To promote interdisciplinary interaction between different faculty members and students on the campus, a weekly meeting has been organized by our postdoc Jialiang Yan since September 2023, called Tsing Ch’a Sessions (清茶会). Its slogan “know thyself and let others know you better.”

### ■Schedule for 2024-2025 academic year (Fall)

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

2024 SEP 12 | 赵博囡 Bonan Zhao |

2024 SEP 19 | John Lindqvist, 李文娟 |

2024 SEP 26 | 杜鹏昊 Penghao Du |

2024 OCT 10 | 罗昊轩 Haoxuan Luo，欧阳文飞 Wenfei Ouyang |

2024 OCT 24 | 何清瑜 Qingyu He |

2024 OCT 31 | 杨曦 Xi Yang |

2024 NOV 07 | 杨思思 Sisi Yang |

2024 NOV 14 | 王威 Wei Wang，张力竹 Lizhu Zhang |

2024 NOV 21 | 郑文龙 Wenlong Zheng， 赵奕辰 Yichen Zhao |

2024 NOV 28 | Working group |

2024 DEC 05 | Working group |

2024 DEC 12 | Working group |

### ■Current Sessions

**2024 October 31 14:00-15:30 Xi Yang (杨曦 Tsinghua University) ***Games for Quantifier Numbers*

*Games for Quantifier Numbers*

Multi-Structural (MS) games and their variants are designed to capture the number of quantifiers needed to express first-order properties. Recently, Carmosino et al. [1] employed MS games to establish tight bounds on the the number of quantifiers needed to define specific properties of ordered structures. In this talk, I will use the techniques and findings from [1] to show that, on the class of finite linear orders, any first-order sentence with a quantifier depth of *n* is equivalent to a sentence with approximately 2*n* quantifiers. Furthermore, I will discuss some potential applications of these games in investigating the succinctness of the finite-variable fragments of first-order logic on linear orders.

Reference:

1. Carmosino, M., Fagin, R., Immerman, N., Kolaitis, P., Lenchner, J., & Sengupta, R. (2024). On the number of quantifiers needed to define boolean functions. *arXiv* preprint arXiv:2407.00688.

**2024 October 24 14:00-15:30 Qingyu He (何清瑜 Tsinghua University) ***Boolean dependence logic*

*Boolean dependence logic*

Baltag and van Benthem[1] introduced a logic of functional dependence (LFD) with local dependence formulas and dependence quantifiers, which can be seen both as a first-order and a modal logic. In the relational semantics of LFD, the dependence quantifiers become modalities and local dependence formulas are treated as special atoms. In particular, the modalities involving multiple variables correspond to intersections of relations. This leads to the study on the interaction between LFD and Boolean Modal Logic [2] (BML)—a poly-modal logic where families of binary relations are closed under the Boolean operations of union, intersection, and complement.In this talk, I will present a BML version of LFD, which can express additional notions of dependence. I will provide an axiomatization, including details about its completeness proof. Furthermore, I will extend the framework by introducing conditional independence atoms, and propose an axiomatization for the extended logic.

This is joint work with Chenwei Shi and Qian Chen.

Reference：

[1] Baltag, Alexandru, and Johan van Benthem. “A simple logic of functional dependence.” Journal of Philosophical Logic 50 (2021): 939-1005.

[2] Gargov, George, and Solomon Passy. “A note on Boolean modal logic.” Mathematical logic. Boston, MA: Springer US, 1990. 299-309.

**2024 October 10 16:00-17:30 Wenfei Ouyang (欧阳文飞 Tsinghua University) ***Understanding Dependence Relation and its Representation Theorem*

*Understanding Dependence Relation and its Representation Theorem*

n Baltag and van Benthem’s paper [1], three representation theorems are proved for the functional dependence relation (Proposition 2.6). In this talk, we will simplify the construction which is key to the proof. Based on this simplification, we give a more detailed characterization of the construction. We will also disscuss other representation theorems in other related works.

