one function from the symmetric group of an infinite set A onto A, which cannot exist even in the presence of the axiom of countable choice. This is a joint work with Jiachen Yuan.
2021-12-30 19:00-21:00 廖备水 浙江大学
2021-12-09 20:00-22:00 Johan van Benthem 阿姆斯特丹大学/斯坦福大学/清华大学
Interleaving Logic and Counting (Joint work with Thomas Icard)
Reasoning with generalized quantifiers in natural language combines logical and arithmetical features, transcending divides between qualitative and quantitative. This practice blends with inference patterns in ‘grassroots mathematics’ such as pigeon-hole principles. Our topic is this cooperation of logic and counting, studied with small systems and gradually moving upward. We start with monadic first-order logic with counting. We provide normal forms that allow for axiomatization, determine which arithmetical notions are definable, and conversely, discuss which logical notions and reasoning principles can be defined out of arithmetical ones. Next we study a series of strengthenings in the same style, including second-order versions, systems with multiple counting, and a new modal logic with counting. As a complement to our fragment approach, we also discuss another way of controlling complexity: changing the semantics of counting to reason about ‘mass’ or other aggregating notions than cardinalities. Finally, we return to natural language, confronting our formal systems with linguistic quantifier vocabulary, monotonicity reasoning, and procedural semantics via semantic automata. We conclude with some pointers to further entanglements of logic and counting in formal systems, in philosophy of logic, and in cognitive psychology.
Paper available at: https://eprints.illc.uva.nl/id/eprint/1813/1/Logic.Counting.pdf
2021-11-27 Thomas Icard 斯坦福大学
Associate Professor of Philosophy and (by courtesy) of Computer Science. Affiliated Faculty, Stanford Artificial Intelligence Laboratory.
Applications of Logic to Causal AI
Much of causality and causal inference can be understood profitably through the lens of modern logic. In this talk we present two applications of this study to artificial intelligence. The first concerns the theoretical and empirical limitations of causal inference from observational and experimental data. The second involves the use of causal-logical tools to derive abstract and human-interpretable analyses of opaque AI systems trained with large, complex data. The broader aim of the talk will be to illustrate the potential for symbiosis between theoretical work in logic and practical work in AI.
2021-11-18 Yifeng Di 北京大学
Propositional Quantifiers and Doxastic Logic
We discuss several questions regarding doxastic logic with propositional quantifiers. First, suppose we take the normal modal logic KD45 as the starting point of the logic of belief, with propositional quantifiers, what logics are available to us, and can we show completeness with respect to some established semantics for belief? To this end, we identify two key principles: the immodesty principle (I believe that everything I believe is true), and the quantificational introspection principle (if no matter what p is, I believe in phi, then I believe that no matter what p is, I believe in phi). We show that, on the one hand, to invalidate the immodesty principle, we need to deviate from the standard possible world semantics, and on the other hand, it is very hard to avoid the quantificational introspection principle since every complete modal algebra validating KD45 also validates it, though it is not derivable in KD45 with the usual axioms for propositional quantifiers. We will also touch on the issue of belief as credence 1. Then, time permitting, we shall consider deviations even from KD45. We will show how rejecting immodesty also puts pressure on introspection (in particular negative introspection) and discuss logical issues specifically with propositional quantifiers coming out of rejecting introspection.
2021-11-11 Asher Jiang 清华大学
Truthmaking Cannot be Done Afar
As concerns the explication of the intuitive notion of truthmaking, Barry Smith has an insight that deserves more attention. Basically, in his view, an object x makes a proposition <p> true iff (α) x necessitates <p> and (β) <p> is representationally closely tied with x. To be more specific, he suggests that (β) is fulfilled only if x is among <p>’s ontological commitments. I appreciate his basic insight but reject his specific suggestion. I argue that we can make a more attractive proposal from his basic insight if we take into consideration that the close tie can also be realized by <p>’s being about x.
2021-11-04 Thomas Studer 伯尔尼大学
Justification Logic – Introduction and Recent Developments
Justification logics are closely related to modal logics and can be viewed as a refinement of the latter with machinery for justification manipulation. Justifications are represented directly in the language by terms, which can be interpreted as formal proofs in a deductive system, evidence for knowledge, and so on. This more expressive language proved beneficial in both proof theory and epistemology and helped investigate problems ranging from a classical provability semantics for intuitionistic logic to the logical omniscience problem.
