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.

Organizing Committee (from September 2021): Junhua Yu, Chenwei Shi, Kaibo Xie, Yinlin Guan, Yiyan Wang, Jialiang Yan, Penghao Du.

### ■Schedule for 2022-2023 Autumn Semester

Date | Speaker |
---|---|

2022 Sep 15 | Changpu Sun 孙昌璞 (China Academy of Engineering Physics) |

2022 Sep 22 | Zhaokuan Hao 郝兆宽 (Fudan University) |

2022 Sep 29 | Heinrich Wansing (Ruhr University Bochum) |

2022 Oct 13 | Sujata Ghosh (Indian Statistical Institute, Chennai) |

2022 Oct 20 | Andreas Herzig (Institut de Recherche en Informatique de Toulouse) |

2022 Oct 27 | Xiao Liu 刘潇 (Tsinghua University) |

2022 Nov 03 | Yi Wang 王轶 (Sun Yat-sen University) |

2022 Nov 10 | Katsuhiko Sano (Hokkaido University) |

2022 Nov 24 | Sonja Smets (University of Amsterdam) |

2022 Dec 01 | Rineke Verbrugge (University of Groningen) |

2022 Dec 04 | Hanti Lin (University of California, Davis) |

2022 Dec 15 | Yong Cheng 程勇 (Wuhan University) |

2022 Dec 22 | Minghui Ma 马明辉 (Sun Yat-sen University) |

2022 Dec 29 | Peng Cui 崔鹏 (Tsinghua University) |

### ■Current Events

#### 2022 Dec 04 09:00~10:30 Hanti Lin 林翰迪 (University of California, Davis): **The Hopelessness of AGM Belief Revision and the Trinity of Statistics**

**The Hopelessness of AGM Belief Revision and the Trinity of Statistics**

The standard theory of belief revision—the AGM theory—has long been challenged with some putative counterexamples, and its defenders often reply by (explicitly or implicitly) following a quite general, powerful strategy. I will describe that reply strategy in detail before I undermine it. More specifically, I will give a class of counterexamples to the AGM theory (and anything stronger) for which the reply strategy no longer works. Worse, my counterexamples are pervasive in science, in the sense that statistical hypothesis testing is pervasive in science. Some weakenings of the AGM theory will then be considered, and their prospects will be assessed (optimistically). I will close by sketching how all this fits into the bigger picture of scientific inference that I defended elsewhere (in the 2022 PSA). If I am right, belief revision theory, when done right, is an important missing part of a good philosophy of statistics.

#### 2022 Nov 24 16:00-17:30 Rineke Verbrugge (University of Groningen): **Zero-one laws for the propositional provability logic GL, S4, and K4**

**Zero-one laws for the propositional provability logic GL, S4, and K4**

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. For modal logics, limit behavior for models and frames may differ. In 1994, Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5. They also proposed zero-one laws for the corresponding classes of frames, but their zero-one law for K-frames has since been disproved, and so has more recently their zero-one law for S4-frames.

In this talk, we prove zero-one laws for provability logic with respect to both model and frame validity. Moreover, we axiomatize validity in almost all irreflexive transitive finite models and in almost all irreflexive transitive finite frames, leading to two different axiom systems. In the proofs, we use a combinatorial result by Kleitman and Rothschild about the structure of finite (strict) partial orders: almost all of them consist of only three layers. Finally, we present empirical results in order to give an idea of the number of elements from which onwards a formula’s almost sure validity or almost sure invalidity stabilizes in such three-layer Kleitman-Rothschild frames. We also discuss possible extensions of the zero-one laws to the modal logics S4 and K4.

