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 1.5 hours in total, with 30 minutes of discussion included.
■Schedule for 2021-2022 Spring Semester
|2022 Feb 24||Chong Chi Tat 庄志达 (National University of Singapore)|
|2022 Mar 03||Zhiguang Zhao 赵之光 (Taishan University)|
|2022 Mar 10||Zhen Liang 梁真 (Guizhou University)|
|2022 Mar 17||Wei Wang 王巍 (Tsinghua University)|
|2022 Mar 24||Hu Liu 刘虎 (Sun Yat-sen University)|
|2022 Mar 31||Jouko Väänänen (University of Helsinki)|
|2022 Apr 07||Yuhao Wang 王禹皓 (Tsinghua University)|
|2022 Apr 14||Valentin Goranko (Stockholm University)|
|2022 Apr 29||Alexandru Baltag (University of Amsterdam)|
|2022 May 07||Adam Bjorndahl (Carnegie Mellon University)|
|2022 May 26||Dag Westerståhl (Stockholm University)|
2022 May 26 16.00-17:30 Dag Westerståhl (Stockholm University) Updates on Carnap’s Problem
Carnap’s Problem, or Carnap’s Question, as Denis Bonnay and I understand it, is to what extent a consequence relation in some logical language fixes the meaning of the logical constants in that language. This can be seen as relevant to the issue of what ‘logical’ means. Also, it seems that people can have fairly robust intuitions about ‘what follows from what’ without having clear ideas about logicality, so it is of some interest to see if and how the former determines the latter. I will give an overview of what has been achieved in this area so far, concerning classical first-order logic, logics with generalized quantifiers, modal logic, and some partial results for intuitionistic propositional logic (the latter is joint work with Haotian Tong). I end by briefly discussing how this approach fares in comparison to other ideas about logicality.
2022 May 07 09:30-11:00 Adam Bjorndahl (Carnegie Mellon University) Knowledge Second
Classical philosophical analyses seek to explain knowledge as deriving from more basic notions. The influential “knowledge first” program in epistemology reverses this tradition, taking knowledge as its starting point. From the perspective of epistemic logic, however, this is not so much a reversal as it is the default—the field arguably begins with the specialization of “necessity” to “epistemic necessity”; that is, it begins with knowledge. In this context, putting knowledge second would be the reversal. This work motivates, develops, and explores such a “knowledge second” approach in epistemic logic, founded on distinguishing what a body of evidence actually entails from what it is (merely) believed to entail. We import a logical framework that captures exactly this distinction, use it to define formal notions of (internal and external) justification, and investigate applications to the KK principle, the regress problem, and the definition of knowledge.
2022 Apr 29 18:30-20:00 Alexandru Baltag (University of Amsterdam): The Topology of Surprise
I present a topological epistemic logic, motivated by a famous epistemic puzzle: the Surprise Exam Paradox. It is a modal logic, with modalities for knowledge (modelled as the universal modality) and knowability of a proposition (represented by the topological interior operator), and (un)knowability of the actual world. The last notion has a non-self-referential reading (modelled by Cantor derivative: the set of limit points of a given set) and a self-referential one (modelled by Cantor’s perfect core of a given set: its largest subset without isolated points). I completely axiomatize this logic, showing that it is decidable and PSPACE-complete. I point its connections to my older joint work on topological mu-calculus, and finally I apply it to the analysis of the Surprise Exam Paradox (in both its non-self-referential and its self-referential versions). This talk is based on recent joint work with Nick Bezhanishvili and David Fernandez-Duque.
Baltag, A.; Bezhanishvili, N.; and Fern´andez-Duque, D. 2022. The topology of surprise. Accepted for presentation at the KR workshop, affiliated with LICS 37. To appear in the KR Proceedings.
Baltag, A.; Bezhanishvili, N.; and Fern´andez-Duque, D. 2021. The topological mu-calculus: completeness and decidability. In Proceedings. of LICS 36, 1–13. IEEE Press.
2022 Apr 14 16:00-17:30 Valentin Goranko (Stockholm University): Logic-based Strategic Reasoning in Social Context
Reasoning in social context has many important aspects, one of which is the reasoning about strategic abilities of individuals (agents) and groups (coalitions) of individuals to guarantee the achievement of their desired objectives while acting within the entire society. Several logical systems have been proposed for formalising and capturing such reasoning, starting with the Coalition Logic (CL), the Alternating Time Temporal Logic (ATL) and some extensions of these, introduced the early 2000s.
Coalition Logic provides a natural, but rather restricted perspective: the agents in the proponent coalition are viewed as acting in full cooperation with each other but in complete opposition to all agents outside of the coalition, which are thus treated as adversaries. The Alternating Time Temporal Logic extends Coalition Logic with temporal operators allowing for expressing long-term temporised goals.
The strategic interaction in real life is much more complex, usually involving various patterns combining cooperation and competition. To capture these, more expressive and versatile logical frameworks are needed.
