Tsing Ch’a Sessions 清茶会

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 2022-2023 academic year (Autumn)

DateSpeaker
2024 FEB 29杜鹏昊 Penghao Du
2024 MAR 07江峰 Feng Jiang,樊瑞 Rui Fan
2024 MAR 14储明亮 Mingliang Chu
2024 MAR 21杨思思 Sisi Yang
2024 MAR 28王威 Wei Wang
2024 APR 11Søren Brinck Knudstorp, 杨曦 Xi Yang
2024 APR 18欧阳文飞 Wenfei Ouyang
2024 MAY 09张力竹 Lizhu Zhang
2024 MAY 16何清瑜 Qingyu He, 王逸骞 Yiqian Wang
2024 MAY 23王威 Wei Wang
2024 MAY 30江峰 Feng Jiang, 杨曦 Xi Yang
2024 JUN 06Yichen Zhao

■Current Sessions

2024 Apr 18 14:00-15.30 Wenfei Ouyang (Tsinghua University) Co-dependence: Interactions between <R, R-1>  Bimodal Logic and LFD

This report will present a preliminary attempt to explore the logical interaction between  Bimodal Logic and the Logic of Functional Dependence (LFD). LFD, proposed by Baltag and Van Benthem (2021), is an extension of classical propositional logic with local dependence formulas and dependence quantifiers. A relational semantics for LFD is established with dependence quantifiers treated as modalities and local dependence formulas treated as modal atoms. This is a good starting point for considering  Bimodal Logic, an extension of standard basic modal logic with the complement  of , proposed by Goranko (1990). We aim to address two main questions: How will LFD behave when we extend the semantics with complemental relations? What is the significance of this interaction? In this presentation, I intend to provide preliminary answers to these questions and offer some insights and results regarding these two logics.

This talk mainly relies on the works of Baltag and Van Benthem (2021) and Goranko (1990).

[1] Baltag A, van Benthem J. A simple logic of functional dependence[J]. Journal of Philosophical Logic, 2021, 50: 939-1005. 
[2] Goranko V. Completeness and Incompleteness in the Bimodal Base L(R, -R) [J]. Mathematical logic, 1990: 311-326.


2024 Apr 11 14:00-15.30 Søren Knudstorp (ILLC, University of Amsterdam) Axiomatizing Step-by-Step: Lessons from Modal Information Logic

This presentation aims to derive general heuristics and specific methods for axiomatization, the Finite Model Property (FMP) and decidability. It will encompass selected excerpts from my recent papers [Knudstorp 2023b; Knudstorp 2023a], along with unpublished work, extending my Master’s thesis (https://eprints.illc.uva.nl/id/eprint/2226/1/MoL-2022-24.text.pdf), ‘Modal Information Logics’, overseen by Johan van Benthem and Nick Bezhanishvili.

Modal information logics (MILs) were first proposed by Van Benthem (1996) to model a theory of information using possible-worlds semantics. Although the logics have been around for some time, not much is known: Van Benthem (2017) and Van Benthem (2019) pose two problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability.

The main results of the first part of the talk are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability ‘via completeness’.

The second part of the talk will explore a selection of belated logical systems. Most notably, the MIL on semilattices is axiomatized with an infinite scheme and shown not to be finitely axiomatizable. Emphasis will be limited to two main aspects: the axiomatization technique employed, and the (seemingly) paradoxical increase in complexity: from the finitely axiomatizable (decidable) MILs on preorders and posets, an infinitely (and not finitely) axiomatizable (undecidable) logic arises by chaffing away most of the posets to only consider the more well-behaved ones with all binary suprema.

The talk will be entirely self-contained, yet attendees may find my Peking talk on April 9th to be a valuable supplement.

References

  • Knudstorp, Søren Brinck (2023a). “Logics of truthmaker semantics: comparison, compactness and decidability”. In: Synthese 202. doi: 10.1007/s11229-023-04401-1.— (2023b).
    • “Modal Information Logics: Axiomatizations and Decidability”. In: Journal of Philosophical Logic 52, pp. 1723–1766. doi: 10.1007/s10992-023-09724-5.
  • Van Benthem, Johan (1996). “Modal Logic as a Theory of Information”. In: Logic and Reality. Essays on the Legacy of Arthur Prior. Ed. by J. Copeland. Clarendon Press, Oxford, pp. 135–168.— (Oct. 2017).
    • “Constructive agents”. In: Indagationes Mathematicae 29. doi: 10.1016/j.indag.2017. 10.004.— (2019). “Implicit and Explicit Stances in Logic”. In: Journal of Philosophical Logic 48.3, pp. 571– 601. doi: 10.1007/s10992-018-9485-y.