#### 2022 Nov 24 16:00-17:30 Sonja Smets (University of Amsterdam): **Learning what Others Know**

**Learning what Others Know**

I will present joint work with A. Baltag on modelling scenarios in which agents read or communicate (or somehow gain access to) all the information stored at specific sources, or possessed by some other agents (including information of a non-propositional nature, such as data, passwords etc). Modelling such scenarios requires us to extend the framework of epistemic logics to one in which we abstract away from the specific announcement and formalize directly the action of sharing ‘all you know’ (with some or all of the other agents). In order to do this, we introduce a general framework for such informational events, that subsumes actions such as “sharing all you know” with a group or individual, giving one access to some folder or database, hacking a database without the owner’s knowledge, etc. We formalize their effect, i.e. the state of affairs in which one agent (or group of agents) has ‘epistemic superiority’ over another agent (or group). Concretely, we express epistemic superiority using comparative epistemic assertions between individuals and groups (as such extending the comparison-types considered in [5]). Another ingredient is a new modal operator for ‘common distributed knowledge’, that combines features of both common knowledge and distributed knowledge, and characterizes situations in which common knowledge can be gained in a larger group of agents (formed of a number of subgroups) by communication only within each of the subgroups. We position this work in the context of other known work such as: the problem of converting distributed knowledge into common knowledge via acts of sharing [4]; the more semantic approach in [2] on communication protocols requiring agents to ‘tell everybody all they know’; the work on public sharing events with a version of common distributed knowledge in [3]; and the work on resolution actions in [6].

References:

[1] A. Baltag and S. Smets, Learning what others know, in L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming, AI and Reasoning, EPiC Series in Computing, 73:90-110, 2020. https://doi.org/10.29007/plm4

[2] A. Baltag and S. Smets, Protocols for Belief Merge: Reaching Agreement via Communication, Logic Journal of the IGPL, 21(3):468-487, 2013. https://doi.org/10.1093/jigpal/jzs049

[3] A. Baltag, What is DEL good for? Lecture at the ESSLLI2010-Workshop on Logic, Rationality and Intelligent Interaction, 16 August 2010.

[4] J. van Benthem, One is a lonely number. In P. Koepke Z. Chatzidakis and W. Pohlers, (eds.) Logic Colloquium 2002, 96-129, ASL and A.K. Peters, Wellesley MA, 2002.

[5] H. van Ditmarsch, W. van der Hoek & B. Kooi, Knowing More – from Global to Local Correspondence, Proc. of IJCAI-09, 955–960, 2009.

[6] T. Agotnes and Y.N. Wang, Resolving Distributed Knowledge, Artificial Intelligence, 252: 1–21, 2017. https://doi.org/10.1016/j.artint.2017.07.002

#### 2022 Nov 10 16:00-17:30 Katsuhiko Sano (Hokkaido University): **Analytic Cut and Mints’ Symmetric Interpolation Method for Bi-intuitionistic Tense Logic**

**Analytic Cut and Mints’ Symmetric Interpolation Method for Bi-intuitionistic Tense Logic**

This talk establishes the Craig interpolation theorem of bi-intuitionistic stable tense logic BiSKt, which is proposed by Stell et al. (2016). First, we define a sequent calculus G(BiSKt) with the cut rule for the logic and establish semantically that applications of the cut rule can be restricted to analytic ones, i.e., applications such that the cut formula is a subformula of the conclusion of the cut rule. Second, we apply a symmetric interpolation method, originally proposed by Mints (2001) for multi-succedent calculus for intuitionistic logic, to obtain the Craig interpolation theorem of the calculus G(BiSKt). Our argument also provides a simplification of Kowalski and Ono (2017)’s argument for the Craig interpolation theorem of bi-intuitionistic logic. This is joint work with Hiroakira Ono (JAIST).

