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, Yinlin Guan, Yiyan Wang, Jialiang Yan, Penghao Du.

### ■Schedule for 2022-2023 academic year

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

2023 Feb 23 | Sonja Smets (University of Amsterdam) |

2023 Mar 02 | Dun Deng 邓盾 (Tsinghua University) |

2023 Mar 09 | Fan Yang 杨帆 (Utrecht University) |

2023 Mar 16 | Feng Ye 叶峰 (Capital Normal University) |

2023 Mar 23 | Xinwen Liu 刘新文 (Chinese Academy of Social Sciences) |

2023 Mar 30 | Frederik van der Putte (Ghent Unibersity) |

2023 Apr 06 | Fengkui Ju 琚凤魁 (Beijing Normal University) |

2023 Apr 20 | Shengyang Zhong 钟盛阳(Peking University） |

2023 May 13 | Wes Holliday (University of California, Berkeley) |

2023 May 18 | Fei Liang 梁飞 (Shandong University) |

2023 May 25 | Marta Bilkova (Czech Academy of Sciences) |

2023 Jun 01 | Yan Zhang 张炎 (Renmin University of China) |

∧2023 Jun 08 | Hao TANG 唐浩 (Tsinghua University) |

### ■Current Events

**2023 Jun 01st 16:00~17:30 Yan Zhang (张炎, Renmin University of China): ***Transitive Logics of Finite Depth and Finite Suc-eq-width*

*Transitive Logics of Finite Depth and Finite Suc-eq-width*

In this talk, I will present some results from the study of transitive logics of finite depth and finite suc-eq-width. They are logics in NExtK4 containing the standard depth axioms and the suc-eq-width axioms, which are generalizations of the standard width axioms. The frame condition for a suc-eq-width axiom requires, in a rooted transitive frame, a finite upper bound of cardinality for antichains of points with different sets of proper successors. Our first result demonstrates that all these logics are finitely axiomatizable, thereby generalizing Rybakov and Chagrov’s result of the finite axiomatizability of extensions of S4 of finite depth and finite width. Applying the well-known result from Segerberg that all transitive logics of finite depth have the finite model property, we then establish that all transitive logics of finite depth and finite suc-eq-width are decidable. Lastly, the complexity of the satisfiability problem for these logics can be shown to fall within the NP class.

#### 2023 May 25th 16:00~17:30 Marta Bilkova (Czech Academy of Sciences): **Belnapian logics for uncertainty**

**Belnapian logics for uncertainty**Reasoning about information, its potential incompleteness, uncertainty, and contradictoriness need to be dealt with adequately. While incompleteness and uncertainty are typically accommodated within one formalism, e.g. within various models of imprecise probability, contradictoriness and uncertainty less so — conflict or contradictoriness of information is rather chosen to be resolved than to be reasoned with. To reason with conflicting information, positive and negative support — evidence in favour and evidence against — a statement are quantified separately in the semantics. This two-dimensionality gives rise to logics interpreted over twist-product algebras or bi-lattices, the well known Belnap-Dunn logic of First Degree Entailment being a prominent example. Belnap-Dunn logic with its double-valuation frame semantics can in turn be taken as a base logic for defining various uncertainty measures on de Morgan algebras, e.g. Belnapian (non-standard) probabilities or belief functions.

In spirit similar to Belnap-Dunn logic, we have introduced many-valued logics suitable to reason about such uncertainty measures. They are interpreted over twist-product algebras based on the [0,1] real interval as their standard semantics and can be seen to account for the two-dimensionality of positive and negative component of (the degree of) belief or likelihood based on potentially contradictory information, quantified by an uncertainty measure. The logics presented in this talk include expansions of Łukasiewicz with a de-Morgan negation which swaps between the positive and negative semantical component.

Our main objective is to utilise apparatus of two-layered logics to formalise reasoning with uncertain information, which itself might be non-classical, i.e., incomplete or contradictory. Many-valued logics with a two-dimensional semantics mentioned above are used on the outer layer to reason about belief, likelihood or certainty based on potentially incomplete or contradictory evidence, building on Belnap-Dunn logic as an inner logic of the underlying evidence. This results in two-layered logics suitable for reasoning scenarios when aggregated evidence yields a Belnapian probability measure or a belief function on a De Morgan algebra.