**References**[1] Baltag, A., van Benthem, J. A Simple Logic of Functional Dependence.

*J Philos Logic*

**50**, 939–1005 (2021).

**2024 **** October 10** 14:00-15:30 Haoxuan Luo (罗昊轩 Tsinghua University) *A Semantic Model Based on Inconsistent Sets and Its Corresponding Frame Properties*

**October 10**14:00-15:30 Haoxuan Luo (罗昊轩 Tsinghua University)

*A Semantic Model Based on Inconsistent Sets and Its Corresponding Frame Properties*

In paraconsistent logic, the Principle of Explosion (ECQ) does not hold, meaning that both a proposition A and its negation ¬A can be true at the same time. In this talk, I will briefly introduce Non-adjunctive Discursive Logic and Paraconsistent Logic with Preservationism, which introduce the concept of sets of inconsistent formulas. I will then build a model composed of inconsistent sets, where these inconsistent formulas can be derived. I will also discuss the relationship between this model and the Kripke model. Furthermore, I will provide a characterization of the semantics for some classes of frames and explore more results on compactness. This talk is based on my master’s thesis.

**2024 September 26 14:00-15:30 Penghao Du (杜鹏昊 Tsinghua University) ***Modal logics for the poison game: axiomatization and undecidability*

*Modal logics for the poison game: axiomatization and undecidability*

Poison modal logic and poison sabotage modal logic have been studied in the existing literature to capture the so-called poison game, which was originally conceived as a paradigm for reasoning about graphical concepts in graph theory and has recently been shown to have significant applications in the theory of abstract argumentation. In this work, we further explore the technical aspects of these two logics and extend existing results by addressing the open questions identified in [Grossi and Rey, 2019, Blando et al., 2020]. Specifically, we show that poison sabotage modal logic has an undecidable satisfiability problem, and we provide both Hilbert-style calculus and tableau calculus for these logics. This is a joint work with Fenrong Liu and Dazhu Li.

**2024 September 19 **16:00-17:30 John Lindqvist (University of Bergen) *Distributed belief – aggregating potentially conflicting information*

In epistemic logic, the knowledge distributed among a group of agents, or the knowledge possible given the information distributed in the group, can be formalized using the intersection modality. Distributed knowledge can potentially be resolved if the information possessed by the group is shared among its members. However, when we consider belief rather than knowledge, the picture is more complicated. The cumulative information possessed by the agents can be contradictory. In such cases, the distributed belief of the group explodes: the group ends up with distributed belief in everything. Similarly, in such cases, resolving using the intersection operation makes the agents inconsistent.We consider non-explosive alternative definitions of distributed belief, both static and dynamic. For the static case, we offer non-explosive alternative definitions for distributed belief that make use of maximal consistent subgroups. For the dynamic case, we discuss ways of preserving belief properties of individual agents.

**2024 September 19 14:00-15:30 Wenjuan Li (**李文娟 Beijing Institute of Mathematical

Sciences and Applications**) ***Determinacy of omega-languages: from non-determinism to probability*

*Determinacy of omega-languages: from non-determinism to probability*

I will talk about the interface of the determinacy of Gale-Stewart games and automata on infinite words. The Gale-Stewart game is a two-player turn-based game with perfect information. Given a winning set X, determinacy of X asserts that one of the two players has a winning strategy. The winning set X can also be defined by variants of finite automata as a set of infinite words accepted by such automata. I will review several variants of finite automata on infinite words and the determinacy studies along this topic, then introduce our studies on determinacy strength of infinite games with winning sets defined by pushdown and probabilistic automata with various acceptance conditions.

**2024 September 12 13:30-15:30 Bonan Zhao (赵博囡 Princeton University) ***Computational models of causal generalization*

*Computational models of causal generalization*

Computational Cognitive Science is an interdisciplinary field seeking to understand human cognition and intelligence through computational principles. Logic has played fundamental roles in the early development of cognitive science, and keeps influencing today’s most cutting-edge research in the field. In this talk, I will briefly introduce the historical connection between logic and cognitive science, and share some of my work combining formal representations, probabilistic inference, and behavioral experiments, to account for how people synthesize concepts from very few data and generalize to novel situations.

### ■Past Sessions

Click HERE to check the past sessions.