In this talk, we will give an introduction to justification logic and present recent developments in the field such as subset models, conflict tolerant logics, and formalizations of zero-knowledge proofs.
2021-10-28 Jan Broersen 乌特勒支大学
Jan Broersen is professor of logical methods in Artificial Intelligence (AI). With a background in mathematics, logic and computer science he studies AI from a humanities perspective. His main interests are responsible AI, knowledge representation and reasoning, and logic theories of agency.
What are suitable logic models of general ability?
I will consider different alternatives for giving logic models of ability. First I will explain the difference between possibilities for action and (general) abilities. Then I will focus on the role of knowledge and knowing how in understanding and modelling ability. The importance of modeling these concepts is motivated by discussing their application in symbolic and responsible AI.
2021 Oct 21 端木昊随 哈尔滨工业大学
Applications of Nonstandard Analysis to Probability, Statistics and Economics
Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in various areas of mathematics such as probability theory, stochastic processes, mathematical physics, functional analysis, and mathematical economics. Nonstandard analysis allows construction of a single object a hyperfinite probability space which satisfies all the first-order logical properties of a finite probability space, but which can be simultaneously viewed as a measure-theoretical probability space via the Loeb construction. As a consequence, the hyperfinite/measure duality has proven to be particularly in porting discrete results into their continuous settings. We present several applications of this novel approach:
(1) Extending known results for discrete Markov processes to analogues results for general Markov processes (e.g., ergodicity of Markov processes, mixing and hitting times of Markov processes);
(2) Establishing tight connections between frequentist optimality and Bayes optimality for general statistical decision problems;
(3) Existence of Walrasian equilibrium for exchange/production economy models
that are specific to climate change.
2021 Oct 14 Malvin Gattinger 阿姆斯特丹大学
Assistant professor at ILLC in Amsterdam. Personal Website: https://malv.in
Symbolic and succinct perspective shifts for faster epistemic planning
Dynamic Epistemic Logic can be used for Epistemic Planning, as shown in several recent works, ranging from theoretical proposals to actual implementations on robots. A crucial part of automated epistemic planning is to compute perspective shifts that let agents take into account the knowledge of others. So far, these perspective shifts are usually done using explicit Kripke models which may grow exponentially in the number of agents or propositions. I will discuss methods to tackle this state-explosion problem and show how to compute perspective shifts without explicit Kripke models. The two methods I will present are based on symbolic structures and succinct models. Both are compact representations from previous literature showing how to speed up model checking DEL. The new definitions aim to make epistemic planning more efficient in the future. Most of the talk will be based on the article available here: (https://malv.in/2020/EpiP-perspective-shifts.pdf) Time permitting, I will also present related software recently developed by my students and myself.
2021 Oct 7, Mingming Liu (Tsinghua University):
刘明明，清华大学外文系助理教授。研究方向为形式语义学与语用学, 研究兴趣包括汉语的焦点副词, 量化, 疑问词及其非疑问用法, 信息结构等。
传统分析认为“都”表示“总括”（吕叔湘，1980）。我们发现[复数性名词成分+“都”]中“都”是否出现受语境制约。大致说来，当复数性名词成分所在的句子没有独立完整回答语境中的问题时，“都”最好不出现；反之，“都”通常需要出现。从“都”的这一语境适用条件出发，我们提出“都”总括的是语境中的话题/问题（Roberts 1996）；“总括”说的是，“都”表达了与之结合的句子包括了当前话题下的所有内容，因而具有“排除谈话中其他人或事物”(陆庆和，2006)的功能。同时，为了满足“总括”，跟“都”结合的句子必须取分配解读，这造成了“都”的“分配效应”。我们认为，这种解释可以让我们对“都”的“总括义”，“甚至义”和“反预期”效果有统一的认识。更进一步，我们提出“都”的“总括义”是一个预设，这使我们可以通过“强制性预设”现象来解释“都”为什么在某些环境下必须出现（Liu 2021）。最后，本次报告将探讨如何将我们的分析推广至“都”与其他名词成分搭配的情况，以及解释“都，就”为何经常出现在无条件句与条件句的后件中。
2021 Sep 30, Online, Olivier Roy (University of Bayreuth):
I am Professor of Philosophy and joined the Department at the start of the Winter Semester 2013-14. I am also external member of the Munich Center for Mathematical Philosophy, where I worked for two years as assistant professor. Before that I worked at the Rijksuniversiteit Groningen in the Faculty of Philosophy. I have completed my PhD in February 2008 at the Institute for Logic, Language and Computation in Amsterdam, under the supervision of Johan van Benthem (Amsterdam and Stanford) and Martin van Hees (Groningen). I am associate editor of Topoi, Theory and Decision Library Series A, and Section Editor for the “Logic, Computation and Agency” Section of the Stanford Encyclopedia of Philosophy (the latter together with Eric Pacuit and Johan van Benthem). From 2011 to 2020 I have also been associate editor of Erkenntnis.