(This talk is rooted in joint work with S. Frittella, D. Kozhemiachenko, O. Majer and S. Nazari.)

#### 2023 May 18th 14:00~15:30 Sujata Ghosh (Indian Statistical Institute, Chennai (ISI, Chennai)): *A modal logic to reason in distributed games*

*A modal logic to reason in distributed games*In distributed games, every player sees only the local game arena, and announces potential joint moves with other players. The global arena resolves these and the game proceeds. We propose a two-level logic to reason in such games, with one layer of local formulas for each player, and the global formulas. We present a complete axiom system for valid formulas and show decidability.

This talk is based on joint work with Lei Li, Fenrong Liu and R. Ramanujam.

#### 2023 May 13th 09:00~10:30 Wesley Holliday (University of California, Berkeley): **The Orthologic of Epistemic Modals**

**The Orthologic of Epistemic Modals**

The epistemic modals ‘might’ and ‘must’ have peculiar logical features that are challenging to account for in a broadly classical framework. In this talk, I will discuss a non-classical approach to epistemic modals from my paper with Matthew Mandelkern, “The Orthologic of Epistemic Modals” (https://escholarship.org/uc/item/0ss5z8g3), with special attention to the new Section 5 (“Constructing possibilities from worlds”).

#### 2023 Apr 20 16:00~17:30 Shengyang Zhong 钟盛阳(Peking University）: **Quantum Measurement and Quantum Entanglement – From the Perspective of the Orthogonality Relation**

**Quantum Measurement and Quantum Entanglement – From the Perspective of the Orthogonality Relation**

This talk is a survey of a project of my research since around 2014. First, I will introduce the aim, the paradigm and the approaches in mathematical foundations of quantum theory which form the background of this talk. Second, I will introduce a toy model of the kind of mathematical structure which I use to model the states of a quantum system and the orthogonality relation between them. Third, I will discuss the way to describe quantum measurement and quantum entanglement only in terms of the orthogonality relation. We will see that such a simple description highlights some essentials and provides some insights.

#### 2023 Apr 06 16:00~17:30 Fengkui Ju 琚凤魁 (Beijing Normal University): *Logic for strategic reasoning in dynamic strategy contexts*

*Logic for strategic reasoning in dynamic strategy contexts*

Strategic reasoning is usually performed in specific strategy contexts, concerning which strategies are in consideration. Strategic reasoning can involve the change of strategy contexts. In this talk, we present a logic for strategic reasoning involving the change of strategy contexts caused by commitments to strategies. The logic has two featured formulas: (1) for some strategy of an agent compatible with the strategy context, if the agent commits to it, a formula is guaranteed to be true; (2) for every strategy of an agent compatible with the strategy context, if the agent commits to it, a formula is guaranteed to be true. Commitments to strategies shrink strategy contexts, which are defined as sets of sets of individual strategies.

This talk is based on a joint work with Valentin Goranko from Stockholm University.

#### 2023 Mar 30 16:00~17:30 Frederik van der Putte (Ghent University): *The problem of no hands : responsibility voids in collective decisions*

*The problem of no hands : responsibility voids in collective decisions*

The problem of no hands concerns the existence of so-called responsibility voids: cases where a group makes a certain decision, yet no individual member of the group can be held responsible for this decision. Criteria-based collective decision procedures play a central role in philosophical debates on responsibility voids. In particular, the well-known discursive dilemma has been used to argue for the existence of these voids. But there is no consensus: others argue that no such voids exist in the discursive dilemma under the assumption that casting an untruthful opinion is eligible. We argue that, under this assumption, the procedure used in the discursive dilemma is indeed immune to responsibility voids, yet such voids can still arise for other criteria-based procedures. We provide two general characterizations of the conditions under which criteria-based collective decision procedures are immune to these voids. Our general characterizations are used to prove that responsibility voids are ruled out by criteria-based procedures involving an atomistic or monotonic decision function. In addition, we show that our results imply various other insights concerning the logic of responsibility voids.