#### 2022 Nov 03 16:00-17:30 Yi Wang 王轶 (Sun Yat-sen University): **认知视角外的社会网络逻辑研究**

讲座以结构平衡逻辑为例介绍非信息因素驱动的社会网络更新模型和逻辑学研究视角，并解释此类工作中常常面临的一些技术难题，顺带介绍报告人在这个领域的近期工作和研究想法。

参考文献：王轶，《逻辑、博弈与计算——社会网络平衡研究》。

#### 2022 Oct 27 16:00-17:30 Xiao Liu 刘潇 (Tsinghua University): **The Consistency of Rationality Measurement**

**The Consistency of Rationality Measurement**

Individual rationality plays a central role in modern economic theory, while how to measure rationality has been quite challenging. In particular, whether the rationality measured in different domains is stable or not is an open question. Combining consumers’ purchase data from a large supermarket chain and their choice in a survey experiment, we directly examine three important questions for rationality measurements: (1) external validity: can rationality measured in the survey experiment successfully predict consumers’ actual purchase behavior; (2) cross validity: is rationality exhibited in risk preference consistent with that in social preference? (3) time stability: does an individual’s rationality level vary with time windows?

#### 2022 Oct 20 16:00-17:30 Andreas Herzig (Institut de Recherche en Informatique de Toulouse): **On logics of knowledge and belief**

**On logics of knowledge and belief**

Epistemic logics are traditionally about the modalities ‘belief-that’ and ‘knowledge-that’. The talk will instead focus on modalities of the ‘knowledge-whether’ kind, providing insights about the principles governing common knowledge and about the interplay between knowledge and belief. As ‘belief whether’ does not exist in natural language we use the term ‘belief about’ instead. Concerning common knowledge, we study the following principle for common knowledge: common knowledge that each agent knows whether p implies common knowledge whether p. If the logic of knowledge is S5 then it provides an equivalent and more intuitive alternative to the standard induction axiom for common knowledge. Concerning the interplay between knowledge and belief we follow, among others, Lenzen and Voorbraak and adopt S4.2 as the logic of knowledge and KD45 as the logic of (strong) belief, plus the interaction axioms ‘knowledge implies belief’, ‘belief implies knowledge to believe’, and ‘belief implies belief to know’. In this framework we study the two modalities ‘true belief about’ andmere ‘belief about’: they lead to an elegant characterisation of epistemic-doxastic situations as well as to the definition of interesting lightweight fragments of epistemic-doxastic logic.

References:

- Andreas Herzig, Elise Perrotin: True Belief and Mere Belief About a Proposition and the Classification of Epistemic-Doxastic Situations. Filosofiska Notiser, 103-117 (2021) http://filosofiskanotiser.com/Herzig_Perrotin.pdf
- Andreas Herzig, Elise Perrotin: On the Axiomatisation of Common Knowledge. AiML 2020: 309-328. http://www.aiml.net/volumes/volume13/Herzig-Perrotin.pdf
- Martin C. Cooper, Andreas Herzig, Faustine Maffre, Frédéric Maris, Elise Perrotin, Pierre Régnier: A lightweight epistemic logic and its application to planning. Artif. Intell. 298: 103437 (2021)

#### 2022 Oct 13 16:00-17:30 Sujata Ghosh (Indian Statistical Institute, Chennai): **What drives people’s choices in turn-taking games?**

**What drives people’s choices in turn-taking games?**

Game theorists have proposed backward induction as the reasoning procedure that rational players follow in turn-taking games. An alternative is forward induction, in which a player rationalizes any previous move by the opponent that does not fit backward induction. Do adult participants’ choices in centipede-like turn-taking games fit better with backward or forward induction? In a couple of experiments, participants played a turn-taking game against a computer, which was programmed to deviate often from the backward induction strategy at the beginning of the game. Participants had been told that the computer was optimizing against some belief about the participant’s future strategy. In the course of the experiments, participants were asked questions about their own and the opponent’s reasoning at all decision nodes of a sample game. We checked how their verbalized strategies fit to their choices in the experimental games. Although in the aggregate, participants tend to favor the forward induction choice, their verbalized strategies usually involve explicit theory of mind, their own attitudes towards risk, and those they assign to the opponent, as well as considerations about cooperativeness.

This talk is based on joint work with Aviad Heifetz, Rineke Verbrugge and Harmen de Weerd.