2024 Apr 11 15:45-17:15 Xi Yang (Tsinghua University) Model Comparison Games for Characterization of Quantifier Number and Other Syntactic Measure

Games can serve as a tool to characterize the expressive power of logics. One example is the Ehrenfeucht-Fraïssé Games (EF-games), which capture the quantifier rank of first-order sentence required to distinguish between two structures. In my presentation, I will discuss combinatorial games that have garnered attention recently, particularly focusing on multi-structural games introduced in [1] and re-discovered in [2]. These games can capture the number of quantifiers of first-order sentences required to separate structures. I will present the findings from [3] regarding the differences between EF games and the multi-structural games. Moreover, I will discuss syntactic games introduced in [3], which can simultaneously capture reasonable syntactic measures and the number of variables of first order sentences.

This talk is mainly based on [3].

References

[1] Immerman, N. (1981). Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences, 22(3), 384-406.

[2] Fagin, R., Lenchner, J., Regan, K. W., & Vyas, N. (2021, June). Multi-structural games and number of quantifiers. In 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (pp. 1-13). IEEE.

[3] Carmosino, M., Fagin, R., Immerman, N., Kolaitis, P., Lenchner, J., & Sengupta, R. (2023). Multi-Structural Games and Beyond. arXiv preprint arXiv:2301.13329.


2024 Mar 28 14:00-15.30 Wei Wang (Tsinghua University) Towards a Logical Approach to AI-Driven Recommendations

In the digital era, users encounter an endless stream of recommendations. The development of recommendation algorithms in AI has attracted extensive attention, yielding a substantial body of literature. However, the contribution of logic has been minimal. In this talk, we propose a new recommendation logic (RL) to study the reasoning behind recommendations, emphasizing their basis in users’ revealed preferences. We explore the expressivity of RL by introducing a new notion of bisimulation and translating RL into a 3-variable fragment of a two-sorted first-order logic. We show that RL-models have the tree model property and that their model-checking problem can be solved in polynomial time, for which we propose an algorithm and prove its correctness. We believe that our approach lays a foundation for AI research and has the potential to advance personalized recommendations.

This is joint work with Fenrong Liu and Sisi Yang.


2024 Mar 21 14:00-15.30 Sisi Yang (Tsinghua University) A New Semantics for Extended Argumentation Framework

The formal study of argumentation plays an important role in knowledge representation, especially in reasoning from contradictory information. Many developments build on Dung’s seminal theory of argumentation. Preference is a key concept in argumentation to represent the comparative strength of arguments, and in particular can be used to resolve conflicts between arguments. It’s essential for preferences to adapt to various scenarios rather than remaining fixed. Consequently, Modgil extended Dung’s framework to reasoning about preferences. However, this extension led to the loss of the general existences of grounded and preferred extensions. In this talk, I will begin with an introduction to Dung’s abstract argumentation framework and semantics, followed by an introduction to Modgil’s extended argumentation framework and semantics. Then I will explain the limitations of Modgil’s semantics. At last, I will present our new semantics based on the extended argumentation framework, which preserves the semantic properties of Dung’s argumentation framework.

This is a joint work with Yan Zhang. 


2024 Mar 14 14:00-15.30 Mingliang Chu (Tsinghua University) Different Interpretations of Ockham’s Ascent and Descent Rules

The differing views on individual terms prompt us to consider Ockham’s rules of ascent and descent from various perspectives. Firstly, interpreting individual terms as elements within the domain of individuals, we see the ascent and descent rules as part of the quantification theory in first-order logic. Secondly, adopting Quine’s approach, which views individual terms as a specific kind of predicate, we interpret the rules within the tradition of the Two-Classes Theory. We believe this interpretation aligns more closely with Ockham’s original intent. Moreover, from this viewpoint, the ascent and descent rules closely coincide with the pattern of monotonic reasoning that represents ‘predicate substitution‘. Finally, to ensure the surface syntactic structure remains unchanged, we draw upon Russell’s theory of descriptions, interpreting individual terms as collections of properties. We will demonstrate that, within the framework of generalized quantifiers, the ascent and descent rules constitute a form of monotonic reasoning.


2024 Mar 7 14:00-15.30 Feng Jiang (Tsinghua University) Generic Absoluteness for the Chang Model

This talk will give an introduction to Woodin’s generic absoluteness theorem for the Chang model. In particular, we will show that if there exists a Woodin cardinal which is a limit of Woodin cardinals, then every set of reals in the Chang model is Lebesgue measurable. The proof presented here follows the approach developed in Paul Larson’s book The Stationary Tower.


2024 Feb 29 14:00-15.30 Penghao Du (Tsinghua University) Modal Logics of Definable Link Variations: Characterization and Satisfiability

Link variations, including link cutting, adding and rotating, are critical updating process on graphs, which play important roles in graph reasoning. Undefinable link variations and their logics have been widely studied. In [Li, 2020], Li introduced a modal logic, LLD, designed for definable link cutting. In this talk, following LLD, I will propose the logics LLA, LLR, and LLV, which respectively address definable link adding, rotating, and combinations of dynamic operations on graphs. Van Benthem-style characterization theorems for these logics will be provided. In addition, I will show that all these logics are undecidable and present decidable fragments of them.
This is a joint work with Qian Chen.


■Past Sessions

Click HERE to check the past sessions.