Reference available at https://biblio.ugent.be/publication/8735886

#### 2023 Mar 23 16:00~17:30 Xinwen Liu 刘新文 (Chinese Academy of Social Sciences) **金岳霖对“刘易斯-海德格尔”问题的回答**

金岳霖系统地分析了真之符合论中的“符合”，认为“符合是‘真’底所谓”，融洽、有效和一致是经验到符合的标准，它们都是真之标准。在金岳霖的理论中，符合论最为关键的成分“符合直观”被解释为符合感。符合感在横的时间上就是符合，但就纵的时间说，符合感与符合不必合一，即判断的对与命题的真不必合一。金岳霖关于“符合”的分析回应了符合论的核心问题“符合是什么”，这个问题在当前文献中也被称为“刘易斯—海德格尔问题”。

#### 2023 Mar 16 16:00~17:30 Feng Ye 叶峰 (Capital Normal University) **Introducing**** Studies in No-Self Physicalism**

**Studies in No-Self Physicalism**

This talk will introduce my recent book *Studies in No-Self Physicalism*. I will first explain the basic ideas of ‘no-Self’ physicalism. This introduces the basic assumptions and overall goal of the researches presented in this book and introduces chapters 1 and 2 of the book. Chapters 3 to 8 of the book develop a series of philosophical theories under the framework of No-Self Physicalism. They include theories on concept and conceptual representation (Chapter 3), thought, truth, analyticity, belief ascription, and modality (Chapter 4), philosophy of mathematics (Chapter 5), epistemic justification, knowledge, apriority, and intuition (Chapter 6), physicalistic ontology (Chapter 7), and coherent formulation of physicalism (Chapter 8). This talk will also very briefly introduce some of the ideas in these chapters.

Speaker’s homepage – http://cnu-cn.academia.edu/FengYe

#### 2023 Mar 09 16:00~17:30 Fan Yang 杨帆 (Utrecht University) **Dependence logic and its axiomatization problem**

**Dependence logic and its axiomatization problem**

Dependence logic was introduced by Väänänen (2007) as a novel formalism for reasoning about dependence and independence relations. The logic adopts the team semantics of Hodges (1997). The basic idea of team semantics is that dependency properties can only manifest themselves in multitudes, and thus formulas of dependence logic are evaluated on sets of assignments (called teams) instead of single assignment as in the usual Tarskian semantics. A team can be naturally viewed as a relational database, a dataset, an information state, etc. Thanks to the simple structure of teams and the abundance of their interpretations in various fields of science, team semantics and dependence logic have recently found a number of applications in addressing issues in database theory, formal linguistics, quantum foundations, social choice and so on. In the first part of this talk, I will provide an overview of the core theory and applications of dependence logic. Teams are essentially relations, which are second-order objects. Dependence logic is known to be equivalent to existential second-order logic, and thus cannot be effectively axiomatized in full. In the second part of the talk, I will survey some recent developments in finding partial axiomatizations for dependence logic.

Speaker’s homepage: https://sites.google.com/site/fanyanghp/

#### 2023 Mar 02nd 16:00~17:30 Dun Deng (邓盾，Tsinghua University) **Internal antisymmetry of Chinese disyllabic coordinative verbs and its theoretical implications**

**Internal antisymmetry of Chinese disyllabic coordinative verbs and its theoretical implications**

In this talk, I will first demonstrate the internal antisymmetry of Chinese disyllabic coordinative verbs (CDCVs) such as \zhi-zao/ ‘manufacture’ and \xiu-li/ ‘repair’. Using a sample of 400 CDCVs and a carefully designed annotation scheme to analyze all the CDCVs, we find that for each of the 400 CDCVs, one of the two root morphemes inside the compound verb can be identified as the more prominent one (call it H), which plays a more important role than the other root morpheme in determining the argument structure of the compound verb. This means that the 400 CDCVs have an asymmetrical internal structure with its two root morphemes being unequal in function. By studying the properties of all the Hs, we find strategies employed by the grammar to decide H, and provide an account for the strategies. Relying on our empirical findings about the internal antisymmetry of CDCVs, I then discuss and try to explain two theoretical issues. The first is about a well-known generalization in Chinese linguistics, namely that disyllabic verbs exhibit nominal behavior which corresponding monosyllabic verbs lack. The other is about the peculiar fact that CDCVs exist in large amount in Chinese whereas other languages like English rarely have equivalents.

#### 2023 Feb 23rd 19:00~20:30 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].

[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

### ■Past Events

Click HERE to check the past events.