#### 2022 Sep 29 16:00-17:30 Heinrich Wansing (Ruhr University Bochum): **Beyond Paraconsistency – A plea for a radical breach with the Aristotelean orthodoxy in logic**

**Beyond Paraconsistency – A plea for a radical breach with the Aristotelean orthodoxy in logic**

The development of systems of paraconsistent, inconsistency-tolerant logics in the 20th century can be seen as a major and bold move in the history of ideas. Ever since Aristotle’s formulation of the law of non-contradiction, when he wrote in 1011b13–14 of what is now called Metaphysics IV that “opposite assertions cannot be true at the same time,” negation consistency has been regarded as absolutely indispensable for theoretically rational theory formation. However, even the founders of paraconsistent, inconsistency-tolerant logic, Stanislaw Jaskowski and Newton da Costa, and the key proponent of dialetheism, Graham Priest, did not liberate themselves completely from the consistency bonds of classical logic and the most prominent non-classical logics in more than one way, especially in not accounting for logically provable (or, semantically, logically valid) contradictions and non-trivial negation inconsistent logics.

I will suggest to radically break with the time-honored Aristotelean tradition of complete banishment of contradictions in science. In particular, I will argued that it is theoretically rational to believe not only that there exist interesting or important non-trivial negation inconsistent theories but also that there exist interesting or important non-trivial negation inconsistent logics. I will present several examples of such logics.

#### 2022 Sep 22 16:00-17:30 Zhaokuan Hao 郝兆宽 (Fudan University): **概念与可定义性**

1885 年，也就是弗雷格的 《算术基础》 出版一年后，康托发表了他对这部著作的评论。 这篇评论只有一页，但涉及一个非常重要也非常有趣的问题，那就是概念外延和集合哪一个更为基础。在本次演讲中，我们试图讨论这一分歧的哲学意义极其所代表的不同传统，并且将可定义性视为把握客观概念的主要工具。我们会论证康托的评论和弗雷格两个月后的回应不仅具有重大的历史意义，而且与当今数学基础的一个重大问题密切相关。 集合论虽然自康托尔以来取得了巨大的成功，但其基础所面临的困难可能与康托对概念的误解有关。这些困难借助弗雷格和哥德尔的概念论哲学思想有可能找到数学解决方案。

#### 2022 Sep 15 16:00-17:30 Changpu Sun 孙昌璞 (China Academy of Engineering Physics): **量子力学的客观性诠释与波普尔哲学**

量子力学奠定了现代科学的基础，成功地推动当代技术革命方面。然而，对于量子力学诠释——理解波函数如何述刻画微观世界，迄今为止人们并未形成共识。本报告将结合报告人二十余年关于量子力学基础问题艰辛探索，简要介绍和评述这些量子力学诠释的基本思想、它们之间的逻辑关系及其实验检验的可能性。报告强调，首先要明确定义什么是量子测量、什么是量子测量的客观性，才能澄清量子力学诠释中的一些基本概念，避免量子观念滥用引起的意识论上的问题、使得量子技术发展误入歧途。

报告着重阐述了量子力学如何描述微观世界的客观属性。我们认为，由于采用了不具唯一性的波包塌缩假设，哥本哈根诠释对哲学基本问题构成的挑战并非根本性的，有人由此得到物质-意识不可分的结论在科学和哲学都是不严谨的。针对卡尔·波普尔“三个世界”哲学，报告基于量子测量 理论描述了多个观察者如何对微观系统进行探测，形成客观的量子测量，产生微观世界的客观知识，从而对 波普尔的客观知识世界(世界 3)给出了基于量子力学本体论的哲学解读:物质世界(世界 1)与精神感知世 界(世界 2)的物化载体(认识主体)相互作用，形成二者的关联和纠缠，它们对应了主观世界在内的精神 感知全体，其中具有客观性的部分构成了微观世界的客观知识。文章还指出，伴随着微观系统客观知识世界 的形成，信息从物质世界流向主观客体，信息流的指向定义了不同于通常物质世界的精神感知的物化载体。

### ■Past Events

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