Epistemic Rights in the Theory of Normative Positions.
For a long time now, deontic logicians have studied the typology of legal rights that Wesley Hohfeld proposed at the beginning of the 20th century. This has become known as the theory of normative positions. However, one prominent type of legal rights, so-called epistemic rights, has not yet been systematically studied in the hohfeldian typology. In this talk, I will present recent and ongoing work with Réka Markovich (Luxembourg) in which we take the first steps towards filling this gap. I will consider two prominent epistemic rights, the right to know and freedom of thought, and one application of the resulting theory to a recent example in US law.
2021 Sep 23, Zhuanghu Liu (Peking University):
Events in 2021-2022 Autumn Semester
2021-11-11 蒋运鹏 清华大学
2021-11-18 丁一峰 北京大学
2021-11-27(Sat. 11:00) Thomas Icard 斯坦福大学
2021-12-02 Hirohiko Kushida 纽约市立大学
2021-12-09 Johan van Benthem 斯坦福大学
2021-12-17(Fri. 19:00) 廖备水 浙江大学
2021-12-23 王禹皓 清华大学
2021-12-30 申国桢 武汉大学
2021 Jun 10, Lingyuan Ye (Tsinghua University): Uniformity, Contingency, and Self-reference in Arithmetic; Xiao Li (Tsinghua University): Towards a Semantic Concept of Aboutness
2021 May 20, Lian Zhou (Tsinghua University): Co-reference Without Referent
2021 May 13, Qingbian Ma (Peking University): Decision Making in the Emergency Room
2021 Apr 29, Qi Feng (Chinese Academy of Sciences): Cantor and Set Theory
2021 Apr 22, Jialong Zhang (Chinese Academy of Social Sciences): Bertrand Russell and Mathematical Logic
2020 Dec 25, Duoyi Fei (China University of Political Science and Law): A Defense for the State of Internal Knowledge
2020 Dec 4, Changsheng Lai (Shanghai Jiaotong University): Epistemic Gradualism and the Gradability of Truth
2020 Dec 11, Kang Liu (Chinese Academy of Sciences): From Vectors to Symbols.
2020 Nov 12, Thomas Bolander and Lasse Dissing (Technical University of Denmark): Implementing Theory of Mind on a Robot Using Dynamic Epistemic Logic. Online
2020 Nov 6, Zhisheng Huang (Vrije University of Amsterdam): Application of Logic in Data Mining
2020 Jan 8, Fengkui Ju (Beijing Normal University): Towards a Logical Theory of Temporal Conditionals; Xinwen Liu (Chinese Academy of Social Sciences): Jin Yuelin’s Encounter with C.P. Peirce
2019 Nov 28, Shengyang Zhong (Peking University): On Quantum Logic
2019 Nov 14, Martin Stokhof (University of Amsterdam): Natural Language, Formal Language: a Complex Relationship
2019 Oct 23, Dazhu Li (UvA and Tsinghua) : Dynamic Epistemic Logic of Social Influence; Kaibo Xie (UvA and Tsinghua) : Formal Semantics for Counterfactuals
2019 Oct 10, Frank Veltman (University of Amsterdam): On Imperatives in Natural Language.