In this talk I will first present briefly Coalition Logic and then will introduce and discuss some more expressive and versatile logical systems, including: (i) the Socially Friendly Coalition Logic (SFCL), enabling formal reasoning about strategic abilities of individuals and groups to ensure achievement of their private goals while allowing for cooperation with the entire society; (ii) the complementary, Group Protecting Coalition Logic (GPCL), capturing reasoning about strategic abilities of the entire society to cooperate in order to ensure achievement of the societal goals, while simultaneously protecting the abilities of individuals and groups within the society to achieve their individual and group goals.
Finally, time permitting, I will discuss briefly conditional strategic reasoning, where agents reason about their strategic abilities conditional on the actions that they expect the other agents to take.
In conclusion, I will take a more general perspective on a unifying logic-based framework for strategic reasoning in social context.
2022 Apr 07 16:00-17:30 Yuhao Wang 王禹皓 (Tsinghua University): Long-term Causal Inference Under Persistent Confounding via Data Combination
We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since the long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.
2022 Mar 31 16:00-17:30 Jouko Väänänen (University of Helsinki): Dependence logic: Some recent developments
In the traditional so-called Tarski’s Truth Definition the semantics of first order logic is defined with respect to an assignment of values to the free variables. A richer family of semantic concepts can be modelled if semantics is defined with respect to a set (a “team”) of such assignments. This is called team semantics. Examples of semantic concepts available in team semantics but not in traditional Tarskian semantics are the concepts of dependence and independence. Dependence logic is an extension of first-order logic based on team semantics. It has emerged that teams appear naturally in several areas of sciences and humanities, which has made it possible to apply dependence logic and its variants to these areas. In my talk I will give a quick introduction to the basic ideas of team semantics and dependence logic as well as an overview of some new developments, such as quantitative analysis of team properties, a framework for a multiverse approach to set theory, and probabilistic independence logic inspired by the foundations of quantum mechanics.
2022 Mar 24 16:00-17:30 Hu Liu 刘虎 (Sun Yat-sen University): A Formal Theory of Public Opinion
Public opinion is a common yet complex phenomenon. We present a formal theory of public opinion for a rigorous platform for the topic, in which opinions are represented by logical formulas. The method of norm forms is used to simplify the problem. We present various aggregation conditions and aggregation functions. We study in detail a specific function. It reflects a common usage that public opinions are the most popular opinions among the public. We prove a characterization theorem for this kind of public opinions, saying that it is the only one that satisfies six fairness conditions.
2022 Mar 17 14:00-15:30 Wei Wang 王巍 (Tsinghua University): 科学定律与因果性
近代来在科学哲学中，因果性已取代定律成为显学。笔者试图论证：James Woodward 的不变性要求太弱，可能有自相矛盾或琐碎无聊的不变性；模态性要求太强，可能出现实际上不太合理的因果关系；定律中所包含的深层次概念，可能无法从因果图中导出；特殊科学实际上很难进行有效操控，数理传统可能比实验传统发挥更大的作用。笔者建议，科学定律与因果性可以有效互补，定律“大处着眼”，因果性“小处着手”。
2022 Mar 10 16:00-17:00 Zhen Liang 梁真 (Guizhou University): Towards Axiomatisation of Social Epistemic Logic
This is a theoretical development of epistemic logic to problems concerning the relationship between perception and knowledge. We closely follow the approach of Seligman, Liu and Girard’s “Logic in the Community” which proposes a two-dimensional multi-agent epistemic logic, in which the model operator K (knows) is supplemented with a ‘social’ operators which allow reasoning about relations between agents. The logic also uses operators from hybrid logic, such as nominals n, which name agents, the perspective shifting operator @n, which moves to agent n’s perspective, and the downarrow operator ↓x, which names the current agent a rigid name x. We propose an axiomatisation and completeness proof, using the step-by-step method, first for the basic logic and then for the case of downarrow, which is more involved. While the framework is very general, we are specifically interested in a perceptual agent-oriented operator S (sees). Axioms for the interaction of seeing and knowing are explored. We then consider dynamic extensions of the basic logic with public announcement and “observational” announcement, in which information is given only to agents who can see the announcer.
2022 Mar 03 16:00-17:00 Zhiguang Zhao 赵之光 (Taishan University): Algebraic Correspondence Theory: A Duality-Theoretic Perspective
The talk is divided into two parts: the first part gives a brief introduction to the topological duality between Boolean algebras with operators and descriptive general frames as well as the discrete duality between complete atomic Boolean algebras and Kripke frames, and we use this framework to discuss canonicity theory. The second part is an introduction of correspondence theory in an algebraic way, which is modular and easy to generalize to other semantic settings.
2022 Feb 24 16:00-17:30 Chong Chi Tat 庄志达 (National University of Singapore): Nonstandard Models of Arithmetic
The notion of a nonstandard model was introduced by Skolem almost 90 years ago. Since then, nonstandard models have been a subject of study in mathematical logic. In recent years, such structures were successively used to investigate combinatorial problems in reverse mathematics. This talk will give a brief introduction of the key features of a nonstandard model, provide some examples, and discuss the role of nonstandard models in metamathematical investigations, as well as in the philosophy of mathematics.
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